On the Existence of Solutions in Modular Fixturing

A fixture is a device that locates and holds parts during machining 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 the case that (1) a feasible design was overlooked or (2) no feasible design exists. Complete algorithms for modular fixturing, such as [Brost and Goldberg 1994], insure 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 3 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 result 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 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 concerning the existence of solutions for other classes of fixtures and parts and suggest a hierarchy of fixturing models.