The new principle of flow self-regulation is applied to hydrostatic screws and nuts. These self-regulating hydrostatic screws and nuts permit a continuous and automatic distribution of the total flow in two half flows in the two recesses merely due to the special shape of the double thread. Formulas are presented and compared with those of ordinary hydrostatic screws and nuts supplied by two pumps. The comparison shows that the self-regulating screws and nuts have a stiffness equal to that of ordinary ones supplied by two pumps, and also that they have pumping and friction dissipated power and therefore a total dissipated power generally equal to those of ordinary ones supplied by two pumps. Their global efficiency is comparable to that of ordinary hydrostatic screws and nuts supplied by two pumps and is consequently better than that of the ordinary ones supplied by only one pump but through two flow regulators. A calculation example is presented, of a self-regulating hydrostatic lead-screw and nut, dissipating minimum pumping power. Finally a prototype of a screw and nut of this kind is shown.

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