— This paper proposes a necessary and sufficient condition for parallel grasps. We extend the use of this condition to the task of regrasp planning. In particular, we propose a graph structure called a switching graph which contains information about primitive grasping operations such as finger switching and finger sliding. The problem of regrasp planning is transformed to a graph search problem. Mainly, this work concentrates on a parallel grasp with force closure. Assuming frictional point contacts, the proposed method has been implemented and some preliminary results are presented.