Closed-Loop Dynamic Modeling of Clearance Friction Flexibility Coupling in a 6-UPS Stewart Platform

Joint clearance, friction, and strut flexibility interact in 6-UPS Stewart platforms, particularly during low-speed reversals, small-amplitude motions, and contact-state transitions. Treating these effects independently can omit feedback among contact geometry, normal load, friction, and strut deformation. This study develops a geometrically consistent three-dimensional closed-loop dynamic model using actual spherical-joint geometry and an equivalent representation of universal joints along their primary load-bearing directions. Normal, tangential, and axial Jacobian matrices are derived, and a nonnegative hysteretic contact model, a vector LuGre friction model under time-varying normal loads, and configuration-dependent strut flexibility are integrated. Numerical simulations were used to evaluate the proposed model through time-step convergence analysis and energy-balance assessment, as well as comparisons with models that omit some of the physical coupling effects. For the simulated intermittent-contact case, the full closed-loop model yields a root-mean-square normalized energy-balance residual of 0.0976%. Compared with the simple additive model, it predicts 326.04% greater maximum strut deformation and 32.33% greater peak normal contact force, but a 53.95% lower peak friction-force magnitude; the global position and orientation tracking errors remain comparable. The results show that comparable global tracking errors can coexist with substantial differences in local dynamic responses. This highlights the importance of closed-loop coupling in predicting local load transfer and maintaining energy-balance consistency. The proposed model provides a theoretical basis for dynamic analysis and parameter optimization of parallel mechanisms with joint clearances.