The use of symmetry groups in analysis of the kinematics aspects of assembly is described. The goal is to find how to assemble a product from a characterization of its final assembly configuration. From such an assembly configuration, a contact state lattice expressed in terms of the contacting faces of mating assembly components is generated. This contact state lattice contains all the partially ordered assembly motion sets (POAMS) that describe the intermediate contact states of an assembly component and the translational motions leading from one contact state to another. POAMS form a detailed task specification for a robot task-level planner and can be used for generating compliant control strategies. The work described forms part a kinematic assembly planning system that reasons about how parts with multiple contacting features fit together and generates assembly task specifications automatically from solid models using symmetry groups.