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Self-motions of pentapods with linear platform

Published online by Cambridge University Press:  02 December 2015

Georg Nawratil  and
Josef Schicho
Georg Nawratil*
Affiliation:
Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10/104, 1040 Vienna, Austria
Josef Schicho
Affiliation:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenberger Strasse 69, 4040 Linz, Austria
*
*Corresponding author. E-mail: nawratil@geometrie.tuwien.ac.at
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Summary

We give a full classification of all pentapods with linear platform possessing a self-motion beside the trivial rotation about the platform. Recent research necessitates a contemporary and accurate re-examination of old results on this topic given by Darboux, Mannheim, Duporcq and Bricard, which also takes the coincidence of platform anchor points into account. For our study we use bond theory with respect to a novel kinematic mapping for pentapods with linear platform, beside the method of singular-invariant leg-rearrangements. Based on our results we design pentapods with linear platform, which have a simplified direct kinematics concerning their number of (real) solutions.

Keywords

PentapodBorel Bricard problemBond theorySelf-MotionDirect kinematicKinematic mapping
Type
Articles
Information
Robotica , Volume 35 , Issue 4 , April 2017 , pp. 832 - 860
Copyright
Copyright © Cambridge University Press 2015 

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