Robotic hands grasp and manipulate objects through the contact forces between the fingers and the objects. The determination of contact forces in grasping is discussed in this paper. To systematically investigate the characteristics of different grasps, the vector space of contact forces is decomposed into four subspaces and their basis is found by an efficient computational method. The vector of contact forces is then formulated into four components: active and passive grasping forces, controllable and uncontrollable internal forces. The dimensions of the subspaces identify uncontrollable internal forces. The contact force is further expressed into an explicit function of the external wrench and the joint torques. The resulting formulation simplifies the computation in the optimization of contact forces and makes the optimal variables controllable. Two numerical cases are given to show the simplicity and validity of the method.
