From characteristic invariants to stiffness matrices

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 will 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 will allow 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.