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 locations on the workpiece be selected automatically. An algorithm is presented to determine optimal fixturing locations which totally restrain the workpart in the fixture without being disturbed by any external force. First, based on observation that form-closure fixturing points exist on a set of surfaces if and only if the convex hull of the vertex contact wrenches resulting from the vertices of the surfaces contains the origin of R⁶, an efficient approach is developed for finding an eligible set of fixturing surfaces. Second, we formulate the problem of determining optimal fixturing points on the eligible set of fixturing surfaces as a quadratic programming (QP) problem with the workpiece positioning accuracy as the performance index and the robust form-closure requirement as the linear constraints. Finally, the implementation for two numerical examples demonstrates the usefulness and efficiency of the proposed algorithm