A motion planning problem of a cooperative multiple manipulator system carrying out grinding work or similar works to the object is considered. One manipulator holds the object rigidly and the other holds the tool and works on the object's surface. At the contact point between the object and the tool there exists friction, so that interaction forces must be taken into consideration in the dynamics of manipulators and the object. We only specify the tool task on the object's surface, so the object and manipulators can move arbitrary paths in the world coordinates frame. We propose an algorithm to generate joint trajectories for cooperative multiple manipulators to accomplish the specified task effectively.