On the area of constrained polygonal linkages

Gaiane Panina; Dirk Siersma

doi:10.1016/j.topol.2018.02.004

On the area of constrained polygonal linkages

Gaiane Panina^*, Dirk Siersma

^*Corresponding author for this work

RAS - Saint Petersburg Department of Steklov Institute of Mathematics

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

Abstract

Consider a mechanical linkages whose underlying graph is a polygon with a diagonal constraint, or more general, a partial two-tree. We show that (with an appropriate definition) the oriented area is a Bott–Morse function on the configuration space of the linkage. Its critical points are described and Bott–Morse indices are computed. This paper is a generalization of analogous results for polygonal linkages (obtained earlier by G. Khimshiashvili, G. Panina, and A. Zhukova).

Original language	English
Pages (from-to)	32-44
Number of pages	13
Journal	Topology and its Applications
Volume	238
DOIs	https://doi.org/10.1016/j.topol.2018.02.004
Publication status	Published - 1 Apr 2018

Funding

This work is supported by the RFBR grant 17-01-00128 . It is our pleasure to acknowledge the hospitality and excellent working conditions of CIRM, Luminy, where this paper was initiated as a ‘research in pairs’ project. We are grateful to George Khimshiashvili for useful remarks and comments.

Keywords

Critical point
Morse index
Partial two-tree
Pitchfork bifurcation
Two-terminal series-parallel graph

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10.1016/j.topol.2018.02.004

1-s2.0-S0166864118300890-mainFinal published version, 379 KB

https://arxiv.org/pdf/1702.07468.pdf

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AB - Consider a mechanical linkages whose underlying graph is a polygon with a diagonal constraint, or more general, a partial two-tree. We show that (with an appropriate definition) the oriented area is a Bott–Morse function on the configuration space of the linkage. Its critical points are described and Bott–Morse indices are computed. This paper is a generalization of analogous results for polygonal linkages (obtained earlier by G. Khimshiashvili, G. Panina, and A. Zhukova).

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KW - Partial two-tree

KW - Pitchfork bifurcation

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On the area of constrained polygonal linkages

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Keywords

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