<p>The exchangeable tool unit for installing on the spindle (12) of a machine tool has a pivoting mechanism which has a rotatable component (28) mounted to rotate around a rotational axis (30) which is parallel to the spindle axis (17) and connected to the tool holder (15) by a transmission (32), wherein the rotatable component is connectable to a machine part and is set in rotation around its rotational axis by means of a relative movement between a support component (20) for the tool holder and the machine part.</p>