Generic singular configurations of linkages

TL;DR

This paper investigates the singularities in the configuration space of mechanical linkages, providing a criterion to identify generic singularities with a mechanical interpretation and examples.

Contribution

It introduces an inductive sufficient condition to determine when a configuration of a linkage is singular, applicable to generic cases and specific mechanisms.

Findings

The criterion accurately identifies all singularities in the example mechanism.

Provides a mechanical interpretation of the topological singularities.

Establishes a method to analyze singularities in high-dimensional Euclidean spaces.

Abstract

We study the topological and differentiable singularities of the configuration space C(\Gamma) of a mechanical linkage \Gamma in d-dimensional Euclidean space, defining an inductive sufficient condition to determine when a configuration is singular. We show that this condition holds for generic singularities, provide a mechanical interpretation, and give an example of a type of mechanism for which this criterion identifies all singularities.