This paper presents a geometrical representation of robot grasping and a definition of “relative form closure” of point contact restraint based on the concepts of positive linear combination,affine combination,convex combination,etc.in the screw space.The dual equivalence theorem,topological equivalence theorem and algebraic equivalence theorem are derived from the defined restraint cone and freedom cone in the dual screw spaces.A J0-function method of computer-aided grasp planning is implemented more efficiently than other proposed methods.The states of restraint and instantaneous motion of a rigid body grasped by a set of point contacts are specified by the unisense degrees of freedom and unisense degrees of restraint.Finally,a quality measure of robot grasping is provided for the synthesis procedure of relatively form-closed grasp. This paper presents a geometrical representation of robot grasping and a definition of “relative form closure ” of point contact restraint based on the concepts of positive linear combination, affine combination, convex combination, etc. in the screw space. The dual equivalence theorem , topological equivalence theorem and algebraic equivalence theorem are derived from the defined restraint cone and freedom cone in the dual screw spaces.A J0 -function method of computer-aided grasp planning is implemented more efficiently than other proposed methods.The states of restraint and instantaneous motion of a rigid body grasped by a set of point contacts are specified by the unisense degrees of freedom and unisense degrees of restraint. Finally, a quality measure of robot grasping is provided for the synthesis procedure of relatively form-closed grasp.