Mobility of Bodies in Contact - II: How Forces are Generated by Curvature Effects

This paper considers how forces are produced by compliance and surface curvature effects in systems where an object B is kinematically immobilized to second-order by finger bodies A1, . . . ,Ak. A class of configuration-space based elastic deformation models is introduced. Using these elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-order is also dynamically locally asymptotically stable with respect to perturbations. Moreover, it is shown that for preloaded grasps kinematic immobility implies that the stiffness matrix of the grasp is positive definite. The stability result provides physical justification for using secondorder effects for purposes of immobilization in practical applications. Simulations illustrate the concepts.