PURPOSE: To accurately index the rotational position of a body of rotation and positively fix it on its position in a turret head rotabing the body of rotation, on which plural sets of spindles are radially arranged.

CONSTITUTION: A turret head device is provided with a body 3 of rotation, rotatably supporting plural sets of spindles 44 around a head rotation axis C, a rotary actuator 35 which drives to rotate the body 3 of rotation and which is numerically controlled to selectively stop each set of spindles 44 at the positions matched with the working positions, and clutches which are arranged on the axes of the spindles 44 matched with the working positions, and which are rotatably supported around the axes and engaged with the spindles 44. Further, a driving shaft 2 to be driven to rotate, and restraint devices 38, 39 for fixing the body 3 of rotation to a set position of angle of rotation, are provided.