An auxiliary shaft (16) mounted coaxially with a main shaft (5) has at the top an eccentric (17) operatively connected via grooving (20, 21) to a tool-fastening plate (13). At the bottom of the auxiliary shaft is a wheel (19) fixed to the eccentric and provided with a recess (18). The recess can engage a fixed lug cam so that a feed motor can cause both the rotary movement of the ball turner and a tool correction effected by a relative rotary movement between the main shaft and the auxiliary shaft. For the sake of accuracy, the angular displacement is limited to an area in which the displacement of the tool-fastening plate caused by the eccentric is substantially linear with the angular displacement. All rotary motions are measured during the operation by a shaft encoder (9) and communicated to a CNC system.