Optimizing fixture layout in a point-set domain

This paper describes an approach to optimal design of a fixture layout with the minimum required number of elements, i.e., six locators and a clamp. The approach applies to parts with arbitrary 3-D geometry and is restricted to be within a discrete domain of locations for placing the fixture elements of nonfrictional contacts. The paper addresses two major issues in the fixture layout design: 1) to develop an efficient algorithm for fixture synthesis in the point set domain and 2) to evaluate the acceptable fixture designs based on several performance criteria and to select the optimal fixture according to practical requirements. The performance objectives considered include the workpiece localization accuracy, and the norm and dispersion of the locator contact forces, respectively, for high precision in workpiece localization and force balance among the fixture contacts. Based on a concept of optimum experiment design, an interchange algorithm with random initiation is developed for the purpose. A study of the interrelationship between locators and clamps leads to two different design strategies. Furthermore, the fixture performance characteristics are evaluated to understand their tradeoffs. Conclusions on the importance of the accurate localization and the contact force balance are made based on empirical observations in the study of several examples.