Stability of assemblies

High level assembly plans prescribe the sequence in which parts come together along with their motions. At each stage of assembly, the stability of subassemblies is an important concern. The authors address the problem of the gravitational stability of assemblies of frictionless rigid bodies. Solution methods to the problems of determining if an assembly is stable, and finding a stable orientation for a given for a given assembly are proposed. The solution methods for the two problems compute constrained motions of individual parts that decrease the gravitational potential energy, in order to determine the stability and search for stable orientations. Linear programming is used to obtain numerical solutions. The problem of finding a stable orientation is formulated as a maximin problem. The solution to this problem is the first general method for automatically determining stable orientations. The program to solve the two problems takes as input a geometric model of the assembly and information related to grounding constraints. Preliminary results are presented.