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

In this paper, we study a rigid body system of one free body (e.g., workpiece) in contact with multiple fixed bodies (e.g., locators). The contacts are unilateral. The investigation is motivated for planning the task of insertion of a workpiece in a fixture. The key issue of the problem is to determine an applied force that can move the workpiece while maintaining all existing contacts with the locators. We first analyze the kinematics of the rigid body constrained by multiple unilateral contacts. The contact constraints are classified into two categories, the configuration constraints and kinematic constraints. We then find a sufficient condition for non-jamming among the multiple contacts in the constrained rigid-body dynamics. This condition is also a necessary condition when the number of contacts is no less than four. 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 quasistatic method.