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 3D geometry and is restricted to be within a discrete domain of locations for placing the fixture elements of non-frictional contacts. The paper addresses two major issues: 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. An interchange algorithm with random initiation is developed. Also, the fixture performance characteristics are evaluated to understand their tradeoffs. The importance of the accurate localization and the contact force balance is discussed.