During recent years, variational models for tolerance analysis, both for rigid and compliant assemblies, have been implemented into CAT (Computer Aided Tolerancing) systems to verify the fulfillment of functional requirements, performing virtual product validation from a dimensional and geometric point of view. In this chapter, starting from a numerical methodology, proposed by the same authors, that allows us to simulate variational features, assembly constraints among parts are modeled and simulated. During assembly operations, an “object” part has to be moved to satisfy constraints of “target” parts. To do this, an assembly transformation matrix is calculated. By using geometric entities such as point, line and plane and their combinations, kinematic joints are modeled; then a numerical procedure is proposed to solve fully- and over-constrained assemblies. Therefore, the proposed model allows us to take into account different assembly sequences. The best fit alignment among mating features is performed using optimization algorithms. Finally, two case studies are described and analyzed.
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