Reasoning about geometric constraints for assembly sequence planning

An approach to geometric reasoning about the feasibility of translation motion of parts of assembly operations is demonstrated. The feasibility problem has been broken down hierarchically such that necessary conditions for less complex motions may be evaluated early, and the problem of planning arbitrarily complex part trajectories is not treated unless required for the specific design implementation. The determination of local motion feasibility using the polyhedral convex cone representation of contact constraints has been extended to the analysis of global transition feasibility using a polyhedral cone algebra. This representation has further been used for the formulation of the multistage translation problem where a simulated annealing optimization strategy and a reachability wave algorithm was used to efficiently search for feasible solutions