Assembly modeling for design analysis

Current CAD systems provide an extensive capability to create detailed part geometry. Support for the specification of assembly information however, is typically limited to the provision of a simple set of geometric contact relations. The thesis of this work is that an assembly framework that incorporates both functional and geometric mating information is needed to model and to reason about the assembly for design analysis, and to establish relative part positions when the part geometry incorporates manufacturing variations.; The assembly mating information consists of contacts, attachments, alignments, enclosures, and assembly dimension relations. Algorithms are presented to automatically generate the geometric mating relations from the "in-place" geometry of the related parts, to reason about the effect of multiple relations on the degrees of freedom of the related parts, and to generate models of assembly information that minimize the computational complexity of design analysis algorithms.; The functional and geometric mating information can be applied to determine the overall configuration of the assembly both when the constituent part CAD geometry is perfect in shape and size, and also when it incorporates simulated manufacturing variations. An algorithm has been developed to determine the overall configuration of the assembly by using a combination of coarse and fine part positioning algorithms.; The coarse positioning algorithm processes a minimal set of assembly relations to establish coordinate systems on the related parts, using simple geometric operations such as offsets and intersections of planes and lines. Final part positions are simply found by matching the coordinate systems together. The coarse positioning algorithm is fast, and avoids the numerical problems associated with solving systems of equality constraints.; The fine positioning algorithm sets up a constrained optimization formulation with non-interference constraints defining the feasible region within which the related parts are positioned, and objective constraints representing the positioning requirements of the assembly relations. In determining the final assembly configuration, the positioning error introduced by the simulated variations is distributed over the relations in a sequence determined from their relative functional significance, and the constraints imposed by the assembly relations selected by the designer are respected to the maximum extent possible.