The Kinematics of Contact and Grasp

The kinematics of contact describe the motion of a point of contact over the surfaces of two contacting objects in response to a relative motion of these objects. Using concepts from differential geometry, I derive a set of equations, called the contact equations, that embody this relationship. I employ the contact equations to design the following applications to be executed by an end-effector with tactile sensing capability: ( 1) determining the curvature form of an unknown object at a point of contact; and (2) following the surface of an unknown object. The contact equations also serve as a basis for an investigation of the kinematics of grasp. I derive the relation ship between the relative motion of two fingers grasping an object and the motion of the points of contact over the object surface. Based on this analysis, we explore the following applications: (1) rolling a sphere between two arbitrarily shaped fingers ; (2) fine grip adjustment ( i.e., having two fingers that grasp an unknown object locally optimize their grip for maximum stability).