Mobile Icosapods

Journal article

Gallet, M, Nawratil, G, Schicho, J and Selig, JM (2017). Mobile Icosapods. Advances in Applied Mathematics. 88 (July), pp. 1-25. https://doi.org/10.1016/j.aam.2016.12.002
AuthorsGallet, M, Nawratil, G, Schicho, J and Selig, JM
Abstract

Pods are mechanical devices constituted of two rigid bodies, the base and the platform, connected by a number of other rigid bodies, called legs, that are anchored via spherical joints. It is possible to prove that the maximal number of legs of a mobile pod, when finite, is 20. In 1904, Borel designed a technique to construct examples of such 20-pods, but could not constrain the legs to have base and platform points with real coordinates. We show that Borel’s construction yields all mobile 20-pods, and that it is possible to construct examples where all coordinates are real.

Keywordsicosapods; line-symmetric motion; body-bar framework; spectrahedra; 0102 Applied Mathematics; Applied Mathematics
Year2017
JournalAdvances in Applied Mathematics
Journal citation88 (July), pp. 1-25
PublisherAcademic Press
ISSN0196-8858
Digital Object Identifier (DOI)https://doi.org/10.1016/j.aam.2016.12.002
Publication dates
Print17 Jan 2017
Publication process dates
Deposited12 Jan 2017
Accepted12 Dec 2016
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