Prediction of passive forces in a frictional workpiece-fixture system is an important problem, since the contact forces have a strong influence on clamp design and on workpiece accuracy during machining. This paper presents a general method for the computation of the contact forces. First, based on the rigid-body kinematics, an indeterminate system of static equilibrium is defined, in which the passive, frictional contact forces cannot be determined arbitrarily as in an actively controlled robotic multi-finger grasp. Then, we define a locally elastic contact model to describe the nonlinear coupling between the contact forces and elastic deformations at the contact point. This model captures the essence of the passive contact. Further, a set of "compatibility" equations are given so that the elastic deformations among all passive contacts in the workpiece-fixture system result in a consistent set of rigid-body displacement of the workpiece in its global system. Finally, combining the locally elastic contact model and the "compatibility" conditions, we transform the force computation problem into a determinate system of nonlinear equations governing all of the elastic deformations at all of the passive contacts. By solving the resulting nonlinear equations with frictional constraints, we can accurately predict all contact forces in the frictional workpiece-fixtures system. This method is illustrated with example cases. The method presented here may also have an application to other passive, indeterminate problems such as power grasps in robotics.
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