Identification of Non-Transversal Bifurcations of Linkages
For researchers studying singularities and mobility of linkages, this work provides a method to distinguish non-transversal motion branches, a previously unaddressed problem.
This paper addresses the identification of non-transversal bifurcations in linkages, where motion branches do not intersect transversally. It shows that the kinematic tangent cone contains all necessary information to separate branches and derives a computational method by amending existing algorithms.
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.