A multi-finger robot which can handle three dimensional objects of unknown weight and unknown surface conditions with the most suitable grasping force has been developed. The hand has three fingers. Each finger is composed of a torsional vibration system consisting of a damping roller, a vibration roller, a rotational support spring, and a rotational absorber spring. A small motor with an eccentric mass mounted on its shaft is placed in each vibration roller. Harmonic torque is generated in each vibration roller by rotating the eccentric mass, so that the vibration rollers and damping rollers are forced to vibrate. Through the initial grasping process, the object is handled by the vibration rollers with the most suitable grasping force. In this paper, the most suitable grasping force is derived through theoretical analysis.