Contact space analysis for narrow-clearance assemblies

A technique is described for modeling the six-dimensional contact space of an assembly with narrow insertion clearances. A nominal assembly mating trajectory is supplied a priori by a high-level planner, using assembly part models with zero clearance at the sites of insertion. Augmented with small, user-specified clearances, the local contact space surrounding any "problematic" configuration in the nominal trajectory is analyzed and represented as an adjacency graph of contact states. The contact states represent the zero- to five-dimensional facets of contact space. The vertices of a local contact space are calculated by intersecting six-tuples of primitive contact surfaces via the multivariable Newton method, whose rapid convergence to vertex configurations provides an efficient means of analyzing local contact space topologies. >