A computational geometry approach to optimum clamping synthesis of machining fixtures

Automatic fixturing configuration is an important task to be addressed in m anufacturing. An optimum clamping planning approach for arbitrarily shaped workpieces based on computational geometry of contacting wrenches is develo ped. A clamping analysis algorithm drawing on the metric of force closure i s presented, in which all feasible clamping points are automatically found by examining whether the convex hull of bounding wrenches associated with c onstraining contacts contains the origin. Optimal clamping points are then chosen from the feasible clamping regions according to a proposed criterion based on the radius of the maximal inscribed hypersphere centred at the or igin within the convex hull. The clamping sequence is in turn decided by th e feasible clamping area where the clamps are situated. A clamping equilibr ium criterion is also proposed so that robust clamping layout can be genera ted. Case studies are included to demonstrate the effectiveness and capabil ities of the developed methodology.