The spindle for fitting vehicle wheel rims on workshop machines, particularly tyre-changing machines or the like, comprises a frame associable in rotation around a work axis with a workshop machine, at least three gripping adapters of the rim of a wheel associable with the frame and moving along respective approach and away movement directions with respect to the work axis, at least a fluid-operated actuator cylinder associated with one of the gripping adapters and suitable for moving the adapter along the corresponding approach and away movement direction, at least three racks, each of which is associated with one gripping adapter and extends substantially parallel with the corresponding approach and away movement directions, and a pinion meshed with the racks.