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The optimal methods for the synthesis of mechanisms in rehabilitation usually require solving constrained optimization problems. Metaheuristic algorithms are frequently used to solve these problems with the inclusion of Constraint-Handling Techniques (CHTs). Nevertheless, the most used CHTs in the synthesis of mechanisms, such as penalty function and feasibility rules, generally prioritize the search for feasible regions over the minimization of the objective function, and it notably influences the exploration and exploitation of the algorithm such that it could induce in the premature convergence to the local minimum and thus the solution quality could deteriorate. In this work, a Neuronal Constraint-Handling (NCH) technique is proposed and its performance is studied in the solution of mechanism synthesis for rehabilitation. The NCH technique uses a neural network to search for the fittest solutions into the feasible and the infeasible region to pass them to the next generation of the evolutionary process of the Differential Evolution (DE) algorithm and consequently improve the obtained solution quality. Two synthesis problems with four–bar and cam–linkage mechanisms are the study cases for developing lower-limb rehabilitation routines. The NCH is compared with four state-of-the-art constraint-handling techniques (penalty function, feasibility rules, stochastic ranking, ϵ-constrained method) included into four representative metaheuristic algorithms. The irace package is used for both the algorithm settings and neuronal network training to fairly and meaningfully compare through statistics to confirm the overall performance. The statistical results confirm that, despite changes in the rehabilitation trajectories, the proposal presents the best overall performance among selected algorithms in the studied synthesis problems for rehabilitation, followed by penalty function and feasibility rule.

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Currently, rehabilitation systems with closed kinematic chain mechanisms are low-cost alternatives for treatment and health care. In designing these systems, the dimensional synthesis is commonly stated as a constrained optimization problem to achieve repetitive rehabilitation movements, and metaheuristic algorithms for constrained problems are promising methods for searching solutions in the complex search space. The Constraint Handling Techniques (CHTs) in metaheuristic algorithms have different capacities to explore and exploit the search space. However, the study of the relationship in the CHT performance of the mechanism dimensional synthesis for rehabilitation systems has not been addressed, resulting in an important gap in the literature of such problems. In this paper, we present a comparative empirical study to investigate the influence of four CHTs (penalty function, feasibility rules, stochastic-ranking, and ϵ-constraint) on the performance of ten representative algorithms that have been reported in the literature for solving mechanism synthesis for rehabilitation (four-bar linkage, eight-bar linkage, and cam-linkage mechanisms). The study involves analysis of the overall performance, six performance metrics, and evaluation of the obtained mechanism. This identified that feasibility rules usually led to efficient optimization for most analyzed algorithms and presented more consistency of the obtained results in these kinds of problems.

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.