Automatic selection of fixturing surfaces and fixturing points for polyhedral workpieces

Fixtures play an important role in many manufacturing operations such as inspection, machining, and part fabrication. In the development of a fixture, it is desired that the feasible fixturing surfaces and optimal fixturing points on the workpiece be selected automatically. An algorithm is presented to automate the generation of optimal fixturing points, which totally restrains the workpiece in the fixture, i.e., satisfies the form-closure condition, as well as minimizes the workpiece positional errors. First, a heuristics is proposed for searching a set of fixturing surfaces capable of providing form-closure. Then, we formulate the problem of determining optimal fixturing points on the eligible set of fixturing surfaces as a quadratic programming problem with the workpiece positioning accuracy as the performance index and the robust form-closure requirement as the linear constraints. Finally, the implementation for three numerical examples demonstrates the usefulness and efficiency of the proposed algorithm.