Contact force pediction and force closure analysis of a fixtured rigid workpiece with friction

Analysis and characterization of workpiece-fixture contact forces are important in fixture design since they define the fixtures stability during clamping and strongly influence workpiece accuracy during manufacturing. This paper presents a method for predicting and analyzing the normal and frictional contact forces between workpiece-fixture contacts. The fixture and workpiece are considered to be rigid bodies, and the model solution is solved as a constrained quadratic optimization by applying the minimum norm principle. The model reveals some intricate properties of the passive contact forces, including the potential of a locator release and the history dependency during a sequence of clamping and/or external force loading. Further, a notion of passive force closure is considered to characterize the passive nature of the fixture forces. Geometric conditions for two types of passive force closure (concordant and discordant closures) are provided, showing a complication of released locator under clamping with a limited role in force closure. Model predictions are shown to be in good agreement with known results of an elastic-contact model prediction and experimental measurements. The passive force closure conditions are illustrated with examples. This presented method is conceptually simple and computationally efficient. It is particularly useful in the early stages of fixture design and process planning.