Dynamic Reconstruction of Degrees of Freedom and Coupling Control in 3RPUR Metamorphic Parallel Mechanism

This study investigates the 3RPUR (3-Revolute–Prismatic–Universal–Revolute) variable parallel mechanism, employing screw theory and linear geometry to analyze the geometric relationships and constraint characteristics of the RPUR (Revolute–Prismatic–Universal–Revolute) limb kinematic pairs. The findings reveal that the constraint moment in the always remains perpendicular to the two axes of the U pair, forming an equivalent plane. Through the locking/unlocking mechanism of universal joints (U pair), the mechanism achieves dynamic degree-of-freedom reconstruction, enabling seamless switching between three translational (3T) and three translational-one-rotation (3T1R) motion modes. The continuity between motion and degrees of freedom during the variable cell process is demonstrated. This research reveals a strict 1:1 linear coupling between the rotational angle of the moving platform around the Z-axis and the U pair’s rotation angle under 3T1R mode. Simulation experiments validate the feasibility and coupling characteristics of both motion modes, providing theoretical and technical support for this mechanism’s adaptation to complex working conditions in mobile robotics applications, particularly where reconfigurable parallel mechanisms are required for multi-task flexibility.