From Symmetry Groups to Stiffness Matrices

Abstract

A fitting relationship in an assembly implies that the relative location of the bodies belongs to a coset of the symmetry group of the mating feature pair. When a symmetry group is continuous, there are infinitesimal displacements which preserve the relationship. Assembly of two bodies normally involves the establishment of successively more constraining relations, many of which are fitting relations. The continuous topological structure of the associated group determines possible directions of assembly at any state in the assembly process. To accommodate to errors, it is necessary to choose a stiffness matrix appropriate to a given assembly state, which allows the robot to comply with wrenches normal to the possible assembly directions. The derivation of such matrices from a computational geometric representation of the mating feature symmetry group is considered