Gallet, M, Nawratil, G, Schicho, J and Selig, JM (2017). Mobile Icosapods. Advances in Applied Mathematics. 88 (July), pp. 1-25.
|Authors||Gallet, M, Nawratil, G, Schicho, J and Selig, JM|
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.
|Keywords||icosapods; line-symmetric motion; body-bar framework; spectrahedra; 0102 Applied Mathematics; Applied Mathematics|
|Journal||Advances in Applied Mathematics|
|Journal citation||88 (July), pp. 1-25|
|Digital Object Identifier (DOI)||doi:10.1016/j.aam.2016.12.002|
|17 Jan 2017|
|Publication process dates|
|Deposited||12 Jan 2017|
|Accepted||12 Dec 2016|
|Accepted author manuscript|
CC BY-NC-ND 4.0
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