The component to be machined (2) is fixed with its axis in a position exactly determined in relation to the machine base (1) and the seat (3), by means of the sides (8) and the rear face (9) of the vee arranged on the seat and by means of the intermediate organ (11) in the form of a sector of ring, the concave cylindrical facets (23) of which are adapted to the component (2). The component (2) is pressed against the facets (23) by the finger (14) operated by the stirrup (15). The component (2) can be driven in rotation by a floating spindle operated by a servomotor into a position determined in relation to the machine seat (1).
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