Non-jamming conditions in multi-contact rigid-body dynamics

This paper addresses an issue related to a multi-rigid-body frictional contact application, the non-jamming condition for the applying force such that the workpiece can move while maintaining existing contacts. The issue arises from the study of fixture loading planning. While rigid-body frictional contacts could restrict workpiece motion in both normal and tangential directions, it is found that the reason for jamming is from the tangential constraints by frictional forces. We first enumerate all the possible contact states for multiple contacts, and the contact constraints are classified into two categories, the configuration constraints and kinematic constraints. We then find an interesting result related with a non-jamming condition. That is, in a general situation, the applying force that can induce all-sliding contacts will never result in jamming. Moreover, a method to find the applied force on the workpiece that results in sliding on all contact points is presented, based on the sufficient condition for non-jamming. Numerical examples are presented and the results of the method are compared with the results of a quasi-static method.