Computational representation for rigid and articulated assembly

With the increasing level of automation in assembly planning and assembly execution, it becomes more obvious that there is a gap between the output of a mechanical designer and an assembly planner. The question is: How to describe a designed assembly to an assembly planning system? The input to almost all the current reported automatic assembly planning systems is one-static-state of the final assembly configuration regardless the assembly is meant to be rigid or articulated. The inability to represent the assembly design completely, accurately and computationally has hindered the power of an assembly planner in dealing with articulated assemblies as simple as taking something out of a drawer. In this paper we identify a computational representation (specification) of an assembly. The basic idea of this representation is to use each oriented surface on a solid as a descriptive primitive and the symmetry group of the surface as a computational primitive. The relative motions (degree of freedom) under various contacts between a part or a subassembly and the rest of the assembly can be efficiently determined by computing these basic symmetry groups in a proved correct manner. The results reported in this paper lay out a more realistic and precise group theoretic framework than our previous work, and provide a concise, complete and computational representation for rigid and articulated assembly.