The invention relates to a lathe comprising a moving headstock (2) arranged for rotating and moving forward, relative to an axis (14) of translation and rotation, a workpiece (8) to be turned, and a guide bush (9) arranged to be attached to a frame (1) of the lathe and comprising a bush spindle (13) and a gripper or a clamping mechanism (5). The guide bush (9) is arranged to operate either in bush mode or in gripper mode and to be axially movable relative to the frame along the axis (14) of translation and rotation. The lathe (9) is arranged to operate in: - a first mode in which the guide bush is driven axially by the moving headstock; and - a second mode in which the axial position of the guide bush is fixed relative to the frame.