Abstract: A roller screw mechanism is provided comprising a screw with an outer thread, and a nut disposed around and coaxially with the screw and comprising an inner thread; and with rollers that each have an outer thread and inserted between the screw and the nut, each roller having two ends each provided with an outer gear teeth, each outer gear teeth having, in cross-section, an outer diameter less than or equal to a root diameter of the outer thread of the rollers; and two synchronizing gear teeth disposed coaxially to the screw and in which the outer gear teeth of the rollers engage, wherein the outer gear teeth of the rollers have teeth with a flank having, in cross-section, a convex hypotrochoidal profile and the synchronizing gear teeth have teeth with a flank having, in cross-section, a hypotrochoidal or epitrochoidal profile.