Contact Space Analysis for Narrow - Clearance Assemblies 1

A technique is described for modelling the 6{dimensional contact space of an assembly with narrow insertion clearances. A nominal assembly mating trajec-tory 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-speciied clearances, the local contact space surrounding any \problematic" connguration in the nominal trajectory is analyzed and represented as an adjacency graph of contact states. The contact states represent the zero-to ve-dimensional facets of contact space. The facets' nonlinear surface representations permit a more exact characterization of contact space topology than described previously 7]. The vertices of a local contact space are calculated by intersecting 6{tuples of primitive contact surfaces via the multivariable Newton method, whose rapid convergence to vertex conngurations provides an eecient means of analyzing local contact space topologies. Subtuples of the vertices' primitive contacts give rise to the adjacent, higher-dimensional facets of contact space, forming an adjacency graph of contact states. As described in a companion paper 6], a heuristic search of the adjacency graph yields a traversable sequence of contact states. Figure 1. The critical points in a nominal trajectory.