Abstract: The machine tool includes a workpiece-holding spindle consisting of a slide capable of being moved along the X-axis perpendicular to the main axis of rotation of the machine. The slide is moved via a tie-rod, actuated at one end by a numerical axis and having at the other end an oblique projection fitted in an oblique hole in the slide. Movement of the tie-rod along the Z-axis therefore causes movement of the slide, hence of the workpiece, along the X-axis. Provision is made for counterbalancing the rotating spindle. The machine tool is thus capable of machining parts having eccentric shoulders.