the numerical control machine for the machining of a workpiece (1) with a line gripper includes at least a pin tool holder and at least one mandrel is carried by a carriage track (21) mounted on the rails and movable in translation guidance along the chute in a motor, characterized in that the mandrel is room includes:a shaft part (200), the front of which is equipped with a blind hole (201) is provided to receive the tail for gripping the workpiece.a sheath (210) engaged in translation on the front part of the shaft part (200).a ablocage mechanism disposed in the front part of the mandrel, which is able to be ablocage mechanism) in the bore in one eye (201) on the tail) to ensure the setting of the play to the mandrel.the mechanism of ablocage being actuated in the direction of the clamping and release of the translation frame (210) and a shaft part (200) in relation to one another.