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arXiv · 1510.03567

On the line-symmetry of self-motions of linear pentapods

Georg Nawratil
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Abstract

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.

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Georg Nawratil. 2015-10-13. On the line-symmetry of self-motions of linear pentapods. https://arxiv.org/abs/1510.03567

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