Homology of planar telescopic linkages

TL;DR

This paper analyzes the topology of configuration spaces of planar telescopic linkages with variable-length legs, providing explicit Betti number calculations using Morse theory, relevant for robotics applications.

Contribution

It introduces a Morse theoretic method to explicitly compute Betti numbers of configuration spaces for telescopic linkages, a novel approach in this context.

Findings

Explicit Betti number formulas derived

Topological insights into telescopic linkage configurations

Applicable to robotics design and analysis

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.