Complementarity Relationships and Critical Configurations in Rigid-Body Collisions of Planar Kinematic Chains With Smooth External Contacts

Abstract

In this article, we consider a special class of collision problems that are frequently encountered in the field of robotics. Such problems can be described as a kinematic chain with one of its ends striking an external surface, while the remaining ends resting on other surfaces. This type of problem involves complementarity relationships between the normal velocities and impulses at the contacting ends. We present a solution method that takes into account the complementarity conditions at the contacting ends. In addition, we study the critical configurations of particle and rigid-body chains where the impulse wave generated by impact gets blocked before it reaches a contacting end.