also within the framework of the present invention for assemblying the handpiece the bushing 30 is first clamped into the grip portion 10 the collar 31 is thus engaged in the corresponding socket of a sleeve like grip portion 10 and prevents axial dislocation of the bushing subsequently the sleeve 18 is inserted into the handpiece portion 10 with the projection 27 engaged in the longitudinal slot 32 of the guide bushing 30 by means of the threaded ring 28 which is rotatably mounted on the sleeve 18 the sleeve 18 is axially fixed within the handpiece portion 10 as the threads of the ring 28 are received in the internal threads 39 the sleeve 14 as already mentioned is connected in a twist proof but axially releasable manner on the drive part 1 by means of the ball catch device 15 the handpiece grip or sleeve portion 10 with the guide bushing 30 supported therein and the sleeve 18 with the cooling agent lines 25 and 25a can now be axially slipped onto the sleeve 14 until the spring washer 16 is received by the groove 17 and the two handpiece parts are then axially fixed or connected together the head part 9 in addition to including the spring like sleeve 38 has a tubular shank or neck part 41 with a portion of the fitting strip 33 extending from one side thereof when the head part 9.