Squared distance function on the configuration space of a planar spider with applications to Hooke energy and Voronoi distance

Maciej Denkowski, Gaiane Panina, Dirk Siersma*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Spider mechanisms are the simplest examples of arachnoid mechanisms, they are one step more complicated than polygonal linkages. Their configuration spaces have been studied intensively, but are yet not completely understood. In the paper we study them using the Morse theory of the squared distance function from the “body” of the spider to some fixed point in the plane. Generically, it is a Morse-Bott function. We list its critical manifolds, describe them as products of polygon spaces, and derive a formula for their Morse-Bott indices. We apply the obtained results to Hooke energy and Voronoi distance.

Original languageEnglish
Article number105424
Number of pages17
JournalJournal of Geometry and Physics
Volume210
DOIs
Publication statusPublished - Apr 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s)

Keywords

  • Critical points
  • Hooke energy
  • Morse-Bott theory
  • Spider linkage
  • Voronoi distance
  • Work space

Fingerprint

Dive into the research topics of 'Squared distance function on the configuration space of a planar spider with applications to Hooke energy and Voronoi distance'. Together they form a unique fingerprint.

Cite this