The mechanism includes a threaded shaft extending along a longitudinal axis; a nut arranged coaxially with the threaded shaft; a plurality of rolling bearings interposed between the threaded shaft and the nut, each of the bearings comprising an outer race fixed to the nut, an inner race which is arranged coaxially with the outer race and is rotatable relative to the outer race about an axis of rotation, and a plurality of rolling members interposed between the outer race and the inner race; and a corresponding plurality of rings, each of which is fixed to the inner race of a respective bearing so as to rotate therewith about the same axis of rotation, and is interposed between the inner race of the bearing and the threaded shaft in such a manner that an inner surface of the ring is in contact with a screw thread of the threaded shaft.