Analysis of rigid body interactions for compliant motion tasks using the Grassmann-Cayley algebra

This paper studies the statics and the instantaneous kinematics of a rigid body constrained to keep an arbitrary number of surface-surface contacts with a rigid static environment during its motion. These properties are analyzed under the frictionless assumption by modelling each contact with a kinematic chain that instantaneously gives the same motion freedom as the contact itself and by studying the resulting parallel chain using the Grassmann-Cayley algebra. With this algebra twists and wrenches can be expressed by means of extensors and operated using the join and meet operators. Moreover, the duality inherent in this algebra is used to reflect the reciprocity condition between possible twists and admissible wrenches between partially constrained rigid bodies.