Relative positioning of assembled parts with small geometric deviations by using hierarchically approximated configuration space

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