A kinematic model of the planetary roller screw mechanism (PRSM) is proposed, which accounts for the run-out errors of the screw, roller, nut, ring gear, and carrier, and the position errors of the nut and the pinhole in the carrier. The roller floating region, which contains all the possible positions of the roller inside the pinhole, is obtained by analyzing the axial clearances between mating thread surfaces and the radial clearance between the roller and carrier. The proposed model is based on the constraint that the set of roller floating region is not empty. Then, the additional rigid-body movement on the nut is derived and the path of motion transfer from the screw to the nut is obtained. According to the fundamental property of rigid-body kinematics, the axial velocity of the nut is derived and the transmission error of the PRSM is calculated. The proposed model is verified by comparing the calculated transmission error with experimental one. The results show that the transmission error of the PRSM with run-out and position errors is cyclic with a period corresponding to the rotation period of the screw and the magnitude of the transmission error can be much larger than the lead error of the screw. Besides, due to the run-out and position errors, the roller can move radially or transversally inside the pinhole of the carrier when the elements in the PRSM are regarded as rigid bodies.

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