This paper investigates the nature of the contact between the load transferring surfaces in the roller screw mechanism, i.e., between the screw and roller threads and between the nut and roller threads. The analysis is applied to both planetary roller screws and recirculating roller screws. Prior work has neglected to take a fundamental approach toward understanding the kinematics of the contact between these components and, as a consequence, detailed analyses of aspects such as contact mechanics, friction, lubrication, and wear are not correctly carried out. Accordingly, in this paper, the principle of conjugate surfaces is used to establish contact at the screw/roller and nut/roller interfaces. The in-plane angles to the contact points are derived and it is shown that for the screw/roller interface, the contact point cannot lie on the bodies' line of centers, as has been the assumption in previous papers. Then, based on the curved profile of the roller thread, the radii of contact on the roller, screw, and nut bodies are also derived. Knowledge of the contact point locations is necessary in order to understand the interaction forces between the key components of the roller screw mechanism. The principal radii of curvature at the contact points and the angle between the principal axes are also derived. Lastly, a brief example is developed showing how the developed theory may be used to design a roller screw for improved stiffness and decreased contact stresses.

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