A Sequential Constraint Solver to Simulate Assembling Operations for Tolerance Analysis

In the variational modeling of assemblies it is important to define the location of a part both in absolute terms and with respect to the position/orientation of other assembled parts. The present paper proposes a programming optimization approach to solve this problem. The algorithm, by using the heuristic Nelder-Mead technique - combined with a penalty function - simulates and solves sequential assembly strategies to find the optimal geometric configuration of a rigid part with variational features satisfying all the assembly constraints in the given sequence. The algorithm best aligns mating features avoiding, at the same time, feature-to-feature interferences, and automatically calculating the amount of movement the part being assembled must obey to satisfy assembly constraints, at that state of the assembly process. Thus, different assembly sequences can be simulated also including variational features.