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Mobile Icosapods
- Source :
- Advances in Applied Mathematics, Volume 88, July 2017, Pages 1-25
- Publication Year :
- 2016
-
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.<br />Comment: 22 pages, 4 figures
- Subjects :
- Computer Science - Robotics
Mathematics - Algebraic Geometry
14L35, 70B15, 14P10
Subjects
Details
- Database :
- arXiv
- Journal :
- Advances in Applied Mathematics, Volume 88, July 2017, Pages 1-25
- Publication Type :
- Report
- Accession number :
- edsarx.1603.07304
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.aam.2016.12.002