Positioning conditions of parts with tolerances in an assembly

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