A Fast Branch-and-Prune Algorithm for the Position Analysis of Spherical Mechanisms

Abstract

Different branch-and-prune schemes can be found in the literature for numerically solving the position analysis of spherical mechanisms. For the prune operation, they all rely on the propagation of motion intervals. They differ in the way the problem is algebraically formulated. This paper exploits the fact that spherical kinematic loop equations can be formulated as sets of 3 multi-affine polynomials. Multi-affinity has an important impact on how the propagation of motion intervals can be performed because a multi-affine polynomial is uniquely determined by its values at the vertices of a closed hyperbox defined in its domain.