## 4 Results
### Algorithm Performance Analysis
#### 4.2.3 Overall Evaluation of the Proposed NCH through Study Cases  
The overall evaluation of the most promising algorithms given in Section 4.2.2 is discussed next.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Trajectory 1**} \\ Hypothesis & & [PERSON] \\ \hline
**R1B-EC** vs. R1B-FR & \(\mathbf{9.0179\times 10^{-4}}\) \\ R1B-EC vs. **R1B-NCH** & \(\mathbf{4.2514\times 10^{-2}}\) \\ R1B-FR vs. **R1B-NCH** & \(\mathbf{3.8933\times 10^{-9}}\) \\ \hline  & \multicolumn{2}{c}{**Trajectory 2**} \\ Hypothesis & & [PERSON] \\ \hline R1B-EC vs. R1B-FR & \(\mathbf{8.4557\times 10^{-2}}\) \\ R1B-EC vs. **R1B-NCH** & \(\mathbf{1.8685\times 10^{-5}}\) \\ R1B-FR vs. **R1B-NCH** & \(\mathbf{5.7132\times 10^{-11}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 13: \(p\)-values for tests in the multiple comparisons among the three outstanding algorithms in study case 2 using both trajectories. R1B-NCH wins two times in both trajectories. R1B-EC wins one time in trajectory 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Trajectory 1**} & & \\
**Algorithm-CHT** & **Set 1** & **Set 2** & **Set 3** & **Set 4** \\ \hline R1B-NCH & \(\mathbf{0.65626}\) & \(\mathbf{0.65628}\) & \(\mathbf{0.65606}\) & \(\mathbf{0.65637}\) \\ R1B-FR & \(0.67261\) & \(0.67827\) & \(0.67514\) & \(0.67639\) \\ R1B-eC & \(0.67012\) & \(0.66972\) & \(0.66852\) & \(0.66230\) \\ \hline  & \multicolumn{2}{c}{**Trajectory 2**} & & \\
**Algorithm-CHT** & **Set 1** & **Set 2** & **Set 3** & **Set 4** \\ \hline R1B-NCH & \(\mathbf{0.64382}\) & \(\mathbf{0.64224}\) & \(\mathbf{0.64307}\) & \(\mathbf{0.64441}\) \\ R1B-FR & \(0.64948\) & \(0.65921\) & \(0.65997\) & \(0.65742\) \\ R1B-eC & \(0.65648\) & \(0.65463\) & \(0.65531\) & \(0.64569\) \\ \hline \hline \end{tabular}
\end{table}
Table 14: Minimum value of the objective function through different sets of thirty algorithms’ executions in study case 2 in both trajectories.  
In the first study case and according to Table 10, the most promising algorithms considering both trajectories are: R1B-NCH, R1B-PF, MUMA-PF, and R1B-FR. In that case, all algorithms draw with each other. Thus, each algorithm presents two draws. In the second study case and according to Table 13, the most promising algorithms are: R1B-NCH, R1B-EC, and R1B-FR. In such a case, the R1B-NCH wins four times, and the R1B-EC wins one time. With this information, a summary of the number of wins and draws for both study cases, and trajectories are presented in Table 15. According to this table, the overall evaluation of the most promising algorithms is analyzed, and it is confirmed that the most promising one is the proposed R1B-NCH because it wins and draws four times. The next best behaviors of the algorithms to solve the synthesis problem are related to R1B-PF and R1B-FR in that order.  
Then, the NCH technique increases the exploration and exploitation capabilities in the ED/RAND/1/BIN algorithm to solve the considered mechanism synthesis problems. The obtained solution (mechanism) could improve the lower limb rehabilitation machine.  
Finally, the best solutions obtained by the R1B-NCH algorithm for each study case are displayed in Tables 16 and 17. In order to validate the obtained mechanism for rehabilitation purposes, the Computer-Aided Design (CAD) of the mechanism in different phases of the crank movement is shown in Figures 9 and 10. Through the figure sequences given by the number 1 to the sequence number 9, it is observed that the coupler point of the mechanism in both figures can provide the proposed rehabilitation routine showing in a continuous line. Furthermore, if we fixed the human ankle joint in the coupler point of the mechanism, the mechanism can reproduce the natural movement of the leg, as is shown in those figures.  
Figure 9: CAD representation of the best mechanism movement obtained by R1B-NCH for study case 1.