Based on the analysis of the interaction between a manipulator for grinding process and a working object in the task space, a model representing the constrained dynamics of the robot is first presented. In the model, the constrained forces are denoted as an algebraic function of states and input generalized forces by using the equation of constraints. Using the result, a new sensorless force control law is proposed based on the redundancy of the input generalized forces to the constrained ones. A controller for a grinding robot, including a estimation mechanism for changable constraints by grinding, is constructed according to the control law not to involve any force sensor. Simulations have been done for evaluating the feasibility of the controller by fitting respectively the constraint surface with linear function, quadratic function and spline curve. Simulated results indicate that the spline curve fitting is the closest to the real constraint surface.