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Edit summary/reason (summary) | 'Very brief, stub-like introduction, mostly in context of Denavit-Hartenberg. ' |
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New page wikitext, after the edit (new_wikitext) | 'The product of exponentials method (POE) is a [[Robotics conventions|robotics convention]] for mapping the links of a spatial [[kinematic chain]]. It is an alternative to [[Denavit-Hartenberg parameter|Denavit-Hartenberg]] parameterization.
==Relationship to Denavit-Hartenberg Parameters==
===Advantages===
The product of exponentials method uses only two [[frames of reference]]: the base frame ''S'' and the tool frame ''T''. Constructing the Denavit-Hartenberg parameters for a robot requires the careful selection of tool frames in order to enable particular cancellations, such that the twists can be represented by four parameters instead of six. In the product of exponentials method, the joint twists can be constructed directly without considering adjacent joints in the chain. This makes the joint twists easier to construct, and easier to process by computer.<ref>{{cite book|last1=Sastry|first1=Richard M. Murray ; Zexiang Li ; S. Shankar|title=A mathematical introduction to robotic manipulation|date=1994|publisher=CRC Press|location=Boca Raton, Fla.|isbn=9780849379819|edition=1. [Dr.]|url=http://www.cds.caltech.edu/~murray/books/MLS/pdf/mls94-complete.pdf}}</ref>
===Conversion===
There is not a one-to-one mapping between twist coordinate mapping in both methods, but algorithmic mapping from POE to Denavit-Hartenberg has been demonstrated. <ref>{{cite journal|last1=Wu|first1=Liao|last2=Crawford|first2=Ross|last3=Roberts|first3=Jonathan|title=An Analytic Approach to Converting POE Parameters Into D–H Parameters for Serial-Link Robots|journal=IEEE Robotics and Automation Letters|date=October 2017|volume=2|issue=4|pages=2174–2179|doi=10.1109/LRA.2017.2723470}}</ref>
==Application to Parallel Robots==
When analyzing [[parallel robots]], the kinematic chain of each leg is analyzed individually and the tool frames are set equal to one another. This method is extensible to grasp analyses.' |
Unified diff of changes made by edit (edit_diff) | '@@ -1,1 +1,10 @@
+The product of exponentials method (POE) is a [[Robotics conventions|robotics convention]] for mapping the links of a spatial [[kinematic chain]]. It is an alternative to [[Denavit-Hartenberg parameter|Denavit-Hartenberg]] parameterization.
+==Relationship to Denavit-Hartenberg Parameters==
+===Advantages===
+The product of exponentials method uses only two [[frames of reference]]: the base frame ''S'' and the tool frame ''T''. Constructing the Denavit-Hartenberg parameters for a robot requires the careful selection of tool frames in order to enable particular cancellations, such that the twists can be represented by four parameters instead of six. In the product of exponentials method, the joint twists can be constructed directly without considering adjacent joints in the chain. This makes the joint twists easier to construct, and easier to process by computer.<ref>{{cite book|last1=Sastry|first1=Richard M. Murray ; Zexiang Li ; S. Shankar|title=A mathematical introduction to robotic manipulation|date=1994|publisher=CRC Press|location=Boca Raton, Fla.|isbn=9780849379819|edition=1. [Dr.]|url=http://www.cds.caltech.edu/~murray/books/MLS/pdf/mls94-complete.pdf}}</ref>
+===Conversion===
+There is not a one-to-one mapping between twist coordinate mapping in both methods, but algorithmic mapping from POE to Denavit-Hartenberg has been demonstrated. <ref>{{cite journal|last1=Wu|first1=Liao|last2=Crawford|first2=Ross|last3=Roberts|first3=Jonathan|title=An Analytic Approach to Converting POE Parameters Into D–H Parameters for Serial-Link Robots|journal=IEEE Robotics and Automation Letters|date=October 2017|volume=2|issue=4|pages=2174–2179|doi=10.1109/LRA.2017.2723470}}</ref>
+
+==Application to Parallel Robots==
+When analyzing [[parallel robots]], the kinematic chain of each leg is analyzed individually and the tool frames are set equal to one another. This method is extensible to grasp analyses.
' |
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3 => 'The product of exponentials method uses only two [[frames of reference]]: the base frame ''S'' and the tool frame ''T''. Constructing the Denavit-Hartenberg parameters for a robot requires the careful selection of tool frames in order to enable particular cancellations, such that the twists can be represented by four parameters instead of six. In the product of exponentials method, the joint twists can be constructed directly without considering adjacent joints in the chain. This makes the joint twists easier to construct, and easier to process by computer.<ref>{{cite book|last1=Sastry|first1=Richard M. Murray ; Zexiang Li ; S. Shankar|title=A mathematical introduction to robotic manipulation|date=1994|publisher=CRC Press|location=Boca Raton, Fla.|isbn=9780849379819|edition=1. [Dr.]|url=http://www.cds.caltech.edu/~murray/books/MLS/pdf/mls94-complete.pdf}}</ref>',
4 => '===Conversion===',
5 => 'There is not a one-to-one mapping between twist coordinate mapping in both methods, but algorithmic mapping from POE to Denavit-Hartenberg has been demonstrated. <ref>{{cite journal|last1=Wu|first1=Liao|last2=Crawford|first2=Ross|last3=Roberts|first3=Jonathan|title=An Analytic Approach to Converting POE Parameters Into D–H Parameters for Serial-Link Robots|journal=IEEE Robotics and Automation Letters|date=October 2017|volume=2|issue=4|pages=2174–2179|doi=10.1109/LRA.2017.2723470}}</ref>',
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Parsed HTML source of the new revision (new_html) | '<div class="mw-parser-output"><p>The product of exponentials method (POE) is a <a href="/enwiki/wiki/Robotics_conventions" title="Robotics conventions">robotics convention</a> for mapping the links of a spatial <a href="/enwiki/wiki/Kinematic_chain" title="Kinematic chain">kinematic chain</a>. It is an alternative to <a href="/enwiki/wiki/Denavit-Hartenberg_parameter" class="mw-redirect" title="Denavit-Hartenberg parameter">Denavit-Hartenberg</a> parameterization.</p>
<p></p>
<div id="toc" class="toc">
<div class="toctitle" lang="en" dir="ltr" xml:lang="en">
<h2>Contents</h2>
</div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Relationship_to_Denavit-Hartenberg_Parameters"><span class="tocnumber">1</span> <span class="toctext">Relationship to Denavit-Hartenberg Parameters</span></a>
<ul>
<li class="toclevel-2 tocsection-2"><a href="#Advantages"><span class="tocnumber">1.1</span> <span class="toctext">Advantages</span></a></li>
<li class="toclevel-2 tocsection-3"><a href="#Conversion"><span class="tocnumber">1.2</span> <span class="toctext">Conversion</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-4"><a href="#Application_to_Parallel_Robots"><span class="tocnumber">2</span> <span class="toctext">Application to Parallel Robots</span></a></li>
</ul>
</div>
<p></p>
<h2><span class="mw-headline" id="Relationship_to_Denavit-Hartenberg_Parameters">Relationship to Denavit-Hartenberg Parameters</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Product_of_exponentials_formula&action=edit&section=1" title="Edit section: Relationship to Denavit-Hartenberg Parameters">edit source</a><span class="mw-editsection-bracket">]</span></span></h2>
<h3><span class="mw-headline" id="Advantages">Advantages</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Product_of_exponentials_formula&action=edit&section=2" title="Edit section: Advantages">edit source</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>The product of exponentials method uses only two <a href="/enwiki/wiki/Frames_of_reference" class="mw-redirect" title="Frames of reference">frames of reference</a>: the base frame <i>S</i> and the tool frame <i>T</i>. Constructing the Denavit-Hartenberg parameters for a robot requires the careful selection of tool frames in order to enable particular cancellations, such that the twists can be represented by four parameters instead of six. In the product of exponentials method, the joint twists can be constructed directly without considering adjacent joints in the chain. This makes the joint twists easier to construct, and easier to process by computer.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1">[1]</a></sup></p>
<h3><span class="mw-headline" id="Conversion">Conversion</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Product_of_exponentials_formula&action=edit&section=3" title="Edit section: Conversion">edit source</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>There is not a one-to-one mapping between twist coordinate mapping in both methods, but algorithmic mapping from POE to Denavit-Hartenberg has been demonstrated. <sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup></p>
<h2><span class="mw-headline" id="Application_to_Parallel_Robots">Application to Parallel Robots</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Product_of_exponentials_formula&action=edit&section=4" title="Edit section: Application to Parallel Robots">edit source</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>When analyzing <a href="/enwiki/wiki/Parallel_robots" class="mw-redirect" title="Parallel robots">parallel robots</a>, the kinematic chain of each leg is analyzed individually and the tool frames are set equal to one another. This method is extensible to grasp analyses.</p>
<div class="mw-references-wrap">
<ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation book">Sastry, Richard M. Murray ; Zexiang Li ; S. Shankar (1994). <a rel="nofollow" class="external text" href="http://www.cds.caltech.edu/~murray/books/MLS/pdf/mls94-complete.pdf"><i>A mathematical introduction to robotic manipulation</i></a> <span style="font-size:85%;">(PDF)</span> (1. [Dr.] ed.). Boca Raton, Fla.: CRC Press. <a href="/enwiki/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/9780849379819" title="Special:BookSources/9780849379819">9780849379819</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+mathematical+introduction+to+robotic+manipulation&rft.place=Boca+Raton%2C+Fla.&rft.edition=1.+%5BDr.%5D&rft.pub=CRC+Press&rft.date=1994&rft.isbn=9780849379819&rft.aulast=Sastry&rft.aufirst=Richard+M.+Murray+%3B+Zexiang+Li+%3B+S.+Shankar&rft_id=http%3A%2F%2Fwww.cds.caltech.edu%2F~murray%2Fbooks%2FMLS%2Fpdf%2Fmls94-complete.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AProduct+of+exponentials+formula" class="Z3988"><span style="display:none;"> </span></span></span></li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation journal">Wu, Liao; Crawford, Ross; Roberts, Jonathan (October 2017). "An Analytic Approach to Converting POE Parameters Into D–H Parameters for Serial-Link Robots". <i>IEEE Robotics and Automation Letters</i>. <b>2</b> (4): 2174–2179. <a href="/enwiki/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<a rel="nofollow" class="external text" href="/enwiki//doi.org/10.1109%2FLRA.2017.2723470">10.1109/LRA.2017.2723470</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Robotics+and+Automation+Letters&rft.atitle=An+Analytic+Approach+to+Converting+POE+Parameters+Into+D%E2%80%93H+Parameters+for+Serial-Link+Robots&rft.volume=2&rft.issue=4&rft.pages=2174-2179&rft.date=2017-10&rft_id=info%3Adoi%2F10.1109%2FLRA.2017.2723470&rft.aulast=Wu&rft.aufirst=Liao&rft.au=Crawford%2C+Ross&rft.au=Roberts%2C+Jonathan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AProduct+of+exponentials+formula" class="Z3988"><span style="display:none;"> </span></span></span></li>
</ol>
</div>
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