Abstract: The device of the invention has a supporting body detachably fixed to a machine spindle, a head element detachably fixed to the supporting body, and at least one slide which can be moved substantially at right angles to the axis of rotation of the head element and which carries a tool or tool carrier. The radial motion of the slide is produced by the action of an axially moving actuator rod and gear means. In addition, there is in the supporting body a coolant channel for hydraulic fluid. The inlet end of the channel is connected to an opening in the spindle and the outlet opens out in the head element. For the operation of the slide, the supporting body has two cylindrical bores disposed coaxial to the axis of rotation and a certain distance apart and in which two rigidly linked pistons are located which can be connected to the actuator rod.