On the prediction of passive contact forces of workpiece-fixture systems

Abstract

The 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 passive contact forces. Firstly, 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 multifinger grasp. Then, a locally elastic contact model is used to describe the non-linear 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 is given so that the relationship can be developed between the elastic deformations at all contacts and the displacement of the workpiece. Finally, combining the force equilibrium, the locally elastic contact model and the ‘compatibility’ conditions, the passive force computation problem is transformed into a determinate system of non-linear equations governing all of the elastic deformations at all of the passive contacts. By solving the resulting non-linear equations, all passive contact forces can be accurately predicted in the frictional workpiece-fixture 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.