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 language | English |
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Article number | 105424 |
Number of pages | 17 |
Journal | Journal of Geometry and Physics |
Volume | 210 |
DOIs | |
Publication status | Published - Apr 2025 |
Bibliographical note
Publisher Copyright:© 2025 The Author(s)
Keywords
- Critical points
- Hooke energy
- Morse-Bott theory
- Spider linkage
- Voronoi distance
- Work space