Volume 10, issue 2 (2010)

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Homology of planar telescopic linkages

Michael Farber and Viktor Fromm

Algebraic & Geometric Topology 10 (2010) 1063–1087
Abstract

We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse theoretic technique, we compute explicitly, in terms of the metric data, the Betti numbers of configuration spaces of these mechanisms.

Keywords
linkage, configuration space, telescopic linkage, Betti number, homology
Mathematical Subject Classification 2000
Primary: 55R80
Secondary: 70B15
References
Publication
Received: 16 March 2010
Revised: 8 April 2010
Accepted: 8 April 2010
Published: 2 May 2010
Authors
Michael Farber
Department of Mathematical Sciences
University of Durham
Durham
DH13LE
United Kingdom
http://maths.dur.ac.uk/~dma0mf/
Viktor Fromm
Department of Mathematical Sciences
University of Durham
Durham
DH13LE
United Kingdom