A new robot hand dynamics model with rolling constraints and with a saddle joint at one finger is proposed, where two saddle-joint actuations are considered to be orderless. Spinning motion around the opposition axis connecting two center points of each finger-tip contact area with an object is faithfully treated, and a viscosity model for damping rotational motion of the object is proposed. A class of control signals without referring to object kinematics or using external sensing is proposed. Finally, numerical simulation results show the stability of motion of the overall closed-loop dynamics supplied with the proposed control input.