This research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

Ankle rehabilitation robots are widely used due to nerve injuries and sports injuries leading to decreased mobility of the ankle joint. However, the motion of most ankle rehabilitation robots has distinctions with human ankle physiological structure. In order to achieve more accurate rehabilitation training of the ankle joint, this paper proposes a novel 3-UPU parallel rehabilitation mechanism. In a certain range, the mechanism can perform rotation around any axis within the midplane, which means that the mechanism can achieve non-fixed-point rotation around the instantaneous axis of the ankle joint. The mechanism has three degrees of freedom and can perform ankle pronation/supination and inversion/eversion movements. Taking into account the structural differences of different human bodies, the rotating axis of the mechanism can be adjusted in both height and angle. Then, the workspace of the mechanism was solved, and the size parameters of the mechanism are analyzed based on the characteristics of the size parameters of the mechanism and the motion range of the ankle. A genetic algorithm was employed to optimize the mechanism’s parameters. Next, the motion trajectory of the mechanism was planned, and the length change of the mechanism driving pair during the motion planning of the angle was obtained through kinematics simulation. Finally, experimental verification of the above rehabilitation training methods indicates that the mechanism meets the requirements of ankle rehabilitation.

In this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.