Homology of planar telescopic linkages

Farber, Michael; Fromm, Viktor

doi:10.2140/agt.2010.10.1063

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Homology of planar telescopic linkages

Michael Farber and Viktor Fromm

Algebraic & Geometric Topology 10 (2010) 1063–1087

DOI: 10.2140/agt.2010.10.1063

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

Volume 10, issue 2 (2010)