Based on the differential principle of thread transmission, an analytical model considering helical directions between screw and roller threads in planetary roller screw mechanism (PRSM) is presented in this work. The model is critical for the design of PRSM with a smaller lead and a bigger pitch to realize a higher transmission accuracy. The kinematic principle of planetary transmission is employed to analyze the PRSM with different screw thread and roller thread directions. In order to investigate the differences with different screw thread and roller thread directions, the numerical model is developed by using the software Adams to validate the analytical solutions calculated by the presented model. The results indicate, when the helical direction of screw thread is identical with the direction of roller thread, that the lead of PRSM is unaffected regardless of whether sliding between screw and rollers occurs or not. Only when the direction of screw thread is reverse to the direction of roller thread, the design of PRSM with a smaller lead can be realized under a bigger pitch. The presented models and numerical simulation method can be used to research the transmission accuracy of PRSM.
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