Identification of Non-Transversal Bifurcations of Linkages

TL;DR

This paper presents a computational method to identify non-transversal bifurcations in linkages by analyzing the kinematic tangent cone, enhancing the understanding of linkage mobility and singularities.

Contribution

It introduces a new approach to distinguish non-transversal motion branches using the kinematic tangent cone, extending previous local analysis techniques.

Findings

The method effectively separates different motion branches.

It improves the analysis of linkage singularities.

The approach is computationally feasible with amended algorithms.

Abstract

The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that point and the tangents to smooth motion curves. It does, however, not immediately allow to distinguish between motion branches that do not intersect transversally (which is a rather uncommon situation that has only recently been discussed in the literature). The mathematical framework for such a local analysis is the kinematic tangent cone. It is shown in this paper that the constructive definition of the kinematic tangent cone already involves all information necessary to separate different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.