## 1 Introduction
\begin{table}
\begin{tabular}{c c c} \hline
**Study** & **Application of the Synthesis Problem** & **Metaheuristic Algorithms** & **CHT** \\ \hline
[19] & Four-bar mechanism & Genetic Algorithm & - \\
[20] & Four-bar mechanism & Genetic Algorithm & - \\  & Stephensors & six-bar mechanism & \\  & Wait six-bar mechanism & & \\
[5] & Four-bar mechanism & Genetic Algorithm & Penalty Function \\
[21] & Hand robot mechanism & Pareto Optimum Evolutionary & Feasibility rules \\  & Multiobjective Algorithm (POEMA) & \\
[22] & Four-bar mechanism & Differential Evolution & Penalty Function \\
[23] & Six-bar mechanism & Differential Evolution & Penalty Function \\
[24] & Four-bar mechanism & Differential Evolution & Penalty Function \\
[25] & Four-bar mechanism & Genetic algorithm-fuzzy logic & Penalty Function \\
[26] & Four-bar and six-bar mechanisms & MUMSA & Penalty Function \\
[27] & Four-bar mechanism & Genetic Algorithm, & Penalty Function \\  & Differential Evolution, & \\  & Particle Swarm Optimization & & \\
[28] & Four-bar mechanism & Ant-gradient & Penalty Function \\
[29] & Four-bar mechanism & GA-DE & Penalty Function \\
[30] & Six-bar mechanism & Cukkoo Search & Penalty Function \\
[31] & Four-bar mechanism & NSGA-II & Feasibility rules \\
[32] & Four-bar mechanism & Imperialistic competitive algorithm, & Penalty Function \\  & Genetic Algorithm, & \\  & Differential Evolution, & \\  & Particle Swarm Optimization & \\
[33] & Four-bar mechanism & Modified Knill Herd & Penalty Function \\
[34] & Four-bar mechanism & TLBO & Penalty Function \\  & Genetic Algorithm, & \\
[35] & Four-bar mechanism & Hybrid Lagrange Interpolation DE & Penalty Function \\
[36] & Four-bar and six-bar mechanisms & Hybridization Differential Evolution & Penalty Function \\  & with Generalized Reduced Gradient & \\ \hline  & Mechanisms for rehabilitation & \\ \hline
[18] & Spherical parallel manipulator & NSGA-II, MOPSO, MOEA/D & Feasibility rules \\  & in prosthetic wrist & & \\
[14] & Six-bar mechanism in & MUMSA & Feasibility rules \\  & finger rehabilitation & Genetic Algorithm & Penalty Function. \\
[15] & Cam-linkage mechanism & & \\  & in gait rehabilitation & & \\
[16] & Four-bar mechanism & Differential Evolution & Feasibility rules \\
[17] & Four-bar mechanism in & Particle Swarm Optimization and TLBO & - \\  & gait rehabilitation and & & \\  & orthotic devices & & \\
[3] & Eight-bar mechanism in & Differential Evolution & Feasibility rules. \\  & lower limb rehabilitation & & \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of investigations tackling metaheuristic algorithms in the kinematic synthesis problem. “-” indicates that the use of CHT is not required. technique to solve the constraint optimization problem. Figure 1 shows the use of CHTs reported in the literature for the synthesis of mechanisms using metaheuristic algorithms. As observed in that figure, 64% of the reviewed literature uses the penalty functions, followed by the feasibility rules with a 24% of use. According to [37; 39; 41], the constraint-handling technique is an essential factor to solve constrained optimization problems because these techniques influence the exploration and exploitation capabilities of algorithms for the search of the most promising solution. However, other CHTs in the second generation, such as stochastic ranking and \(\epsilon\)-constraint have not been evaluated in solving these types of problems. Depending on the problem nature in the kinematic synthesis for rehabilitation (multimodality, types of functions, design variable space, and the feasible space ratio), the most frequently used algorithms and the constraint-handling techniques can be suitable during the search process of the metaheuristic algorithms. Nevertheless, the high interactions in the problem nature and the metaheuristic algorithms make it difficult to suggest a constraint-handling technique that is more likely to perform well against different algorithms.