Optimal fixture layout design for 3-d workpieces

Fixtures are tools to locate and securely hold workpieces for manufacturing operations such as inspection and machining. This paper presents a simple and complete algorithm for automatic and optimal fixture design on 3-D workpieces represented by discrete points. A new performance index is proposed to simultaneously address three fundamental requirements: form-closure constraint, minimum locating errors of the workpiece, and even load distribution among the fixturing points. To find the optimal future, the algorithm combines a local optimization procedure with a recursive problem decomposition strategv. The local optimization procedure searches for a solution in the direction of minimizing the performance index. When the performance index reaches a local minimum, the algorithm decomposes the discrete point set into subsets, and then carries out new rounds of local search in the subsets. The algorithm ends when a locally optimal solution is obtained. Compared to the exhaustive search, this algorithm is more efficient; and compared to other heuristic methods, the proposed algorithm is complete. The efficiency of this algorithm is demonstrated by numerical examples.