On the Existence of Solutions in Modular Fixturing

Abstract

A fixture is a device that locates and holds parts during ma chining or assembly. A modular fixture employs reusable components on a regular lattice. Given a part, machinists combine intuition with trial and error to design an appropriate fixture. When a machinist is unable to find a design, it may be that (1) a feasible design was overlooked or (2) no feasible design exists. Complete algorithms for modular fixturing, such as those in Brost and Goldberg (1994), ensure that no fixture design is overlooked. But the question remains: are there Parts for which no modular fixture exists?

For the class of modular fixtures using three locators and a clamp, we show that there exists a class of polygonal parts that cannot be fixtured. We believe that this is the first negative re sult in the area of fixturing. We also show two positive results, namely, that a modular fixture always exists when we broaden the class of fixtures to include a T-slot and narrow the class of parts. We show that one class of fixtures strictly dominates the other. These results raise a number of open problems concern ing the existence of solutions for other classes of fixtures and parts and suggest a hierarchy of fixturing models.

1. Nguyen used the term "force-torque closure" to describe what is more commonly called form closure (Trinkle 1992).

2. Nguyen used the term independent regions of contact.