Symmetric configuration spaces of linkages

David Blanc; Nir Shvalb

doi:10.1007/s41468-023-00114-z

Symmetric configuration spaces of linkages

David Blanc, Nir Shvalb

University of Haifa, Ariel University

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

Abstract

A configuration of a linkage Γ is a possible positioning of Γ in R^d , and the collection of all such forms the configuration space C(Γ) of Γ . We here introduce the notion of the symmetric configuration space of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.

Original language	American English
Pages (from-to)	527-569
Number of pages	43
Journal	Journal of Applied and Computational Topology
Volume	7
Issue number	3
DOIs	https://doi.org/10.1007/s41468-023-00114-z
State	Published - Sep 2023

Keywords

Configuration space
Linkage
Planar polygon
symmetries

All Science Journal Classification (ASJC) codes

Geometry and Topology
Computational Mathematics
Applied Mathematics

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10.1007/s41468-023-00114-z

Cite this

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abstract = "A configuration of a linkage Γ is a possible positioning of Γ in Rd , and the collection of all such forms the configuration space C(Γ) of Γ . We here introduce the notion of the symmetric configuration space of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.",

keywords = "Configuration space, Linkage, Planar polygon, symmetries",

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AB - A configuration of a linkage Γ is a possible positioning of Γ in Rd , and the collection of all such forms the configuration space C(Γ) of Γ . We here introduce the notion of the symmetric configuration space of a linkage, in which we identify configurations which are geometrically indistinguishable. We show that the symmetric configuration space of a planar polygon has a regular cell structure, provide some principles for calculating this structure, and give a complete description of the symmetric configuration space of all quadrilaterals and of the equilateral pentagon.

KW - Configuration space

KW - Linkage

KW - Planar polygon

KW - symmetries

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U2 - 10.1007/s41468-023-00114-z

DO - 10.1007/s41468-023-00114-z

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JO - Journal of Applied and Computational Topology

JF - Journal of Applied and Computational Topology

IS - 3

ER -

Symmetric configuration spaces of linkages

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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