An optimum design for 3-D fixture synthesis in a point set domain

This article addresses the problem of fixture synthesis for 3-D workpieces with a set of discrete locations on the workpiece surface as a point set of candidates for locator and clamp placement. A sequential optimization approach is presented in order to reduce the complexity associated with an exhaustive search. The approach is based on a concept of optimum experimental design, while the optimization focuses on the fixture performance of workpiece localization accuracy. In using the D-optimality criterion to minimize the workpiece positioning errors, two different greedy algorithms are developed for force-closure fixturing in the point set domain. Both 2-D and 3-D examples are presented to illustrate the effectiveness of the synthesis approach.