Nature-Inspired Intelligent Synthesis of a Spherical Mechanism for Passive Ankle Rehabilitation Using Differential Evolution

The ankle rehabilitation in certain injuries requires passive movements to aid in the prompt recovery of ankle movement. In the last years, parallel ankle rehabilitation robots with multiple degrees of freedom have been the most studied for providing such movements in a controlled way. Nevertheless, the high cost does not make it viable for home healthcare. Then, this paper presents an optimization approach where a spherical mechanism of one-degree-of-freedom is proposed as a low-cost ankle rehabilitation device to provide the passive rehabilitation exercise for plantar flexion/dorsiflexion and adduction/abduction ankle movements. The approach is formulated as a mono-objective constraint optimization problem where the relative motion angle of the mechanism, the Grashof criterion, the force transmission, and the rehabilitation routine are included. The link lengths of the mechanism parameterized in Cartesian coordinates are found by the two most representative differential evolution variants. The statistical analysis of optimizers indicates that the DE/rand/1/bin finds, on average, more promising solutions through algorithm executions than the DE/best/1/bin. The numerical simulation results and the motion simulation of the CAD model illustrate the obtained ankle rehabilitation mechanism, indicating that the percentage error between the desired rehabilitation path and the curve generated by the coupler point of the mechanism is in the interval [{0.036,0.437}]\%. Manufacturing the ankle rehabilitation mechanism with a 3D printer validates the optimization approach and verifies the resulting mechanism.