Relative positioning of toleranced polyhedral parts in an assembly

Parts with geometric (size and shape) variations generate uncertainties in every assembly configuration. The resultant uncertain assemblies are far more complicated than the nominal assembly configurations. To perform tolerance analysis, the real positions of variant parts in a variant assembly configuration need to be investigated. In this paper, a relative positioning scheme is proposed to determine the optimal configuration of variant parts in an assembly. A method of calculating and representing positions of 3D polyhedral parts in assembly has been presented. Translational and rotational constraints, which are developed corresponding to the extra degrees of freedom caused by the shape and size variation of parts, have been formulated. By computing translational and rotational constraints, the allowed motion space for each mating pair is obtained. Assembly configuration uncertainties caused by part variations are clarified by realizing the transformation of the object part according to the objective function. A 3D example is given to explain how the proposed relative positioning scheme is used in tolerance analysis of assemblies.