On the Qualitative Structure of a Mechanical Assembly

A mechanical assembly is usually described by the geometry of its parts and the spatial relations defining their positions. This model does not directly provide the information needed to reason about assembly and disassembly motions. We propose another representation, the non-directional blocking graph, which describes the qualitative internal structure of the assembly. This representation makes explicit how the parts prevent each other from being moved in every possible direction of motion. It derives from the observation that the infinite set of motion directions can be partitioned into a finite arrangement of subsets such that over each subset the interferences among the parts remain qualitatively the same. We describe how this structure can be efficiently computed from the geometric model of the assembly. The (dis)assembly motions considered include infinitesimal and extended translations in two and three dimensions, and infinitesimal rigid motions.