This paper presents a novel ankle rehabilitation (2-CRS+PU)&R hybrid mechanism, which can meet the size requirements of different adult lower limbs based on the three-movement model of the ankle. This model is related to three types of movement modes of the ankle movement, without axis offset, which can cover the ankle joint movements. The inverse and forward position/kinematics results analysis of the mechanism is established based on the closed-loop vector method and using the optimization of particle groups algorithm. Four groups of position solutions of the mechanism are obtained. The kinematics simulation is analyzed using ADAMS software. The variations of the velocity and acceleration of all limbs are stable, without any sudden changes, which can effectively ensure the safety and comfort of the ankle model end-user. The dexterity of the mechanism is analyzed based on the transport function, and the results indicate that the mechanism has an excellent transfer performance in yielding the structure parameters. Finally, the rehabilitation evaluation is conducted according to the three types of movement modes of the ankle joint. The results show that this ankle rehabilitation mechanism can provide a superior rehabilitation function.

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.