International Journal of Robotics Research to appear On the Existence of Solutions in Modul.pdf

International Journal of Robotics Research: to appear On the Existence of Solutions in Modular Fixturing  Yan Zhuang Ken Goldberg Department of Computer Science Institute of Robotics and Intelligent Systems University of Southern California, Los Angeles, CA, USA August 21, 1995 Abstract 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. 1 Introduction A fixture is a device that lo