On the line-symmetry of self-motions of linear pentapods
This work addresses a theoretical gap in kinematics for researchers in robotics and mechanical engineering, though it appears incremental as it builds on over a century of prior studies.
The paper tackles the problem of self-motions in linear pentapods by proving that all such motions for Type 1 and Type 2 can be generated by line-symmetric motions, closing a historical gap and providing a new solution set for the Borel Bricard problem.
We show that all self-motions of pentapods with linear platform of Type 1 and Type 2 can be generated by line-symmetric motions. Thus this paper closes a gap between the more than 100 year old works of Duporcq and Borel and the extensive study of line-symmetric motions done by Krames in the 1930's. As a consequence we also get a new solution set for the Borel Bricard problem. Moreover we discuss the reality of self-motions and give a sufficient condition for the design of linear pentapods of Type 1 and Type 2, which have a self-motion free workspace.