From c62d0c3864e24ebb88bff22f0445290fdea7a4b3 Mon Sep 17 00:00:00 2001 From: Henry Chang Date: Tue, 21 Jul 2020 15:07:47 -0700 Subject: [PATCH] first commit by Henry --- .DS_Store | Bin 0 -> 6148 bytes .vscode/settings.json | 3 + Openmdao/.DS_Store | Bin 0 -> 6148 bytes Openmdao/Henry_Chang_FinalProject.zip | Bin 0 -> 598500 bytes .../__pycache__/_sub_comp_fk.cpython-37.pyc | Bin 0 -> 51859 bytes Openmdao/__pycache__/_sub_func.cpython-37.pyc | Bin 0 -> 3418 bytes .../_sub_obj_bar_length.cpython-37.pyc | Bin 0 -> 1332 bytes .../bar_length_comp.cpython-37.pyc | Bin 0 -> 1166 bytes .../__pycache__/bar_length_obj.cpython-37.pyc | Bin 0 -> 1162 bytes Openmdao/__pycache__/comp_fk.cpython-37.pyc | Bin 0 -> 51849 bytes Openmdao/__pycache__/comp_ik.cpython-37.pyc | Bin 0 -> 2713 bytes .../__pycache__/con_lift_point.cpython-37.pyc | Bin 0 -> 1977 bytes .../con_stance_point.cpython-37.pyc | Bin 0 -> 1991 bytes .../con_swing_point.cpython-37.pyc | Bin 0 -> 1984 bytes 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zL|cY56Y~H|i>BU@u6-rq?4L+7!~n z{B>z9W+E;%85eD@>GDRY%HnMqMy2J2M|bA#&FHP);4{x6>9_ojEB%m{9{b!4HX;#j zF;AAli18M6!&2;XwjqTJ(NMIDQTseo4*XbpVJn)qpkgRLg*vlKj5Fa%_TmCv4nofj z;`!o5ib%l=?hfp%(gzI+SXorIBi0A1f};qJl;sNHwv{Dx{Y+UMCc;=50prTr3_@2b zLzkvVS!J(2R{u)F?je%HCU!^`XSI*xX*^42aFK}H w@H$h#BL$!ZG+ls(1w&bUw-vR;bqE3QzZ(aw9bD^_TOr*I*gVKK5Z)nw0a(%Y^#A|> literal 0 HcmV?d00001 diff --git a/Openmdao/_main_five_bar_opt.py b/Openmdao/_main_five_bar_opt.py new file mode 100755 index 0000000..3df795f --- /dev/null +++ b/Openmdao/_main_five_bar_opt.py @@ -0,0 +1,73 @@ +import numpy as np +import sympy as sp +''' +setting up initial values to feed------------------------- +''' +from _sub_func import SineTrajectory, Ik_5_link + +x = SineTrajectory()[0] +y = SineTrajectory()[1] + +thetaL = np.zeros(len(x),dtype=float) +thetaR = np.zeros(len(x),dtype=float) + +for i in range(len(x)): + theta = Ik_5_link(x[i], y[i]) + thetaL[i] = theta.x[0] + thetaR[i] = theta.x[1] + +''' +model building--------------------------------------------- +''' +import openmdao.api as om +from openmdao.api import IndepVarComp +from _sub_comp_fk import FkComp +from _sub_obj_bar_length import BarLengthObj + +prob = om.Problem() + +# during one iteration, l1, l2 would be scalar, while thetaL, R would be vector of number of point +comp = IndepVarComp() +comp.add_output('l1', val=0.09) +comp.add_output('l2', val=0.16) +comp.add_output('thetaL', val=np.array(thetaL)) +comp.add_output('thetaR', val=thetaR) +prob.model.add_subsystem('comp_i', comp) + +comp = FkComp() +prob.model.add_subsystem('comp_fk', comp) + +comp = BarLengthObj() +prob.model.add_subsystem('obj_bar', comp) + +prob.model.connect('comp_i.l1',['comp_fk.l1','obj_bar.l1']) +prob.model.connect('comp_i.l2',['comp_fk.l2','obj_bar.l2']) +prob.model.connect('comp_i.thetaL','comp_fk.thetaL') +prob.model.connect('comp_i.thetaR','comp_fk.thetaR') + +''' +setting up model---------------------------------------------- +''' +from openmdao.api import Problem, ScipyOptimizeDriver + +prob.driver = om.ScipyOptimizeDriver() +prob.driver.options['optimizer'] = 'SLSQP' + +prob.model.add_design_var('comp_i.l1',lower=0) +prob.model.add_design_var('comp_i.l2',lower=0) +prob.model.add_design_var('comp_i.thetaL', lower=-0.2*np.pi, upper=0.2*np.pi) +prob.model.add_design_var('comp_i.thetaR', lower=0.7*np.pi, upper=1.2*np.pi) + +prob.model.add_objective('obj_bar.length') + +prob.model.add_constraint('comp_fk.x',equals=x) +prob.model.add_constraint('comp_fk.y',equals=y) + +prob.setup() +prob.run_model() +prob.model.list_outputs() + +prob.run_driver() +print('L1= ',prob['comp_i.l1']) +print('L2= ',prob['comp_i.l2']) +print('Total=',prob['obj_bar.length']) diff --git a/Openmdao/_sub_comp_fk.py b/Openmdao/_sub_comp_fk.py new file mode 100755 index 0000000..686a171 --- /dev/null +++ b/Openmdao/_sub_comp_fk.py @@ -0,0 +1,120 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +class FkComp(ExplicitComponent): + + def initialize(self): + # define indicies + self.options.declare('num_point', default=100, types=int) + + def setup(self): + num_point = self.options['num_point'] + self.add_input('l1') + self.add_input('l2') + self.add_input('thetaL', shape=(num_point, 1)) + self.add_input('thetaR', shape=(num_point, 1)) + + self.add_output('x', shape=(num_point, 1)) + self.add_output('y', shape=(num_point, 1)) + + rows_indices = np.arange(num_point) + cols_indices = np.zeros(num_point) + self.declare_partials('x','l1', rows=rows_indices, cols=cols_indices) + self.declare_partials('x','l2', rows=rows_indices, cols=cols_indices) + self.declare_partials('y','l1', rows=rows_indices, cols=cols_indices) + self.declare_partials('y','l2', rows=rows_indices, cols=cols_indices) + + self.declare_partials('x','thetaL', rows=rows_indices, cols=rows_indices) + self.declare_partials('x','thetaR', rows=rows_indices, cols=rows_indices) + self.declare_partials('y','thetaL', rows=rows_indices, cols=rows_indices) + self.declare_partials('y','thetaR', rows=rows_indices, cols=rows_indices) + + def compute(self, inputs, outputs): + thetaL = inputs['thetaL'] + thetaR = inputs['thetaR'] + l1 = inputs['l1'] + l2 = inputs['l2'] + + w = 0.07 + a = np.sqrt(w ** 2 + l1 ** 2 - 2 * w * l1 * np.cos(thetaR)) + alpha = np.arcsin(l1 * np.sin(thetaR) / a) + L = np.sqrt(l1 ** 2 + a ** 2 - 2 * l1 * a * np.cos(np.pi - alpha - thetaL)) + beta = np.arcsin(a * np.sin(np.pi - alpha - thetaL) / L) + thetaL2 = np.pi - beta + + ''' + Transmission Matrix + ''' + def T(theta, x, y): + return np.array([[np.cos(theta), -np.sin(theta), x], + [np.sin(theta), np.cos(theta), y], + [0, 0, 1]]) + + Fk = T(thetaL, w/2, 0) @ T(thetaL2, l1, 0) @ np.array( [L/2, -np.sqrt(l2 ** 2 - (L/2) ** 2), 1]) + Fk = Fk[:2] + + outputs['x'] = Fk[0] + outputs['y'] = Fk[1] + + def compute_partials(self, inputs, partials): + thetaL = inputs['thetaL'] + thetaR = inputs['thetaR'] + l1 = inputs['l1'] + l2 = inputs['l2'] + + # These are (num_point, 1) vectors + px_pl1 = -((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*(-0.25*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.5*l1 - 0.25*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.0175*np.cos(thetaR)) + 0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1 + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*np.cos(thetaR)) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*np.cos(thetaR))*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) - (-(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 + np.cos(thetaL) + px_pl2 = -l2*((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + py_pl1 = 0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1 + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*np.cos(thetaR)) - (-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*(-0.25*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.5*l1 - 0.25*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.0175*np.cos(thetaR)) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*((l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) + (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) - (-(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*np.cos(thetaR))*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 + np.sin(thetaL) + py_pl2 = -l2*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + + partials['x','l1'][:] = px_pl1.flatten() + partials['x','l2'][:] = px_pl2.flatten() + partials['y','l1'][:] = py_pl1.flatten() + partials['y','l2'][:] = py_pl2.flatten() + + # These are (num_point, num_point) matrix + px_pthetaL = -0.25*l1*((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.5*l1*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*np.sin(thetaL) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2 - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.cos(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) - (-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2*np.cos(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.sin(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) + px_pthetaR = -((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.0175*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.0175*l1*np.sin(thetaR))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + 0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) - (-0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 + py_pthetaL = -0.5*l1*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.25*l1*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*np.cos(thetaL) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2*np.cos(thetaL) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.sin(thetaL) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) - (-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2 - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.cos(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) + py_pthetaR = 0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5) - (-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.0175*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.0175*l1*np.sin(thetaR))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) + (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) - (-0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 + + partials['x','thetaL'][:] = px_pthetaL.flatten() + partials['x','thetaR'][:] = px_pthetaR.flatten() + partials['y','thetaL'][:] = py_pthetaL.flatten() + partials['y','thetaR'][:] = py_pthetaR.flatten() + +if __name__ == '__main__': + + from _sub_func import SineTrajectory, Ik_5_link + x = SineTrajectory()[0] + y = SineTrajectory()[1] + + thetaL = np.zeros(len(x),dtype=float) + thetaR = np.zeros(len(x),dtype=float) + + for i in range(len(x)): + theta = Ik_5_link(x[i], y[i]) + thetaL[i] = theta.x[0] + thetaR[i] = theta.x[1] + + from openmdao.api import Problem, Group, IndepVarComp + group = Group() + + comp = IndepVarComp() + comp.add_output('thetaL', val=thetaL) + comp.add_output('thetaR', val=thetaR) + comp.add_output('l1', val=0.09) + comp.add_output('l2', val=0.16) + group.add_subsystem('comp1', comp, promotes_outputs=['thetaL','thetaR','l1','l2']) + + comp = FkComp() + group.add_subsystem('comp2', comp, promotes_inputs=['thetaL','thetaR','l1','l2']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() + prob.check_partials(compact_print=True) diff --git a/Openmdao/_sub_func.py b/Openmdao/_sub_func.py new file mode 100755 index 0000000..070e51d --- /dev/null +++ b/Openmdao/_sub_func.py @@ -0,0 +1,100 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.optimize import minimize +from scipy.optimize import fsolve + +def SineTrajectory(DownAMP = 0.01, UpperAMP = 0.05, StanceHeight = 0.18, StepLength = 0.12): + + CurrentPercent = np.array([a/100+0.01 for a in range(100)]) + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + + x = np.zeros(len(CurrentPercent), dtype=float) + y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + x[i] = -(StepLength / 2) + (CurrentPercent[i] / StancePercent) * StepLength + y[i] = DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + StanceHeight + else: + x[i] = (StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * StepLength + y[i] = -UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + StanceHeight + + return x, y + + + +def Ik_5_link(x, y, l1 = 0.09, l2 = 0.16, w = 0.07): + + def leg_wide(var): + return np.linalg.norm([var[0], var[1] - np.pi]) + + def x_constraint_equation(var): + # should be equal to zero when the + return l1**2 - l2**2 + (x - w/2)**2 + y**2 - 2*l1*(y*np.sin(var[0]) + (x - w/2)*np.cos(var[0])) + + def y_constraint_equation(var): + return l1**2 - l2**2 + (x + w/2)**2 + y**2 - 2*l1*(y*np.sin(var[1]) + (x + w/2)*np.cos(var[1])) + + + res = minimize(leg_wide, (0.1, 9*np.pi/10), method="SLSQP", constraints= ({"type": "eq", "fun": x_constraint_equation}, + {"type": "eq", "fun": y_constraint_equation})) + + + return (res) + +def FkGetPosition(thetaL, thetaR, l1 = 0.09, l2 = 0.16): + + w = 0.07 + a = np.sqrt(w ** 2 + l1 ** 2 - 2 * w * l1 * np.cos(thetaR)) + alpha = np.arcsin(l1 * np.sin(thetaR) / a) + L = np.sqrt(l1 ** 2 + a ** 2 - 2 * l1 * a * np.cos(np.pi - alpha - thetaL)) + beta = np.arcsin(a * np.sin(np.pi - alpha - thetaL) / L) + thetaL2 = np.pi - beta + + ''' + Transmission Matrix + ''' + def T(theta, x, y): + return np.array([[np.cos(theta), -np.sin(theta), x], + [np.sin(theta), np.cos(theta), y], + [0, 0, 1]]) + + # Fk = T(thetaL, w/2, 0).dot( T(thetaL2, l1, 0) ).dot(np.array( [L/2, -np.sqrt(l2 ** 2 - (L/2) ** 2), 1]) ) + # Fk = multi_dot([T(thetaL, w/2, 0), T(thetaL2, l1, 0), np.array( [L/2, -np.sqrt(l2 ** 2 - (L/2) ** 2), 1])]) + Fk = T(thetaL, w/2, 0) @ T(thetaL2, l1, 0) @ np.array( [L/2, -np.sqrt(l2 ** 2 - (L/2) ** 2), 1]) + Fk = Fk[:2] + + x = Fk[0] + y = Fk[1] + + return x, y + + +if __name__ == '__main__': + + x = SineTrajectory()[0] + y = SineTrajectory()[1] + + thetaL = np.zeros(len(x),dtype=float) + thetaR = np.zeros(len(x),dtype=float) + + for i in range(len(x)): + theta = Ik_5_link(x[i], y[i]) + # print(theta.x[0], theta.x[1]) + thetaL[i] = theta.x[0] + thetaR[i] = theta.x[1] + + x_ = FkGetPosition(thetaL, thetaR)[0] + y_ = FkGetPosition(thetaL, thetaR)[1] + + plt.plot(x_, y_, x, y, marker='*') + plt.show() + + j = np.min(y_) + print(j) + + p = FkGetPosition(0, np.pi) + q = FkGetPosition(0.25*np.pi, 0.75*np.pi) + r = FkGetPosition(0.5*np.pi, 0.5*np.pi) + print(p, q, r) \ No newline at end of file diff --git a/Openmdao/_sub_obj_bar_length.py b/Openmdao/_sub_obj_bar_length.py new file mode 100755 index 0000000..e83e584 --- /dev/null +++ b/Openmdao/_sub_obj_bar_length.py @@ -0,0 +1,41 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +class BarLengthObj(ExplicitComponent): + + def setup(self): + self.add_input('l1') + self.add_input('l2') + + self.add_output('length') + + self.declare_partials('length', 'l1', val=1) + self.declare_partials('length', 'l2', val=1) + + def compute(self, inputs, outputs): + l1 = inputs['l1'] + l2 = inputs['l2'] + outputs['length'] = l1 + l2 + +if __name__ == '__main__': + from openmdao.api import Group, Problem, IndepVarComp + group = Group() + + comp = IndepVarComp() + comp.add_output('l1', val=0.09) + comp.add_output('l2', val=0.16) + group.add_subsystem('comp1', comp) + + comp = BarLengthObj() + group.add_subsystem('comp2', comp) + + group.connect('comp1.l1', 'comp2.l1') + group.connect('comp1.l2', 'comp2.l2') + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() + prob.check_partials(compact_print=True) \ No newline at end of file diff --git a/Openmdao/_sub_partials.py b/Openmdao/_sub_partials.py new file mode 100755 index 0000000..5c409cd --- /dev/null +++ b/Openmdao/_sub_partials.py @@ -0,0 +1,52 @@ +import numpy as np +import sympy as sp +import pprint +from sympy.utilities.lambdify import lambdify + +thetaL = sp.symbols('thetaL') +thetaR = sp.symbols('thetaR') +l1 = sp.symbols('l1') +l2 = sp.symbols('l2') +w = 0.07 + +a = sp.sqrt(w ** 2 + l1 ** 2 - 2 * w * l1 * sp.cos(thetaR)) +alpha = sp.asin(l1 * sp.sin(thetaR) / a) +L = sp.sqrt(l1 ** 2 + a ** 2 - 2 * l1 * a * sp.cos(sp.pi - alpha - thetaL)) +beta = sp.asin(a * sp.sin(sp.pi - alpha - thetaL) / L) +thetaL2 = sp.pi - beta + +def T(theta, x, y): + return sp.Matrix([[sp.cos(theta), -sp.sin(theta), x], + [sp.sin(theta), sp.cos(theta), y], + [0, 0, 1]]) + +Fk = T(thetaL, w/2, 0) @ T(thetaL2, l1, 0) @ sp.Matrix([L/2, -sp.sqrt(l2 ** 2 - (L/2) ** 2), 1]) +Fk = Fk[:2,:] + +''' +px_pl1 px_pl2 +py_pl1 py_pl2 +''' +px_pl = Fk.jacobian([l1,l2]).evalf() +# np.array(px_pl.tolist()).astype(np.float64) +# px_pl1 = px_pl[0,0] +# px_pl2 = px_pl[0,1] +# py_pl1 = px_pl[1,0] +# py_pl2 = px_pl[1,1] + +print('shape of px_pl:',np.shape(px_pl)) +# pprint.pprint(px_pl[1,1]) + +''' +px_pthetaL px_pthetaR +py_pthetaL py_pthetaR +''' +px_ptheta = Fk.jacobian([thetaL,thetaR]).evalf() +# np.array(px_ptheta).astype(np.float64) +# px_pthetaL = px_ptheta[0,0] +# px_pthetaR = px_ptheta[0,1] +# py_pthetaL = px_ptheta[1,0] +# py_pthetaR = px_ptheta[1,1] + +print('shape of px_pθ:',np.shape(px_ptheta)) +# pprint.pprint(px_ptheta[1,1]) diff --git a/Openmdao/_test.py b/Openmdao/_test.py new file mode 100755 index 0000000..d88bfa6 --- /dev/null +++ b/Openmdao/_test.py @@ -0,0 +1,59 @@ +import numpy as np +import sympy as sp + +l1 = 10 +l2 = 10 +thetaL = 1 +thetaR = 2 + +''' +---------------------------------------------------------------------------------------------------------------- +px_pl1 +---------------------------------------------------------------------------------------------------------------- +''' +-((-(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.np.sin(thetaL) - (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))*np.np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.035*l1*np.np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*(-0.25*l1*(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.25*l1*(-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.5*l1 - 0.25*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.0175*np.np.cos(thetaR)) + 0.5*(-(-(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.np.cos(thetaL) - (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaL)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*(l1*(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - l1*(-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 2.0*l1 + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.07*np.np.cos(thetaR)) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(-(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaL)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - (-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaL)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.np.cos(thetaR))*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) - (-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.14*np.np.cos(thetaR))*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**2)*np.np.cos(thetaL) - (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.07*np.np.cos(thetaR))*np.np.sin(thetaL)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))) - (-(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))*np.np.cos(thetaL) - (-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + (-(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.np.cos(thetaR))*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) - (-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.14*np.np.cos(thetaR))*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**2)*np.np.sin(thetaL) - (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.np.cos(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-1.5)*np.np.sin(thetaR) + (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**(-0.5)*np.np.sin(thetaR))*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.07*np.np.cos(thetaR))*np.np.sin(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)))*np.np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049)**0.5*np.np.cos(thetaL + np.arcsin(l1*np.np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.np.cos(thetaR) + 0.0049))) + 0.035*l1*np.np.cos(thetaR) + l2**2 - 0.001225)**0.5 + np.np.cos(thetaL) + +''' +---------------------------------------------------------------------------------------------------------------- +px_pl2 +---------------------------------------------------------------------------------------------------------------- +''' +-l2*((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) +''' +---------------------------------------------------------------------------------------------------------------- +py_pl1 +---------------------------------------------------------------------------------------------------------------- +''' +0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1 + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*np.cos(thetaR)) - (-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*(-0.25*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.5*l1 - 0.25*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.0175*np.cos(thetaR)) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*((l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) + (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) - (-(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.5*(2.0*l1 - 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-2.0*l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 4.0*l1 - 2.0*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.14*np.cos(thetaR))*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*(-l1*(l1 - 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1*(-l1 + 0.07*np.cos(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 2.0*l1 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*np.cos(thetaR))*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 + np.sin(thetaL) +''' +---------------------------------------------------------------------------------------------------------------- +py_pl2 +---------------------------------------------------------------------------------------------------------------- +''' +-l2*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.arcsin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + + +''' +---------------------------------------------------------------------------------------------------------------- +px_pthetaL +---------------------------------------------------------------------------------------------------------------- +''' +-0.25*l1*((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.5*l1*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*np.sin(thetaL) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2 - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.cos(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) - (-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2*np.cos(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.sin(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) +''' +---------------------------------------------------------------------------------------------------------------- +px_pthetaR +---------------------------------------------------------------------------------------------------------------- +''' +-((-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.0175*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.0175*l1*np.sin(thetaR))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + 0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) - (-0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 +''' +---------------------------------------------------------------------------------------------------------------- +py_pthetaL +---------------------------------------------------------------------------------------------------------------- +''' +-0.5*l1*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.25*l1*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*np.cos(thetaL) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2*np.cos(thetaL) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.sin(thetaL) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))) - (-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2 - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**1.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**3/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2 - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049))*np.cos(thetaL) + (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) +''' +---------------------------------------------------------------------------------------------------------------- +py_pthetaR +---------------------------------------------------------------------------------------------------------------- +''' +0.5*(-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL))*(0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5) - (-(-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**0.5*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.0175*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.25*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.0175*l1*np.sin(thetaR))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**(-0.5) + 0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL) + (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.sin(thetaL) + (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL)) - (-0.07*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaL)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - (-(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(-0.07*l1*np.sin(thetaR)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - (-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049) - 0.5*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)*(-0.14*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 2.0*l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.sin(thetaR))*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)))**2/(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**2)*np.cos(thetaL) - (l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.sin(thetaR)*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + l1*(-0.07*l1**2*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaR)**2 + l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**(-0.5)*np.cos(thetaR))*(-l1**2*np.sin(thetaR)**2/(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049) + 1.0)**(-0.5)*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.07*l1*np.sin(thetaR))*(2.0*l1**2 + 2.0*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) - 0.14*l1*np.cos(thetaR) + 0.0049)**(-1.5)*np.sin(thetaL)*np.sin(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))))*(-0.5*l1**2 - 0.5*l1*(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049)**0.5*np.cos(thetaL + np.sin(l1*np.sin(thetaR)/np.sqrt(l1**2 - 0.14*l1*np.cos(thetaR) + 0.0049))) + 0.035*l1*np.cos(thetaR) + l2**2 - 0.001225)**0.5 diff --git a/Openmdao/example/01_paraboloid_min.py b/Openmdao/example/01_paraboloid_min.py new file mode 100755 index 0000000..3778dca --- /dev/null +++ b/Openmdao/example/01_paraboloid_min.py @@ -0,0 +1,28 @@ +import openmdao.api as om + +# build the model +prob = om.Problem() +indeps = prob.model.add_subsystem('indeps', om.IndepVarComp()) +indeps.add_output('x', 3.0) +indeps.add_output('y', -4.0) + +prob.model.add_subsystem('paraboloid', om.ExecComp('f = (x-3)**2 + x*y + (y+4)**2 - 3')) + +prob.model.connect('indeps.x', 'paraboloid.x') +prob.model.connect('indeps.y', 'paraboloid.y') + +prob.driver = om.ScipyOptimizeDriver() +prob.driver.options['optimizer'] = 'SLSQP' + +prob.model.add_design_var('indeps.x', lower=-50, upper=50) +prob.model.add_design_var('indeps.y', lower=-50, upper=50) +prob.model.add_objective('paraboloid.f') + +prob.setup() +prob.run_driver() + +# minimum value +print(prob['paraboloid.f']) +# location of the minimum +print(prob['indeps.x']) +print(prob['indeps.y']) \ No newline at end of file diff --git a/Openmdao/example/02_opt_sellar_porb.py b/Openmdao/example/02_opt_sellar_porb.py new file mode 100755 index 0000000..cabe2c2 --- /dev/null +++ b/Openmdao/example/02_opt_sellar_porb.py @@ -0,0 +1,31 @@ +import openmdao.api as om +from openmdao.test_suite.components.sellar_feature import SellarMDA + +prob = om.Problem() +prob.model = SellarMDA() + +prob.driver = om.ScipyOptimizeDriver() +prob.driver.options['optimizer'] = 'SLSQP' +# prob.driver.options['maxiter'] = 100 +prob.driver.options['tol'] = 1e-8 + +prob.model.add_design_var('x', lower=0, upper=10) +prob.model.add_design_var('z', lower=0, upper=10) +prob.model.add_objective('obj') +prob.model.add_constraint('con1', upper=0) +prob.model.add_constraint('con2', upper=0) + +prob.setup() +prob.set_solver_print(level=0) + +# Ask OpenMDAO to finite-difference across the model to compute the gradients for the optimizer +prob.model.approx_totals() + +prob.run_driver() + +print('minimum found at') +print(prob['x'][0]) +print(prob['z']) + +print('minumum objective') +print(prob['obj'][0]) \ No newline at end of file diff --git a/Openmdao/example/02_sellar_MDA.py b/Openmdao/example/02_sellar_MDA.py new file mode 100755 index 0000000..9399c47 --- /dev/null +++ b/Openmdao/example/02_sellar_MDA.py @@ -0,0 +1,28 @@ +import numpy as np +import openmdao.api as om + +class SellarMDA(om.Group): + """ + Group containing the Sellar MDA. + """ + + def setup(self): + indeps = self.add_subsystem('indeps', om.IndepVarComp(), promotes=['*']) + indeps.add_output('x', 1.0) + indeps.add_output('z', np.array([5.0, 2.0])) + + cycle = self.add_subsystem('cycle', om.Group(), promotes=['*']) + cycle.add_subsystem('d1', SellarDis1(), promotes_inputs=['x', 'z', 'y2'], + promotes_outputs=['y1']) + cycle.add_subsystem('d2', SellarDis2(), promotes_inputs=['z', 'y1'], + promotes_outputs=['y2']) + + # Nonlinear Block Gauss Seidel is a gradient free solver + cycle.nonlinear_solver = om.NonlinearBlockGS() + + self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', + z=np.array([0.0, 0.0]), x=0.0), + promotes=['x', 'z', 'y1', 'y2', 'obj']) + + self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1'), promotes=['con1', 'y1']) + self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0'), promotes=['con2', 'y2']) \ No newline at end of file diff --git a/Openmdao/example/Ozone/__pycache__/initial_condition_comp.cpython-36.pyc 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b/Openmdao/example/Ozone/projectile_system.py @@ -0,0 +1,51 @@ +import numpy as np + +from openmdao.api import ExplicitComponent + + +# Dynamics---original, 2nd order: +# x''=0 +# y''=-g +# Dynamics---modified, 1st order: +# (x )' = x' +# (y )' = y' +# (x')' = 0 +# (y')' = -g +# Initial conditions: +# (x )_0 = 0 +# (y )_0 = 0 +# (x')_0 = v * cos(theta) +# (y')_0 = v * sin(theta) +# Constraints: +# (y )_f = 0 +# Objective: +# (x )_f [maximize!] + +class ProjectileSystem(ExplicitComponent): + + def initialize(self): + self.options.declare('num_nodes', default=1, types=int) + + self.g = -9.81 + + def setup(self): + num = self.options['num_nodes'] + + self.add_input('vx', shape=(num, 1)) + self.add_input('vy', shape=(num, 1)) + + self.add_output('dx_dt', shape=(num, 1)) + self.add_output('dy_dt', shape=(num, 1)) + self.add_output('dvx_dt', shape=(num, 1)) + self.add_output('dvy_dt', shape=(num, 1)) + + self.declare_partials('*', '*', dependent=False) + + self.declare_partials('dx_dt', 'vx', val=1., rows=np.arange(num), cols=np.arange(num)) + self.declare_partials('dy_dt', 'vy', val=1., rows=np.arange(num), cols=np.arange(num)) + + def compute(self, inputs, outputs): + outputs['dx_dt'] = inputs['vx'] + outputs['dy_dt'] = inputs['vy'] + outputs['dvx_dt'] = 0. + outputs['dvy_dt'] = self.g diff --git a/Openmdao/example/Ozone/run_driver.py b/Openmdao/example/Ozone/run_driver.py new file mode 100755 index 0000000..e900c64 --- /dev/null +++ b/Openmdao/example/Ozone/run_driver.py @@ -0,0 +1,82 @@ +import numpy as np +import matplotlib.pyplot as plt +from openmdao.api import Problem, Group, IndepVarComp, ExecComp, ScipyOptimizeDriver +from ozone.api import ODEIntegrator +from projectile_function import ProjectileFunction + + +ode_function = ProjectileFunction() + +t0 = 0. +t1 = 1. +initial_conditions = { + 'x': 0., + 'y': 0., + # 'vx': 1., + # 'vy': 1., +} + +num = 100 +method_name = 'ForwardEuler' +formulation = 'time-marching' + +initial_time = 0. +normalized_times = np.linspace(0., 1, num) + +integrator = ODEIntegrator( + ode_function, formulation, method_name, + initial_time=initial_time, normalized_times=normalized_times, + initial_conditions=initial_conditions, +) + +group = Group() +group.add_subsystem('final_time_comp', IndepVarComp('final_time', val=1.0)) +group.add_subsystem('theta_comp', IndepVarComp('theta', val=np.pi/3.)) +group.add_subsystem('v_comp', IndepVarComp('v', val=1.)) +group.add_subsystem('vx_comp', ExecComp('vx = v * cos(theta)')) +group.add_subsystem('vy_comp', ExecComp('vy = v * sin(theta)')) +group.add_subsystem('integrator_group', integrator) + +group.connect('final_time_comp.final_time', 'integrator_group.final_time') +group.connect('theta_comp.theta', 'vx_comp.theta') +group.connect('theta_comp.theta', 'vy_comp.theta') +group.connect('v_comp.v', 'vx_comp.v') +group.connect('v_comp.v', 'vy_comp.v') + +group.connect('vx_comp.vx', 'integrator_group.initial_condition:vx') +group.connect('vy_comp.vy', 'integrator_group.initial_condition:vy') + +group.add_design_var('final_time_comp.final_time', lower=1e-3) +group.add_design_var('theta_comp.theta', lower=0., upper=np.pi/2.) +group.add_constraint('integrator_group.state:y', indices=[-1], equals=0.) +group.add_objective('integrator_group.state:x', index=-1, scaler=-1.) + +prob = Problem() +prob.model = group + +prob.driver = ScipyOptimizeDriver() +prob.driver.options['optimizer'] = 'SLSQP' +# from openmdao.api import pyOptSparseDriver +# prob.driver = driver = pyOptSparseDriver() +# driver.options['optimizer'] = 'SNOPT' +# driver.opt_settings['Verify level'] = 0 +# driver.opt_settings['Major iterations limit'] = 200 #1000 +# driver.opt_settings['Minor iterations limit'] = 1000 +# driver.opt_settings['Iterations limit'] = 100000 +# driver.opt_settings['Major step limit'] = 2.0 +# driver.opt_settings['Major feasibility tolerance'] = 1.0e-6 +# driver.opt_settings['Major optimality tolerance'] = 1.0e-6 +# driver.opt_settings['Minor feasibility tolerance'] = 1.0e-6 + +prob.setup() +prob.run_model() +# prob.check_partials(compact_print=True); exit() +prob.run_driver() + +print(prob['theta_comp.theta']) + +plt.plot(prob['integrator_group.state:x'], prob['integrator_group.state:y']) +plt.xlabel('x') +plt.ylabel('y') +plt.axis('equal') +plt.show() diff --git a/Openmdao/example/Ozone/run_model.py b/Openmdao/example/Ozone/run_model.py new file mode 100755 index 0000000..b0f8c49 --- /dev/null +++ b/Openmdao/example/Ozone/run_model.py @@ -0,0 +1,37 @@ +import numpy as np +import matplotlib.pyplot as plt +from openmdao.api import Problem +from ozone.api import ODEIntegrator +from projectile_function import ProjectileFunction + + +ode_function = ProjectileFunction() + +t0 = 0. +t1 = 1. +initial_conditions = { + 'x': 0., + 'y': 0., + 'vx': 1., + 'vy': 1., +} + +num = 100 + +times = np.linspace(t0, t1, num) + +method_name = 'RK4' +formulation = 'solver-based' + +integrator = ODEIntegrator(ode_function, formulation, 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index 0000000..5f271ef --- /dev/null +++ b/Openmdao/example/dist_example/d_comp.py @@ -0,0 +1,55 @@ +import numpy as np + +from openmdao.api import ExplicitComponent + + +class DComp(ExplicitComponent): + + def setup(self): + self.add_input('v_m_s') + self.add_input('theta_rad') + self.add_input('tf') + self.add_output('d') + self.declare_partials('d', 'v_m_s') + self.declare_partials('d', 'theta_rad') + self.declare_partials('d', 'tf') + + def compute(self, inputs, outputs): + v_m_s = inputs['v_m_s'] + theta_rad = inputs['theta_rad'] + tf = inputs['tf'] + + d = v_m_s * np.cos(theta_rad) * tf + outputs['d'] = d + print(theta_rad, d) + + def compute_partials(self, inputs, partials): + v_m_s = inputs['v_m_s'] + theta_rad = inputs['theta_rad'] + tf = inputs['tf'] + partials['d', 'v_m_s'] = np.cos(theta_rad) * tf + partials['d', 'theta_rad'] = -v_m_s * np.sin(theta_rad) * tf + partials['d', 'tf'] = v_m_s * np.cos(theta_rad) + + +if __name__ == '__main__': + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('v_m_s') + comp.add_output('theta_rad') + comp.add_output('tf') + group.add_subsystem('comp1', comp) + + comp = DComp() + group.add_subsystem('comp2', comp) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() + prob.check_partials(compact_print=True) \ No newline at end of file diff --git a/Openmdao/example/dist_example/dist_group.py b/Openmdao/example/dist_example/dist_group.py new file mode 100755 index 0000000..46def88 --- /dev/null +++ b/Openmdao/example/dist_example/dist_group.py @@ -0,0 +1,45 @@ +import numpy as np + +from openmdao.api import Group, IndepVarComp +from vy_comp import VyComp +from t_comp import TComp +from d_comp import DComp + + +class DistGroup(Group): + + def setup(self): + comp = IndepVarComp() + comp.add_output('v_m_s') + comp.add_output('theta_rad') + self.add_subsystem('i_comp', comp, promotes=['*']) + + comp = VyComp() + self.add_subsystem('vy_comp', comp, promotes=['*']) + + comp = TComp() + self.add_subsystem('t_comp', comp, promotes=['*']) + + comp = DComp() + self.add_subsystem('d_comp', comp, promotes=['*']) + + +if __name__ == '__main__': + from openmdao.api import Problem, ScipyOptimizeDriver + + prob = Problem() + prob.model = DistGroup() + + prob.model.add_design_var('theta_rad', lower=0, upper=np.pi/2.) + prob.model.add_objective('d', scaler=-1.) + + prob.driver = ScipyOptimizeDriver() + prob.driver.options['optimizer'] = 'SLSQP' + + prob.setup() + prob.run_model() + prob.model.list_outputs() + # prob.check_partials(compact_print=True) + + prob.run_driver() + print(prob['i_comp.v_m_s']) diff --git a/Openmdao/example/dist_example/n2.html b/Openmdao/example/dist_example/n2.html new file mode 100755 index 0000000..ad4fc09 --- /dev/null +++ b/Openmdao/example/dist_example/n2.html @@ -0,0 +1,4132 @@ + + + +OpenMDAO Model Hierarchy and N2 diagram + + + + + + + + + + + + +
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+ + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/Openmdao/old/comp_ik.py b/Openmdao/old/comp_ik.py new file mode 100755 index 0000000..9ea56b8 --- /dev/null +++ b/Openmdao/old/comp_ik.py @@ -0,0 +1,68 @@ +import numpy as np +import sympy as sp +from sympy.utilities.lambdify import lambdify +from scipy.optimize import minimize +from scipy.optimize import fsolve +from openmdao.api import ExplicitComponent + +class IkComp(ExplicitComponent): + + def setup(self): + + self.add_input('x') + self.add_input('y') + self.add_input('l1') + self.add_input('l2') + self.add_output('thetaL') + self.add_output('thetaR') + + def compute(self, inputs, outputs): + + x = inputs['x'] + y = inputs['y'] + l1 = inputs['l1'] + l2 = inputs['l2'] + + def IK_5_link(x, y, l1, l2, w = 0.07): + + def leg_wide(var): + return np.linalg.norm([var[0], var[1] - np.pi]) + + def x_constraint_equation(var): + # should be equal to zero when the + return l1**2 - l2**2 + (x - w/2)**2 + y**2 - 2*l1*(y*np.sin(var[0]) + (x - w/2)*np.cos(var[0])) + + def y_constraint_equation(var): + return l1**2 - l2**2 + (x + w/2)**2 + y**2 - 2*l1*(y*np.sin(var[1]) + (x + w/2)*np.cos(var[1])) + + res = minimize(leg_wide, (0.1, 9*np.pi/10), method="SLSQP", constraints= ({"type": "eq", "fun": x_constraint_equation}, + {"type": "eq", "fun": y_constraint_equation})) + + return (res) + + outputs['thetaL'] = IK_5_link(x, y, l1, l2).x[0] + outputs['thetaR'] = IK_5_link(x, y, l1, l2).x[1] + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('x', val=-0.024021708847354217) + comp.add_output('y', val=0.12411037295149752) + comp.add_output('l1', val=0.09) + comp.add_output('l2', val=0.16) + group.add_subsystem('comp1', comp, promotes=['*']) + + comp = IkComp() + group.add_subsystem('comp2', comp, promotes=['*']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() + print('theta should be: [0.5, np.pi]') diff --git a/Openmdao/old/con_dist.py b/Openmdao/old/con_dist.py new file mode 100755 index 0000000..cc0cffe --- /dev/null +++ b/Openmdao/old/con_dist.py @@ -0,0 +1,52 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +from fk_comp import FkComp +from sin_trajectory_comp import SineTrajectoryComp + +class DistCon(ExplicitComponent): + + def setup(self): + + self.add_input('x') + self.add_input('y') + self.add_input('TestPoint_x') + self.add_input('TestPoint_y') + self.add_output('dist') + + def compute(self, inputs, outputs): + + x = inputs['x'] + y = inputs['y'] + TestPoint_x = inputs['TestPoint_x'] + TestPoint_y = inputs['TestPoint_y'] + outputs['dist'] = np.linalg.norm([x - TestPoint_x, y - TestPoint_y]) + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('thetaL') + comp.add_output('thetaR') + comp.add_output('l1') + comp.add_output('l2') + group.add_subsystem('i_comp', comp, promotes=['*']) + + comp = FkComp() + group.add_subsystem('fk_comp', comp, promotes=['*']) + + comp = SineTrajectoryComp() + group.add_subsystem('sin_trajectory_comp', comp, promotes=['*']) + + comp = DistCon() + group.add_subsystem('dist_comp', comp, promotes=['*']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() \ No newline at end of file diff --git a/Openmdao/old/con_lift_point.py b/Openmdao/old/con_lift_point.py new file mode 100755 index 0000000..0fa5115 --- /dev/null +++ b/Openmdao/old/con_lift_point.py @@ -0,0 +1,67 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +from comp_fk import FkComp + +class LiftPointCon(ExplicitComponent): + + def setup(self): + + self.add_input('x') + self.add_input('y') + self.add_output('life_dist') + + def compute(self, inputs, outputs): + + x = inputs['x'] + y = inputs['y'] + + DownAMP = 0.01 + UpperAMP = 0.05 + StanceHeight = 0.18 + StepLength = 0.12 + + CurrentPercent = np.array([a/100+0.01 for a in range(100)]) + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + + trajectory_x = np.zeros(len(CurrentPercent), dtype=float) + trajectory_y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + trajectory_x[i] = -(StepLength / 2) + (CurrentPercent[i] / StancePercent) * StepLength + trajectory_y[i] = DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + StanceHeight + else: + trajectory_x[i] = (StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * StepLength + trajectory_y[i] = -UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + StanceHeight + + TestPoint_x = trajectory_x[59] + TestPoint_y = trajectory_y[59] + + outputs['life_dist'] = np.linalg.norm([x - TestPoint_x, y - TestPoint_y]) + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('l1') + comp.add_output('l2') + group.add_subsystem('i_comp', comp, promotes=['*']) + + comp = FkComp() + group.add_subsystem('fk_comp', comp, promotes=['*']) + + comp = LiftPointCon() + group.add_subsystem('lift_con', comp, promotes=['*']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() + diff --git a/Openmdao/old/con_sin_trajectory.py b/Openmdao/old/con_sin_trajectory.py new file mode 100755 index 0000000..d0a5221 --- /dev/null +++ b/Openmdao/old/con_sin_trajectory.py @@ -0,0 +1,53 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +class SineTrajectoryComp(ExplicitComponent): + + def setup(self): + + self.add_output('TestPoint_x') + self.add_output('TestPoint_y') + + def compute(self, inputs, outputs): + + DownAMP = 0.01 + UpperAMP = 0.05 + StanceHeight = 0.18 + StepLength = 0.12 + + CurrentPercent = np.array([a/100+0.01 for a in range(100)]) + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + + trajectory_x = np.zeros(len(CurrentPercent), dtype=float) + trajectory_y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + trajectory_x[i] = -(StepLength / 2) + (CurrentPercent[i] / StancePercent) * StepLength + trajectory_y[i] = DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + StanceHeight + else: + trajectory_x[i] = (StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * StepLength + trajectory_y[i] = -UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + StanceHeight + + # return the furthest points + print(trajectory_x[59], trajectory_y[59]) + + outputs['TestPoint_x'] = trajectory_x[59] + outputs['TestPoint_y'] = trajectory_y[59] + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = SineTrajectoryComp() + group.add_subsystem('comp1', comp) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() \ No newline at end of file diff --git a/Openmdao/old/con_stance_point.py b/Openmdao/old/con_stance_point.py new file mode 100755 index 0000000..e689b7e --- /dev/null +++ b/Openmdao/old/con_stance_point.py @@ -0,0 +1,66 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +from comp_fk import FkComp + +class StancePointCon(ExplicitComponent): + + def setup(self): + + self.add_input('x') + self.add_input('y') + self.add_output('stance_dist') + + def compute(self, inputs, outputs): + + x = inputs['x'] + y = inputs['y'] + + DownAMP = 0.01 + UpperAMP = 0.05 + StanceHeight = 0.18 + StepLength = 0.12 + + CurrentPercent = np.array([a/100+0.01 for a in range(100)]) + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + + trajectory_x = np.zeros(len(CurrentPercent), dtype=float) + trajectory_y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + trajectory_x[i] = -(StepLength / 2) + (CurrentPercent[i] / StancePercent) * StepLength + trajectory_y[i] = DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + StanceHeight + else: + trajectory_x[i] = (StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * StepLength + trajectory_y[i] = -UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + StanceHeight + + TestPoint_x = trajectory_x[29] + TestPoint_y = trajectory_y[29] + + outputs['stance_dist'] = np.linalg.norm([x - TestPoint_x, y - TestPoint_y]) + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('l1') + comp.add_output('l2') + group.add_subsystem('i_comp', comp, promotes=['*']) + + comp = FkComp() + group.add_subsystem('fk_comp', comp, promotes=['*']) + + comp = StancePointCon() + group.add_subsystem('stance_con', comp, promotes=['*']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() \ No newline at end of file diff --git a/Openmdao/old/con_swing_point.py b/Openmdao/old/con_swing_point.py new file mode 100755 index 0000000..142f654 --- /dev/null +++ b/Openmdao/old/con_swing_point.py @@ -0,0 +1,66 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +from comp_fk import FkComp + +class SwingPointCon(ExplicitComponent): + + def setup(self): + + self.add_input('x') + self.add_input('y') + self.add_output('swing_dist') + + def compute(self, inputs, outputs): + + x = inputs['x'] + y = inputs['y'] + + DownAMP = 0.01 + UpperAMP = 0.05 + StanceHeight = 0.18 + StepLength = 0.12 + + CurrentPercent = np.array([a/100+0.01 for a in range(100)]) + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + + trajectory_x = np.zeros(len(CurrentPercent), dtype=float) + trajectory_y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + trajectory_x[i] = -(StepLength / 2) + (CurrentPercent[i] / StancePercent) * StepLength + trajectory_y[i] = DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + StanceHeight + else: + trajectory_x[i] = (StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * StepLength + trajectory_y[i] = -UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + StanceHeight + + TestPoint_x = trajectory_x[79] + TestPoint_y = trajectory_y[79] + + outputs['swing_dist'] = np.linalg.norm([x - TestPoint_x, y - TestPoint_y]) + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('l1') + comp.add_output('l2') + group.add_subsystem('i_comp', comp, promotes=['*']) + + comp = FkComp() + group.add_subsystem('fk_comp', comp, promotes=['*']) + + comp = SwingPointCon() + group.add_subsystem('swing_con', comp, promotes=['*']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() diff --git a/Openmdao/old/con_touch_point.py b/Openmdao/old/con_touch_point.py new file mode 100755 index 0000000..636547a --- /dev/null +++ b/Openmdao/old/con_touch_point.py @@ -0,0 +1,66 @@ +import numpy as np +from openmdao.api import ExplicitComponent + +from comp_fk import FkComp + +class TouchPointCon(ExplicitComponent): + + def setup(self): + + self.add_input('x') + self.add_input('y') + self.add_output('touch_dist') + + def compute(self, inputs, outputs): + + x = inputs['x'] + y = inputs['y'] + + DownAMP = 0.01 + UpperAMP = 0.05 + StanceHeight = 0.18 + StepLength = 0.12 + + CurrentPercent = np.array([a/100+0.01 for a in range(100)]) + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + + trajectory_x = np.zeros(len(CurrentPercent), dtype=float) + trajectory_y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + trajectory_x[i] = -(StepLength / 2) + (CurrentPercent[i] / StancePercent) * StepLength + trajectory_y[i] = DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + StanceHeight + else: + trajectory_x[i] = (StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * StepLength + trajectory_y[i] = -UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + StanceHeight + + TestPoint_x = trajectory_x[99] + TestPoint_y = trajectory_y[99] + + outputs['touch_dist'] = np.linalg.norm([x - TestPoint_x, y - TestPoint_y]) + +if __name__ == '__main__': + + from openmdao.api import Problem, Group, IndepVarComp + + group = Group() + + comp = IndepVarComp() + comp.add_output('l1') + comp.add_output('l2') + group.add_subsystem('i_comp', comp, promotes=['*']) + + comp = FkComp() + group.add_subsystem('fk_comp', comp, promotes=['*']) + + comp = TouchPointCon() + group.add_subsystem('touch_con', comp, promotes=['*']) + + prob = Problem() + prob.model = group + + prob.setup() + prob.run_model() + prob.model.list_outputs() diff --git a/Openmdao/old/group_five_bar_opt.py b/Openmdao/old/group_five_bar_opt.py new file mode 100755 index 0000000..1066344 --- /dev/null +++ b/Openmdao/old/group_five_bar_opt.py @@ -0,0 +1,56 @@ +import numpy as np +import openmdao.api as om +from openmdao.api import Group, IndepVarComp + +from comp_fk import FkComp +from obj_bar_length import BarLengthObj + +class FiveBarOptGroup(Group): + + def setup(self): + + comp = IndepVarComp() + comp.add_output('l1') + comp.add_output('l2') + comp.add_output('thetaL') + comp.add_output('thetaR') + self.add_subsystem('i_comp', comp, promotes=['*']) + + comp = FkComp() + self.add_subsystem('comp_fk', comp, promotes=['*']) + + comp = BarLengthObj() + self.add_subsystem('bar_length_obj', comp, promotes=['*']) + + +from openmdao.api import Problem, ScipyOptimizeDriver + +prob = Problem() +prob.model = FiveBarOptGroup() + +prob.driver = ScipyOptimizeDriver() +prob.driver.options['optimizer'] = 'SLSQP' +prob.driver.options['tol'] = 1e-8 + +from func import SineTrajectory +x = SineTrajectory()[0] +y = SineTrajectory()[1] + +prob.model.add_design_var('l1',lower=0, upper=0.09) +prob.model.add_design_var('l2',lower=0, upper=0.16) +prob.model.add_design_var('thetaL', lower=0, upper=np.pi) +prob.model.add_design_var('thetaR', lower=0, upper=np.pi) +prob.model.add_objective('length') +prob.model.add_constraint('x', equals=x) +prob.model.add_constraint('y', equals=y) + +prob.setup() +prob.run_model() +prob.model.list_outputs() + +prob.run_driver() +print(prob['l1']) +print(prob['l2']) +print(prob['length']) + + diff --git a/Report/.DS_Store b/Report/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..5008ddfcf53c02e82d7eee2e57c38e5672ef89f6 GIT binary patch literal 6148 zcmeH~Jr2S!425mzP>H1@V-^m;4Wg<&0T*E43hX&L&p$$qDprKhvt+--jT7}7np#A3 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z-3{w8K4SvCmN6Z+`+H^I9iJ*5NcKmjzn^otSv@A&bV;`hdx;^@CNcA>n-TqmHe z0p5AX5}W^iqI(}m_`JpVzsMj@53`dKj>g=Uf8`^4|BD)`iSb*err3Y9=^YcABBZ~SGcXAeo*yyVb#|Pm9PBw+yC%y z-~Mu;@{MaNpM3F~PrVgH9tnr=g~-)NnDtbcwG!4kSIC=f&O>_m4YBv4dv*yId??x` zcLke2j-4iNAox)9-yzR=13|k3kDipMt1b0&vrkF z%OTGN?cPPnvuH(Mz_)#*0dJuiJc*Lu5dmMLS$Mt3d0F_WAlI4=d!<62W}biJ%|a0Q zr$XRi;q?&7-Y%5s>*VyKJ6-%0@Q)!vt_#VJ2t117Ti_hS_sONkG5B+F~5dEe$ ze=goWgC_F2mp$)V%`;ZL;x2mWryDQVKmFWU&wQcTv}}sy&buXi;r-98YGu)lK5E|V z@;}0B@f|c7cq+`oAthW=?vE!M`31c#Q7oDkIUGsjqE&FF;W9UAQTk`ntM?O>I+(aqUf4^~+Gbmwo~-0(vVA zu&9@W{m(eIWJu!(4!MS@N65F1L9gH8k~Mvbp5PSp7EEbN8NUqNiK^rhl--o#B^!N@ z|CDlhK5Q#&2_75ZnZa)j@vyZCR+ie@qj{n&b~C!UP51yvwT$3v|CK-F-*0>eMjhXV zCtPHoE%cH23OaphioR4YF^zTncmCh2mvvx(@LdHE1;9CnI(x#Nrl{~T^()J8;e#*z z`;RKNy;t{Q?CS5P-9?_slOK zK0oPW=UK}xTXlCncmCySy%Ij{`OFm??g`xBId&c6i7L+&AfZ-l_5!k}b2=Nyh 0 and (y - g[1]) < 0: + thetaL -= tune + g = self.FK_get_position(thetaL, thetaR) + elif (x - g[0]) > 0 and (y - g[1]) > 0: + thetaR -= tune + g = self.FK_get_position(thetaL, thetaR) + else: + thetaL += tune + g = self.FK_get_position(thetaL, thetaR) + if (x - g[0]) < 0 and (y - g[1]) < 0: + thetaR += tune + g = self.FK_get_position(thetaL, thetaR) + elif (x - g[0]) > 0 and (y - g[1]) < 0: + thetaL -= tune + g = self.FK_get_position(thetaL, thetaR) + elif (x - g[0]) > 0 and (y - g[1]) > 0: + thetaR -= tune + g = self.FK_get_position(thetaL, thetaR) + else: + thetaL += tune + g = self.FK_get_position(thetaL, thetaR) + iteration += 1 + t = t1 - t0 + # print('Target point: ', [x, y], '\nConverge point: ', g, '\nConverge theta θ:', [thetaL, thetaR]) + print('Iteration: ', iteration, '\nTime: ', t) + return thetaL, thetaR + ''' + --------------------------------------------------------------------------------------------------------------------- + Symbolic Jacobian Matrix + ''' + def get_J_s(self): + J_s = (self.get_FK_s()).jacobian([self.thetaL_s, self.thetaR_s]).evalf() + return J_s + ''' + Symbolic Pre-calculated Jacobian Matrix + ''' + def pre_J_s(self): + J_s = sp.Matrix([ + [ -0.0225*((-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.sin(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.045*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.cos(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**0.5*((-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**1.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**3/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2)*sp.sin(self.thetaL_s) + (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.cos(self.thetaL_s) + (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.cos(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2*sp.cos(self.thetaL_s)) + 0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**0.5*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**1.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**3/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2)*sp.cos(self.thetaL_s) + (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.sin(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2) - 0.09*sp.sin(self.thetaL_s), -((-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.sin(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s))*(-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**(-0.5)*(0.0225*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.00014175*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.001575*sp.sin(self.thetaR_s)) + 0.5*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.cos(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))))*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*(-0.09*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.0063*sp.sin(self.thetaR_s)) - (-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**0.5*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.cos(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.5*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.001134*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2 - 0.0063*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211))*sp.sin(self.thetaL_s) - 0.0063*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*(0.09*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0063*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s)) + 0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**0.5*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.5*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.001134*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2 - 0.0063*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211))*sp.cos(self.thetaL_s) - 0.0063*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*(0.09*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0063*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))))], + [-0.045*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.sin(self.thetaL_s) + (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0225*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.cos(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**0.5*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**1.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**3/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2)*sp.cos(self.thetaL_s) + (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.sin(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2) + 0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**0.5*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**1.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**3/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2)*sp.sin(self.thetaL_s) - (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.cos(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.cos(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2*sp.cos(self.thetaL_s)) + 0.09*sp.cos(self.thetaL_s), 0.5*(-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.sin(self.thetaL_s) + (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s))*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*(-0.09*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.0063*sp.sin(self.thetaR_s)) - (-(-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**0.5*sp.cos(self.thetaL_s) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))))*(-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**(-0.5)*(0.0225*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.00014175*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.001575*sp.sin(self.thetaR_s)) - (-0.045*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) + 0.00315*sp.cos(self.thetaR_s) + 0.020325)**0.5*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.5*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.001134*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2 - 0.0063*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211))*sp.cos(self.thetaL_s) - 0.0063*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaL_s)*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*(0.09*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0063*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))) + 0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**0.5*((1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.cos(self.thetaL_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - (-(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) + 1.0)**(-0.5)*(-(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211) - 0.5*(-0.0126*sp.cos(self.thetaR_s) + 0.013)*(0.18*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.001134*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**2 - 0.0063*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))**2/(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211))*sp.sin(self.thetaL_s) + 0.0063*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-0.5)*sp.sin(self.thetaR_s)*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s) + (-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*(0.18*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0126*sp.cos(self.thetaR_s) + 0.0211)**(-1.5)*(0.09*(1.0 - 0.0081*sp.sin(self.thetaR_s)**2/(-0.0126*sp.cos(self.thetaR_s) + 0.013))**(-0.5)*(-0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-1.5)*sp.sin(self.thetaR_s)**2 + 0.09*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.cos(self.thetaR_s))*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**0.5*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.000567*(-0.0126*sp.cos(self.thetaR_s) + 0.013)**(-0.5)*sp.sin(self.thetaR_s)*sp.cos(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013))) - 0.0063*sp.sin(self.thetaR_s))*sp.sin(self.thetaL_s + sp.asin(0.09*sp.sin(self.thetaR_s)/sp.sqrt(-0.0126*sp.cos(self.thetaR_s) + 0.013)))*sp.cos(self.thetaL_s))]]) + # print('\nJacobian: (shape)', np.shape(J_s)) + # pprint.pprint(J_s) + return J_s + ''' + Jacobain Matrix + ''' + +class trajectory(object): + + def __init__(self, par = [0.12, 0.03, 0.05, 0.18]): + self.StepLength = par[0] + self.DownAMP = par[1] + self.UpperAMP = par[2] + self.StanceHeight = par[3] + ''' + Sinesoid Trajectory + ''' + def SineTrajectory(self, num_point = 100): + StancePercent = 0.6 + SwingPercent = 1 - StancePercent + CurrentPercent = np.array([(a + 1) / num_point for a in range(num_point)]) + + x = np.zeros(len(CurrentPercent), dtype=float) + y = np.zeros(len(CurrentPercent), dtype=float) + + for i in range(len(CurrentPercent)): + if (CurrentPercent[i] <= StancePercent): + x[i] = -(self.StepLength / 2) + (CurrentPercent[i] / StancePercent) * self.StepLength + y[i] = self.DownAMP * np.sin(np.pi * CurrentPercent[i] / StancePercent) + self.StanceHeight + else: + x[i] = (self.StepLength / 2) - ((CurrentPercent[i] - StancePercent) / SwingPercent) * self.StepLength + y[i] = -self.UpperAMP * np.sin(np.pi * (CurrentPercent[i] - StancePercent) / SwingPercent) + self.StanceHeight + return x, y diff --git a/_main.py b/_main.py new file mode 100755 index 0000000..27a4e7a --- /dev/null +++ b/_main.py @@ -0,0 +1,50 @@ +import numpy as np +import sympy as sp +import matplotlib.pyplot as plt +from sympy.utilities.lambdify import lambdify + +from _function import five_bar, trajectory + +# Set up geomytry-------------------------------------------------------- +thetaL_s = sp.symbols('thetaL_s') +thetaR_s = sp.symbols('thetaR_s') + +opt = five_bar(thetaL_s, thetaR_s, l1=0.09, l2=0.16, w=0.07) + +# Computing Forward Kinematics-------------------------------------------- +FK_s = opt.get_FK_s() + +# Forward Kinematics Test------------------------------------------------- +s_top = opt.FK_get_position(0, np.pi) +s_bottom = opt.FK_get_position(np.pi/2, np.pi/2) +s_test = opt.FK_get_position(0.2 * np.pi, 0.7 * np.pi) +print('\nStarting:', s_top, '\nFurthest:', s_bottom, '\nTest: ', s_test) + +# Converge test----------------------------------------------------------- +theta = opt.PIK_get_theta(-5.80000000e-02, 0.19075104) + +# Computing Jacobian------------------------------------------------------ +J_s = opt.pre_J_s() + +# Generating Sine Trajectory---------------------------------------------- +par = [0.12, 0.03, 0.05, 0.18] +ideal_tar = trajectory(par) +[x, y] = ideal_tar.SineTrajectory(num_point = 100) +x_ = np.zeros(len(x), dtype=float) +y_ = np.zeros(len(x), dtype=float) + +for i in range(len(x)): + print(i) + # [thetaL, thetaR] = opt.PIK_get_theta(x[i], y[i]) + [thetaL, thetaR] = opt.IK_5_link(x[i], y[i]) + # thetaL_[i] = thetaL + # thetaR_[i] = thetaR + g = opt.FK_get_position(thetaL, thetaR) + [x_[i], y_[i]] = g + # x_[i] = g[0] + # y_[i] = g[1] + +plt.plot(x, y, x_, y_, marker = '*') +plt.title('SineTrajectory') +plt.grid() +plt.show()