Comparative analysis and optimization of an ankle rehabilitation redundantly actuated robot and its non-redundant counterpart using a modified trajectory and new dynamic indices

Trajectory planning and dynamic analysis are essential for the parallel ankle rehabilitation manipulators (PARMs) in practical applications. To enhance rehabilitation outcomes and optimize the dynamic performance of ankle rehabilitation manipulators, this paper proposes a modified rehabilitation trajectory and two new dynamic performance indices. Firstly, the inverse kinematic solutions are derived for the redundantly actuated parallel manipulator (PM) and its non-redundantly actuated counterpart. The velocities and accelerations of the links and moving platform (MP) are then obtained through time differentiation. Subsequently, inverse dynamic models for both PMs are established using the principle of virtual work. In addition, the modified trajectory with stretching capability is derived based on the seventh-order polynomial and the biomechanics of ankle soft tissues, and the established dynamic model is validated through this trajectory. Moreover, two new indices—the average limb inertia coupling (ALIC) and the variation of the average inertia coupling (VAIC)—are proposed to evaluate the overall limb inertia coupling and its dispersion at a certain configuration, respectively. Finally, the NSGA-II algorithm is applied to optimize the manipulators’ limb inertia coupling and workspace characteristics.