A robot machining with a flexible manipulator has an end effector which may either hold the tool to perform the machining or the work piece to be machined. A signal representative of a force applied by said tool to said work piece is used to control either the relative motion between the tool and the work piece to give a controlled material removal rate (CMRR) or the relative position between the tool or the work piece to provide deformation compensation or both CMRR and deformation compensation. A force sensor provides the signal for deformation compensation. For CMRR the signal may be obtained from either a force sensor or the current flowing in the motor of the robot's spindle. The force sensor can be mounted either on the robot or together with either the tool or work piece adjacent to the robot.