On the existence of modular fixtures

Modular fixtures are gaining wide use for flexible manufacturing and job shop machining. A modular fixture is an arrangement of fixture elements (fixels) that will locate and securely hold a given part. Typically, a human combines intuition with trial-and-error to design fixtures. In some cases designers are unable to design a fixture with given fixels and must resort to custom tooling. It is possible that human designers have overlooked a solution. It is also possible that no solution exists. In this paper the authors explore the existential question: given a fixture model and a part, does a fixture exist that will hold this part in form closure? If so, the authors say that the part is fixturable. The authors consider two classes of fixtures, one using 3 locators and a clamp, the other using 4 clamps. The authors provide one negative result-a class of cross-sections that is not fixturable-and two positive results-two classes of cross-sections that are guaranteed to be fixturable. These results give insight into the application range for different models of modular fixtures