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bond theory

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Self-motions of pentapods with linear platform
Georg Nawratil, Josef Schicho
Journal:

Robotica / Volume 35 / Issue 4 / April 2017

Published online by Cambridge University Press:

02 December 2015, pp. 832-860
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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.