Effect of passive rotation in UPU/UPRU branches on kinematics and calibration of Stewart platforms

• Established 6-6 UPRU-Stewart's precise kinematic model considering passive helix. • Developed a complete parameter calibration process for 6-6 UPRU Stewart. • Calibration experiments confirm the validity of the proposed model. • Determines the 17-parameter requirement for 6-6 UPRU Stewart platform kinematics. • Assembly experiments verify kinematic model and calibration correctness and accuracy. This study examines the passive helical properties of 6-6 UPRU Stewart and their implications for kinematics and calibration. Unlike UPS/SPS branches, the UPRU branch exhibits passive helical behavior. The study explores the passive helical mechanism associated with the UPRU branch and develops a 17-parameter kinematic model that incorporates the spatial orientations of both the upper and lower Hooke joints. The correctness of the model was verified through simulation. Compared with the conventional UPS-model-based motion control method for the UPRU-Stewart platform, the proposed method achieves up to 10 4 times improvement in kinematic control precision. Furthermore, the research assesses the impact of the proposed method on parameter calibration, resulting in a comprehensive calibration process. Experimental results demonstrate that the kinematic parameter calibration error is substantially reduced, decreasing from the conventional method's order of 10 -3 m to 10 -12 m, resulting in a precision improvement of 10 9 times. Utilizing the calibrated parameters, a hole-shaft assembly experiment is conducted to evaluate the practical implications of the findings. The results demonstrate that the platform positioning error of the proposed method is reduced from 0.6mm to about 10 -10 m, enhancing precision by 10 6 times. This study provides a solid theoretical foundation for assembling heavy and super-heavy equipment.