The numerical control machine for machining a workpiece (1) provided with a stem (4), comprises, at least one shaft carries - tool (14) and at least one mandrel door - part (20) carried by a carriage (21) mounted on slides (22), and movable in translation along the slides (22) by a motor assembly (25), characterized in that the mandrel has - part comprises: - a shaft carries - part (200) whose front part is provided with a blind bore (201) designed to receive the tail of the handle (4) of the part to be machined, - a sheath (210) engaged in translation on the front part of the shaft carries - part (200), - a mechanism for clamping disposed in the front part of the mandrel, which mechanism of clamping is able to act by clamping in the blind bore (201), on the shank of the handle (4) in order to ensure the fixing of the part (1) to the mandrel (20), said mechanism of clamping being actuated in the direction of tightening and loosening by translation of the sheath (210) and of the shaft carries - part (200) with respect to the other.
