On the basis of a analysis of the interaction between a manipulator for grinding process and a working object in the task space, motions of the constrained dynamics of the robot is modeled first in this paper. In the model, the constrained forces are expressed as an algebraic function of the state and input generalized forces by using the equation of constraints. Using this result, a new sensorless force control law is proposed by taking the advantage of the redundancy of input generalized forces to the constrained forces. A controller for a grinding robot is then constructed according to this control law and without involving any force sensors. Grinding experiments have been done for evaluating the feasibility of the controller by taking an articulated planar two-link manipulator as an example. Results show that the constrained force is explicitly controlled by proposed control law. The effectiveness of the controller for real grinding task has been verified.