Total restraint analysis is used to evaluate the ability of a machining fixture to restrain workpiece motion. Thus far models have been limited to point contact and frictionless planar contact. This paper shows how to apply restraint analysis to a fixture which relies on frictionless or frictional surface contact. It presents models of the wrench systems defined by frictionless and frictional planar, spherical, and cylindrical contact as well as hard point contact. These models are applicable to the restraint analysis of other work holding devices such as gripper and assembly fixtures. In addition, they are the basis for other types of fixture analysis. This paper also presents a linear program which uses static equilibrium constraints to directly prove the existence of total restraint. Both the models and the linear program are applied to the analysis of a modular fixture.

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