A spindle for fastening rims of vehicle wheels on repair shop machines, which comprises a frame (2) that can be associated rotationally about a working axis (A) with a repair shop machine (M), six or more movable arms (3) that are associated with the frame (2), are distributed around the working axis (A) and can rotate about respective rotation axes (R) that lie on a plane that is substantially perpendicular to the working axis (A), and claws (5) for gripping the rim of a vehicle wheel, which are associated with the arms (3) and on which it is possible to fit the internal cylindrical portion of the rim.
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