## 4 Optimization Method
### Computational Implementation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Link 1**} & \multicolumn{4}{c}{**Link 2**} \\ \cline{2-9}  & & \multicolumn{2}{c}{**Thickness**} & \multicolumn{1}{c}{**Width**} & \multicolumn{1}{c}{**Type**} & \multicolumn{1}{c}{**Thickness**} & \multicolumn{1}{c}{**Width**} & \multicolumn{1}{c}{**Total**} \\
**Rank** & **Type** & **(m)** & **(m)** & **Type** & **(m)** & **(m)** & **Weight (N)** \\ \hline
1 & **1** & **0.00725** & **0.02409** & **1** & **0.00672** & **0.01772** & **0.77042** \\
2 & 1 & 0.00720 & 0.02444 & 1 & 0.00780 & 0.01585 & 0.77990 \\
3 & 1 & 0.00615 & 0.02382 & 1 & 0.00686 & 0.02149 & 0.78011 \\
4 & 1 & 0.00866 & 0.01990 & 1 & 0.01021 & 0.01383 & 0.78143 \\
5 & 1 & 0.00951 & 0.01806 & 1 & 0.00563 & 0.02514 & 0.81949 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: First five best solutions of ImHS. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Link 1**} & \multicolumn{4}{c}{**Link 2**} \\ \cline{2-9}  & & \multicolumn{2}{c}{**Thickness**} & \multicolumn{1}{c}{**Width**} & \multicolumn{1}{c}{**Type**} & \multicolumn{1}{c}{**Thickness**} & \multicolumn{1}{c}{**Width**} & \multicolumn{1}{c}{**Total**} \\
**Algorithm** & **Type** & **(m)** & **(m)** & **Type** & **(m)** & **(m)** & **Weight (N)** \\ \hline
**ImHS** & \(1\) & 0.00725 & 0.02409 & 1 & 0.00672 & 0.01772 & 0.77042 \\
**DE** & \(1\) & 0.01097 & 0.01593 & 1 & 0.01099 & 0.01590 & 0.86021 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Best solutions of ImHS and ED\(/\)rand\(/1/\)bin. ## 6 Discussion

In this paper, the structural design of a wrist rehabilitation system is carried out by a concurrent methodology, with a novel approach where the optimization process works simultaneously on both the material selection and the constraint meeting. A metaheuristic is applied to the dimensional synthesis and the material selection of more than one structural element at a time, considering the interaction and joint effect while designing. The modeling of the system as an optimization problem adds flexibility to its solution. Once it is modeled, the problem can be adapted to configuration changes. There is no limitation on the materials to be chosen, and the geometries to be analyzed can be as complex as is required by the design, demonstrating the versatility of the method. The associated optimization problem is a complex one solved with the Improved Harmony Search algorithm, modified for handling constraints and mixed variables. It generates design alternatives that can be evaluated from different perspectives such as cost, ease of manufacture and assembly. The results show that the performance of ImHS is stable and with a low computational cost, making it a good option to solve real-life problems if they are modeled as constrained cases. The quality of the design results guarantees that the physical implementation of the rehabilitation system will be safe for the patients, since they met the safety constraints established in the problem modeling. As future work, we consider the manufacturing of a prototype of the wrist rehabilitation device designed with the proposed method, in order to test it with real users. For the prototype, it is necessary to develop a control system, but the considerations for the concurrent design will simplify that task. Finally, we suggest considering to implement a strategy for dynamic parameter tuning to improve the performance of ImHS. Figure 3: FEM analysis of both links using ANSYS Workbench 2015. **Author Contributions:** Conceptualization and methodology, V.V.-C. and E.A.P.-F.; validation and formal analysis, M.B.C.-Y. and G.S.-C.; investigation and software, E.V.-A. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Data is contained within the article.