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

2015/10/13 by Georg Nawratil, Nawratil, Georg
Computer Science · #FOS: Computer and information sciences #Robotics (cs.RO) #cs.RO

paper · pdf · doi:10.48550/arxiv.1510.03567

16 pages, 7 figures

arxiv created 2015/12/01 · arxiv updated 2015/12/02

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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