The roller screw mechanism (RSM) is a mechanical transmission device for converting rotary motion to linear motion, similar to a ball screw mechanism (BSM). The goal of this research was to develop the fundamental mechanics of the Planetary Roller Screw Mechanism (PRSM), which is the most common type of RSM. Much of the analysis can also be applied to the Recirculating Roller Screw Mechanism (RRSM), which is the other main type of RSM. As such, this work will allow for improved understanding of the mechanism and ultimately allow for mechanisms that are cheaper to manufacture and have improved efficiency and durability.;The kinematics of the PRSM with an emphasis on the effects of a pitch mismatch between the spur/ring gear pair and nut/roller helical threaded interface are derived. It is shown that this mismatch leads to the axial migration of the rollers relative to the nut, which can damage the mechanism. Expressions are derived for the axial migration of the rollers and it is shown that it does not affect the lead of the overall mechanism. Then the contact geometry of the PRSM is developed, including the in-plane angle to the contact points, the radii of contact on the various bodies, the exact principal radii of curvature at the contact points, and the angles between the principal axes of the contacting bodies.;A stiffness model for the PRSM is developed which also gives the distribution of load across the threads. Last, the dynamics of the PRSM are developed, including an effective inertia of the mechanism, the constraint force on the spur/ring gear pair, the steady-state angular velocities, the screw/roller slip velocity, and efficiency of the mechanism. Several examples are developed throughout showing how the theory can be used to design mechanisms that are stiffer, have longer life, and are more efficient.
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