## 1 Introduction
A summary of various studies found in the literature that use metaheuristic algorithms in the synthesis problem of mechanisms is presented in Table 1.  
The particular interest in this study is in the works related to the mechanism design for rehabilitation presented at the end of such table. For instance, [PERSON] et al. [14] proposed a mechanism for finger rehabilitation, where the direct search algorithm Malaga University Mechanism Synthesis Algorithm (MUMA) was used, and a penalty function was implemented as a constraint-handling technique in the synthesis process. [PERSON] et al. [15] designed a rehabilitation system using a cam-linkage mechanism for the lower limb rehabilitation to perform the gait. The synthesis problem was solved by a genetic algorithm, where a penalty function was considered as the constraint-handling technique. [PERSON] et al. [16] designed a gait rehabilitation system for children using a four-bar linkage mechanism. The indirect search algorithm Sequential Quadratic Programming (SQP) and the direct one given by Differential Evolution (DE) algorithm were used in the synthesis process. In this work, feasibility rules were considered as a constraint-handling technique. [PERSON] et al. [17] designed knee-ankle-foot, hip-knee-ankle-foot, and knee orthoses using a four-bar linkage mechanism. Metaheuristic algorithms, such as Particle Swarm Optimization (PSO) and the Teaching-Learning-Based Optimization (TLBO) algorithm, were considered. In this work, mechanical constraints in the synthesis process are not considered. [PERSON] et al. [18] presented the design of a wrist prosthesis using a spherical parallel manipulator. In the synthesis process, Nondominated Sorting Genetic Algorithm (NSGA-II), Multiobjective Particle Swarm Optimization (MOPSO), and Multiobjective EvolutionaryAlgorithm based on Decomposition (MOEA/D) algorithms were considered, and the feasibility rules were implemented as constraint-handling technique. [PERSON] et al. [3] designed a lower limb rehabilitation machine. The differential evolution algorithm was considered in the synthesis process, and the feasibility rules were used as the constraint-handling technique. We observed in the literature that metaheuristic algorithms in their original versions were proposed to solve unconstrained optimization problems. Thus, it is important to find the most promising techniques for including real-word constraints [37; 38; 39]. Currently, for the solution of constrained optimization problems, CHTs have been proposed. According to [40], these can be classified into two generations, where the penalty functions, decoders, special operators, and separation of the objective function and constraints are included in the first generation. On the other hand, the feasibility rules, stochastic ranking, and \(\epsilon\)-constraint involve the second generation. The first generation is characterized by a high calibration complexity and a high probability of convergence to local minimums. The second generation is characterized by overcoming the mentioned limitations in the first generation. From the literature review regarding the design of closed-chain mechanisms for rehabilitation and the general framework of kinematic synthesis of mechanisms, both included in Table 1, the metaheuristic algorithms incorporate only one constraint-handling