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+<?xml version="1.0" encoding="utf-8" ?>
+<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN"
+                  "JATS-publishing1.dtd">
+<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="1.2" article-type="other">
+<front>
+<journal-meta>
+<journal-id></journal-id>
+<journal-title-group>
+<journal-title>Journal of Open Source Software</journal-title>
+<abbrev-journal-title>JOSS</abbrev-journal-title>
+</journal-title-group>
+<issn publication-format="electronic">2475-9066</issn>
+<publisher>
+<publisher-name>Open Journals</publisher-name>
+</publisher>
+</journal-meta>
+<article-meta>
+<article-id pub-id-type="publisher-id">3967</article-id>
+<article-id pub-id-type="doi">10.21105/joss.03967</article-id>
+<title-group>
+<article-title>TriP: A Python package for the kinematic modeling of
+serial-parallel hybrid robots</article-title>
+</title-group>
+<contrib-group>
+<contrib contrib-type="author">
+<contrib-id contrib-id-type="orcid">0000-0002-7825-3476</contrib-id>
+<name>
+<surname>Baumgärtner</surname>
+<given-names>Jan</given-names>
+</name>
+<xref ref-type="aff" rid="aff-1"/>
+</contrib>
+<contrib contrib-type="author">
+<name>
+<surname>Miller</surname>
+<given-names>Torben</given-names>
+</name>
+<xref ref-type="aff" rid="aff-2"/>
+</contrib>
+<aff id="aff-1">
+<institution-wrap>
+<institution>Heidelberg University</institution>
+</institution-wrap>
+</aff>
+<aff id="aff-2">
+<institution-wrap>
+<institution>Independent Researcher</institution>
+</institution-wrap>
+</aff>
+</contrib-group>
+<pub-date date-type="pub" publication-format="electronic" iso-8601-date="2021-10-28">
+<day>28</day>
+<month>10</month>
+<year>2021</year>
+</pub-date>
+<volume>7</volume>
+<issue>71</issue>
+<fpage>3967</fpage>
+<permissions>
+<copyright-statement>Authors of papers retain copyright and release the
+work under a Creative Commons Attribution 4.0 International License (CC
+BY 4.0)</copyright-statement>
+<copyright-year>2022</copyright-year>
+<copyright-holder>The article authors</copyright-holder>
+<license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/">
+<license-p>Authors of papers retain copyright and release the work under
+a Creative Commons Attribution 4.0 International License (CC BY
+4.0)</license-p>
+</license>
+</permissions>
+<kwd-group kwd-group-type="author">
+<kwd>Python</kwd>
+<kwd>robotics</kwd>
+<kwd>inverse kinematics</kwd>
+<kwd>kinematics</kwd>
+<kwd>parallel manipulator</kwd>
+<kwd>serial manipulator</kwd>
+</kwd-group>
+</article-meta>
+</front>
+<body>
+<sec id="summary">
+  <title>Summary</title>
+  <p>Robots can be classified according to their mechanical structure.
+  Serial mechanisms like robotic arms are mechanisms where each moving
+  part (called a link) is connected to only the one before and the one
+  after it. They are often used when a large workspace is required,
+  meaning the robot needs a long reach. In parallel mechanisms, the
+  links of the robot form loops causing them to be structurally stronger
+  and stiffer.</p>
+  <p>If both a large workspace and structural strength are required,
+  hybrids that contain both serial and parallel mechanisms are used.
+  While hybrid mechanisms combine the mechanical advantages of both
+  parallel and serial mechanisms, they also combine their modeling
+  disadvantages:</p>
+  <list list-type="bullet">
+    <list-item>
+      <p>Finding an explicit solution for either forward or inverse
+      kinematics is often impossible. Using numerical approaches instead
+      leads to complicated constrained optimization problems for both
+      forward and inverse kinematics.</p>
+    </list-item>
+    <list-item>
+      <p>While serial mechanisms are very well supported by current
+      robotic frameworks, parallel mechanisms and hybrid mechanisms
+      especially are often not supported at all. A great overview of the
+      supported robot types for different robotic frameworks was
+      compiled by Kumar
+      (<xref alt="2019" rid="ref-kumar" ref-type="bibr">2019</xref>).</p>
+    </list-item>
+  </list>
+  <p>TriP is a python package designed to close this gap using a modular
+  modeling framework akin to the one described by Kumar et al.
+  (<xref alt="2020" rid="ref-survey" ref-type="bibr">2020</xref>). It
+  allows the modeling of arbitrary hybrid mechanisms and is capable of
+  calculating forward and inverse kinematics.</p>
+  <p>The calculations are performed using a symbolic framework. This
+  makes it easy for users to implement custom case-dependent
+  mathematical solvers.</p>
+</sec>
+<sec id="statement-of-need">
+  <title>Statement of Need</title>
+  <p>While a huge number of researchers, such as Pisla et al.
+  (<xref alt="2013" rid="ref-PISLA" ref-type="bibr">2013</xref>), Kanaan
+  et al. (<xref alt="2009" rid="ref-verne" ref-type="bibr">2009</xref>),
+  and Zoss et al.
+  (<xref alt="2006" rid="ref-berkley" ref-type="bibr">2006</xref>), use
+  hybrid serial parallel systems, most modern kinematics frameworks
+  still lack support for such systems. Examples include OpenRAVE
+  (<xref alt="Diankov &amp; Kuffner, 2008" rid="ref-openrave" ref-type="bibr">Diankov
+  &amp; Kuffner, 2008</xref>), used in the MoveIt! stack
+  (<xref alt="Chitta et al., 2012" rid="ref-moveit" ref-type="bibr">Chitta
+  et al., 2012</xref>), the MATLAB robotics toolbox
+  (<xref alt="Corke, 2017" rid="ref-matlabrobot" ref-type="bibr">Corke,
+  2017</xref>), Klampt
+  (<xref alt="Hauser, 2021" rid="ref-Klampt" ref-type="bibr">Hauser,
+  2021</xref>), and the inverse kinematics Python library
+  (<xref alt="Manceron, 2021" rid="ref-ikpy" ref-type="bibr">Manceron,
+  2021</xref>). While all these frameworks and libraries offer fast
+  computation of forward and inverse kinematics, they only support
+  branching serial mechanisms. This lack of support often leaves
+  developers with essentially two choices:</p>
+  <p>Either shoehorn their hybrid robots into a framework not designed
+  to handle them or be left to implement their own kinematic
+  solvers.</p>
+  <p>TriP is a lightweight and easy-to-use package for directly modeling
+  hybrid mechanisms and calculating their kinematics. Although TriP is
+  fast for a Python package, it is not built for robust hard-real time
+  control applications. Instead, it is aimed at researchers and
+  engineers who quickly want to build kinematic models to test their
+  mechanical designs. For this reason it also exposes a interface to the
+  nonlinear optimization and algorithmic differentiation tool CasADi
+  (<xref alt="Andersson et al., 2019" rid="ref-casadi" ref-type="bibr">Andersson
+  et al., 2019</xref>). This allows researchers to investigate the
+  kinematic properties of their robots, for example, by using CasADi to
+  find singular configurations or to compute manipulability ellipsoides.
+  Similar to MoveIt!, TriP also enables researchers to build their own
+  inverse kinematic solvers.</p>
+</sec>
+<sec id="overview">
+  <title>Overview</title>
+  <p>TriP models robots using its <italic>Robot</italic> class. A
+  <italic>Robot</italic> object is made up of
+  <italic>Transformation</italic> and <italic>KinematicGroup</italic>
+  objects. The <italic>KinematicGroup</italic> objects are used to model
+  parallel mechanisms while the <italic>Transformation</italic> objects
+  model serial mechanisms. See Figure
+  <xref alt="1" rid="hybrid_chain_taxonomy_groups">1</xref> for
+  reference, where the links of each robot are colored according to the
+  <italic>KinematicGroup</italic> or <italic>Transformation</italic> it
+  belongs to, while joints are either light green or orange, depending
+  on whether they are actuated or not.</p>
+  <fig>
+    <caption><p>Different Hybrid Robot types and their object structure
+    <styled-content id="hybrid_chain_taxonomy_groups"></styled-content></p></caption>
+    <graphic mimetype="image" mime-subtype="png" xlink:href="hybrid_chain_taxonomy_groups.png" xlink:title="" />
+  </fig>
+  <p>Both <italic>KinematicGroups</italic> and
+  <italic>Transformations</italic> can be connected to form branching
+  mechanisms as indicated in Figure
+  <xref alt="1" rid="hybrid_chain_taxonomy_groups">1</xref>.</p>
+  <p><italic>Transformation</italic> objects implement homogeneous
+  coordinate transformations between coordinate frames. These can be
+  either dynamic or static with dynamic transformations implementing
+  joints. A few example joints can be seen in Figure
+  <xref alt="2" rid="sample_trafo">2</xref>.</p>
+  <fig>
+    <caption><p>Sample Joints using the Transformation class
+    <styled-content id="sample_trafo"></styled-content></p></caption>
+    <graphic mimetype="image" mime-subtype="png" xlink:href="sample_transformations.png" xlink:title="" />
+  </fig>
+  <p>While all example joints use Euler angles in roll pitch yaw
+  convention to describe rotation, quaternions are also supported.</p>
+  <p><italic>KinematicGroups</italic> model parallel mechanisms using
+  the abstraction approach described by Kumar et al.
+  (<xref alt="2020" rid="ref-survey" ref-type="bibr">2020</xref>). This
+  approach models a parallel manipulator as a virtual serial manipulator
+  and a mapping that maps the virtual joint state to the true actuated
+  joint state of the parallel manipulator.</p>
+  <p>An illustrative example of this model is an excavator with two
+  hydraulic cylinders. Each cylinder is part of a parallel mechanism
+  resulting in two <italic>KinematicGroups</italic>. Both can be seen in
+  Figure <xref alt="3" rid="group_structure">3</xref>, where one is
+  green and the other one is blue.</p>
+  <fig>
+    <caption><p>Excavator Arm build from two Groups (green and blue)
+    <styled-content id="group_structure"></styled-content></p></caption>
+    <graphic mimetype="image" mime-subtype="png" xlink:href="group_structure.png" xlink:title="" />
+  </fig>
+  <p>The abstraction approach models the excavator as a serial
+  manipulator where the joints are directly actuated. Using two mappings
+  to convert the state of the hydraulic cylinders to the state of the
+  joints and vice versa, it is possible to calculate both forward and
+  inverse kinematics. In this example, the mapping between cylinders and
+  joints can be expressed using trigonometry. Since an explicit
+  formulation of the mappings might not always be possible, TriP can
+  also compute the mapping by solving the closure equation of the
+  parallel manipulator.</p>
+  <p>TriP can generate symbolic representations of robots using CasADi
+  (<xref alt="Andersson et al., 2019" rid="ref-casadi" ref-type="bibr">Andersson
+  et al., 2019</xref>). This symbolic representation can be used to set
+  up a solver object that then solves the inverse kinematics. While the
+  library already implements a simple inverse kinematics solver, the
+  symbolic representation makes it easy to implement custom solvers.</p>
+  <p>All features of TriP are thoroughly documented with tutorials and
+  examples to help people get started.</p>
+</sec>
+</body>
+<back>
+<ref-list>
+  <ref-list>
+    <ref id="ref-Klampt">
+      <element-citation publication-type="webpage">
+        <person-group person-group-type="author">
+          <name><surname>Hauser</surname><given-names>Kris</given-names></name>
+        </person-group>
+        <article-title>Kris’ locomotion and manipulation planning toolbox - Klamp’t</article-title>
+        <year iso-8601-date="2021">2021</year>
+        <date-in-citation content-type="access-date"><year iso-8601-date="2021-03-31">2021</year><month>03</month><day>31</day></date-in-citation>
+        <uri>https://github.com/krishauser/Klampt</uri>
+      </element-citation>
+    </ref>
+    <ref id="ref-ikpy">
+      <element-citation publication-type="webpage">
+        <person-group person-group-type="author">
+          <name><surname>Manceron</surname><given-names>Pierre</given-names></name>
+        </person-group>
+        <article-title>IKPy - an inverse kinematics library aiming performance and modularity</article-title>
+        <year iso-8601-date="2021">2021</year>
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+        <uri>https://github.com/Phylliade/ikpy</uri>
+      </element-citation>
+    </ref>
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+      </element-citation>
+    </ref>
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+          <name><surname>Rawlings</surname><given-names>James B</given-names></name>
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+    </ref>
+  </ref-list>
+</ref-list>
+</back>
+</article>