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.

The configuration synthesis and kinematic analysis of reconfigurable parallel mechanisms are performed for two motion modes: three-translation (3T) and three-translation-one-rotation (3T1R). Firstly, the degrees of freedom and constraint conditions of the moving platform and the limbs of the mechanism are analyzed. The limb configurations satisfying the degrees of freedom are synthesized by using the equivalent motion screw method, and the RUPU/2UPU reconfigurable parallel mechanism is synthesized by reasonably arranging the limbs. The degrees of freedom and motion continuity of the mechanism are analyzed by using the geometric constraint method based on screw theory. It has been proved that the mechanism can switch motion modes via the revolute joint R. The inverse position solution and workspace of the mechanism are analyzed, and its full Jacobian matrix is established. Based on this matrix, the reconfigurability and singularity of the mechanism were analyzed. At the same time, the dexterity of the mechanism is evaluated based on the velocity Jacobian matrix and the actuation Jacobian matrix. The results of the two methods are consistent. Finally, the mechanism’s degrees of freedom, motion continuity, and reconfigurable characteristics are verified through virtual simulation experiments. The experimental results are consistent with the theoretical analysis.