Mobile Icosapods

Jon Selig

doi:10.1016/j.aam.2016.12.002

Mobile Icosapods

Jon Selig

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1-25
Number of pages	24
Journal	Advances in Applied Mathematics
DOIs	https://doi.org/10.1016/j.aam.2016.12.002
Publication status	Published - 17 Jan 2017
Externally published	Yes

Keywords

0102 Applied Mathematics
spectrahedra
line-symmetric motion
icosapods
body-bar framework
Applied Mathematics

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10.1016/j.aam.2016.12.002Licence: CC BY-NC-ND 4.0

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title = "Mobile Icosapods",

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{\textquoteright}s construction yields all mobile 20-pods, and that it is possible to construct examples where all coordinates are real.",

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AB - 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.

KW - 0102 Applied Mathematics

KW - spectrahedra

KW - line-symmetric motion

KW - icosapods

KW - body-bar framework

KW - Applied Mathematics

U2 - 10.1016/j.aam.2016.12.002

DO - 10.1016/j.aam.2016.12.002

M3 - Article

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EP - 25

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

Mobile Icosapods

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Keywords

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