Linear drive mechanism of the screw and nut type with perfect rolling contact

Linear drive mechanism comprising a threaded shaft extending along a longitudinal axis and a nut arranged coaxially with the threaded shaft, the threaded shaft and the nut being shifted relative to each other along the longitudinal axis (z) as a result of relative rotation of the threaded shaft with respect to the nut about the longitudinal axis, wherein the mechanism further comprises

• 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,
• wherein the rings and the bearings are arranged in such a manner that their respective axes of rotation are both inclined by a first angle and positioned at a first distance with respect to the longitudinal axis of the threaded shaft, said first angle and said first distance being the same for all the rings, and
• wherein the shape of the screw thread of the threaded shaft and the shape of the inner surface of each ring are configured in such a manner that each ring is in perfect rolling contact with the threaded shaft along a respective contact line that is fixed relative to the nut and is both inclined by a second angle and positioned at a second distance with respect to the longitudinal axis of the threaded shaft,
• characterized in that said first angle, said first distance, said second angle and said second distance are linked by the following equations:
• tan=h/b
• tan=h/a,
• where h is the pitch of the screw thread measured in lead per radian.