Abstract: The frame of the whirling head comprises the rigid casing (7), in which the part (10) contains the drive pulley (15) solidly attached to the coupling member (17) connected to the drive shaft of the spindle (26). By means of the belt (19), this pulley (15) drives the pulley (8) solidly attached to the connecting cone (4), which in turn comprises the internal milling cutter (1) which cuts the thread of the screw shaft (27) supported between the bar advance unit (28) and the tailstock centre (29). The latter is mounted as an exchangeable tool on the return unit (32).