Abstract: The caging grasps of 3D polyhedron and polyhedron-like objects with a three-finger gripper are studied. For the detection problem of grasp configuration, the high-dimensional cage is converted into several lower-dimensional cage sets, to reduce the computation cost. A detection method of the caging grasp configuration is proposed based on the constraint region formed by the gripper fingers in the configuration space. The caging grasp configurations detected by the proposed method can converge to a partial form-closure grasp configuration. Finally, the effectiveness of the proposed method is demonstrated by experiments on a Barrett hand.