This paper firstly shows Lagrange's equation of a pair of robot fingers with hemishperical tips pinching a rigid object under four geometric constraints. In derivation of the equation, it is assumed that the rigid object has two parallel flat surfaces, motion of the overall system is confined to a horizontal plane and the effect of gravity is ignored. It is then shown that there exists a sensory feedback signal not only for secure pinching with the desired contact force but also for control the object orientation at a specified rotational angle. It is also shown that the method of computer simulation based on the non-linear differential equation with four geometric constraints is discussed together with presenting some computational results.