Dynamic Modeling of the 6-UPRU Stewart Platform and Analysis of the Passive Screw Effect

The passive screw effect of the UPRU limbs can materially affect the predicted driving forces of a 6-UPRU Stewart platform. To address this issue, this paper presents dynamic modeling and analysis that account for the passive screw influence. Based on the Newton–Euler formulation and with full consideration of the axial-moment transmission of the screw pair and the moment-transmission characteristics of the Hooke joints, a complete dynamic model is established, and analytical expressions for the limb constraint forces and the joint driving forces are derived. The consistency of the model is assessed by comparing numerical calculations in Python 3.13 with Adams 2024 simulations, and the influence of the passive screw on the system dynamics is quantified. The results show that the theoretical and simulated driving forces exhibit close agreement, indicating good consistency between the two implementations. When the passive screw is omitted, the discrepancy between the theoretical and simulated driving forces increases substantially, demonstrating the significant influence of the passive screw on the dynamic analysis. These comparisons suggest that the passive screw effect should be retained when accurate modeling of the dynamic characteristics of the 6-UPRU Stewart platform is required, particularly under dynamic excitation. The formulation can therefore serve as a basis for evaluating dynamic-compensation and force-control strategies for the 6-UPRU Stewart platform.