Identification of Non-Transversal Motion Bifurcations of Linkages

Abstract

The local analysis is an established approach to the study of singularities and mobility of linkages. The 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 distinguish different motion branches. A computational method is derived by amending the algorithmic framework reported in previous publications.