A new method for analyzing position uncertainties of two parts in an assembly is proposed if certain shape variations of individual parts are allowed by tolerances. Assembled parts are considered to satisfy three conditions relating to their positions, which are nonpenetration condition, contact condition of mating faces, and optimization condition concerning their assembling method. Proposed method achieves the analysis by computing a variation bound of the configuration of the toleranced parts if nonnominal parts allowed by tolerances satisfy the positioning conditions. An experimental program for computing a variation bound is implemented and demonstrated. This program is applicable to 2D polygon models of machine parts, for example sections of polyhedron parts in an assembly.

A new algorithm for positioning two nonnominal parts in an assembly is proposed. Part positions are determined by optimizing a certain objective function within the feasible configuration space in which the parts do not collide. This algorithm is applicable to 2D polygon models of machine parts, for example sections of polyhedron parts in an assembly. Since manufacturing variations in part geometries are relatively small in comparison with the nominal geometry, the requisite translations and rotations for positioning the parts are small. Based on this characteristic of the part positioning problem, "bounding polygon" and "bounded polygon" based algorithm is developed for hierarchically approximating the configuration space. The efficient search of the optimum solution of the objective function is realized by using the hierarchical structure of the space. The algorithm is implemented and examples are shown.