Abstract: An apparatus equipped with a round cutter, a rotation drive mechanism for the cutter, a workpiece stand, a rotary servo-mechanism for rotating the workpiece stand, a rectilinear servo-mechanism for letting the workpiece stand get near to or away from the cutter, an input device for enabling an input operation of at least a diameter or a radius of the cutter, a diameter or a radius of the workpiece, a length of a straight portion of an oriental flat of the workpiece and a radius of curvature of a circular-arc portion at its both sides, and a computer computing a distance between a rotation center of the workpiece and a locus generated by a rotation center of the cutter which revolves while making contact with and relatively to the orientation flat of the workpiece forming a machining standard, as a function in relation to a rotation angle of the workpiece, previously memorizing its operation program and electrically connected to the rotary sevo-mechanism, the rectilinear servo-mechanism and the input device.