Mobile Icosapods
Robotics
2017-07-19 v1 Algebraic Geometry
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 with all real coordinates.
Cite
@article{arxiv.1603.07304,
title = {Mobile Icosapods},
author = {Matteo Gallet and Georg Nawratil and Josef Schicho and J. M. Selig},
journal= {arXiv preprint arXiv:1603.07304},
year = {2017}
}
Comments
22 pages, 4 figures