Document Zbl 1550.70006

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J. Comput. Methods</a> <a href="/?q=in%3A478313" title="Articles in this Issue">18, No. 10, Article ID 2150050, 15 p. (2021)</a>. </div> <div class="abstract">Summary: Some situations that change the parameters of the kinematic structure may cause the robot end effector to deviate [<span class="zbmathjax-textit">J. P. Merlet</span>, Parallel robots. Dordrecht: Springer (2006; <a href="/1110.70002">Zbl 1110.70002</a>)] from the desired trajectory. This effect is called the robustness of the robot by Merlet. One of the ways to correct the robustness is by updating the robot trajectory. The jerk vector of the robot end effector is the third-order positional variation of the TCP and defined as thus the time derivative of the acceleration vector. If there is a high curvature on the transition curve trajectory of robot, then there is a tangential jerk along the trajectory. In this study, the geometrically offset trajectory of the robot end effector from the current trajectory was obtained by using the curvature theory. The angular velocity and angular acceleration of the offset trajectory were calculated. An example of the main trajectory of robot end effector and its offset is given. Also, the jerk of the robot end effector of the offset trajectory was calculated according to the curvature of the trajectory surface in case of a jerk problem caused by a high curvature in the transition curve along the offset trajectory curve.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7488890">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A70B15" title="MSC2020">70B15</a> </td> <td class="space"> Kinematics of mechanisms and robots </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65L05" title="MSC2020">65L05</a> </td> <td class="space"> Numerical methods for initial value problems involving ordinary differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aruled+surfaces">ruled surfaces</a>; <a href="/?q=ut%3Aoffset+curves">offset curves</a>; <a href="/?q=ut%3Arobot+end+effector">robot end effector</a>; <a href="/?q=ut%3Arobot+trajectory">robot trajectory</a>; <a href="/?q=ut%3Acurvature+theory">curvature theory</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1110.70002">Zbl 1110.70002</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1550.70006" data-ciurl="/ci/07488890" data-biburl="/bibtex/07488890.bib" data-amsurl="/amsrefs/07488890.bib" data-xmlurl="/xml/07488890.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07488890.pdf" title="Zbl 1550.70006 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1142/S021987622150050X" aria-label="DOI for “Offset trajectory planning of robot end effector and its jerk with curvature theory”" title="10.1142/S021987622150050X">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aldossary, M. 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