Relative positioning of variational part models for design analysis

Abstract A collection of functionally oriented assembly relations serves as an implicit representation for part positions in an assembly. The actual determination of part positions from the assembly relations has been extensively researched for assemblies in which parts are at their nominal shapes and sizes. However, design-analysis algorithms such as those used in tolerance analysis require the determination of the final assembly configuration, where the individual part geometries incorporate simulated manufacturing variations. The paper describes a constrained-optimization technique for the determination of part positions in assemblies of nonideal parts. Because the manufacturing variations are relatively small, the authors' technique linearizes the rotational elements in the constraint formulation. The constraint-optimization formulation seeks to satisfy the assembly relations to the maximum extent possible that is consistent with their relative functional significance. Noninterference constraints between the mating parts are enforced.