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 err or to design an appropriate fixture. When a machinist is unable to fin d 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 de sign is overlooked. But the question remains: are there parts for whic h no modular fixture exists? For the class of modular fixtures using t hree locators and a clamp, we show that there exists a class of polygo nal parts that cannot be fixtured. We believe that this is the first n egative result in the area of fixturing. We also show two positive res ults, 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. W e show that one class of fixtures strictly dominates the other These r esults Mise a number of open problems concerning the existence of solu tions for other classes of fixtures and parts and suggest a hierarchy of fixturing models.