Abstract: A two fingered hand with two under-actuated fingers can complete the task of grasping and pick-and-place of different objects by imitating people’s fingers. For general objects, the fingers with tendon-driven can be more like people’s to grasp and to pick and place by using just two fingers. The two-fingered hand’s grasping objects with frictional contracts using grasp matrix is modeled and the grasp matrix is expanded to the joints of fingers to build the expanded grasp matrix of every rank. By using grasp matrix of the contracts, the position condition is derived that the contracts must satisfy for a kind of planar objects and the magnitude of the contract forces is computed with different positions and orientations under the principle of minimum force. Using the planned contracts above, the inverse kinematics is done and the moment of two coupling joints of the under-actuated fingers is obtained from grasp matrix of the two coupling joints, to design the radius and inverse springs for tendon-driven. The moment obtained from the expanded grasp matrix proves that this method and normal method are equal which prove it is right and effective, and then the position and force of the tendon driven are computed.

Key words: expanded grasp matrix, grasp planning, tendon-driven, under-actuated finger