This paper is concerned with the dynamics and control of grasping and regulating motion generated by a thumb index finger robot. Thumb index finger model is the optimized model to manipulate an object without joint redundancy. To manipulate an object, the overall motion of the finger needs to be restricted by the object states. Therefore, we derive the kinematics of model governed by the object states by using four constraints which are based on the nonslipping assumption between the rigid fingertips and the surface of an object. Then, the control input is derived via Lyapunov stability analysis including the dynamics of the overall system. Further, we propose a solution of the contact forces between the fingertips and an object via physical analysis, which can not be solved mathematically. Finally, computer simulations are presented to verify the effectiveness of the proposed concept and method.