## 3 Results  
### Identification of Real Performance Parameters  
This section discusses the results obtained from the application of the methodology, the modes of operation in each of the readings, the ERMIS position data, representative position charts, the points in the workspace of the movements, and the permissible error rate for the position analysis. The exercises are involved the movement of at least one degree of freedom. The constructed anthropomorphic mechanism was connected to the ERMIS exoskeleton, as seen in Figure 5.  
The trajectories were discretized during the time that each movement or rehabilitation case lasted. The times for these are presented in Table 4. During the ERMIS testing it was possible to identify alterations and the correct functioning of the system. Position accuracy, repeatability, and absolute error have the same analysis conditions but use different calculation methods. For accuracy and repeatability, the formulas reported in ISO 9283 [43] are used. The values of the reported results are in millimeters in all cases. The movement was repeated ten times in the different cases. With the data acquired in the experimental measurement, different values and graphs were obtained, showing the absolute error, repeatability, and accuracy of the movements for each joint involved in the execution of the exercise. Figure 6 shows the trajectories of one of the unloaded readings  
Figure 5: Configuration for position reading in ERMIS. from which the points are taken for analysis. These are of the movement corresponding to case 3 and demonstrates its variation during the repetitions. Figure 7 shows the Gaussian bells of the position of one of the case studies that corresponds to a series of exercises by the exclusive articulation, which helps us observe how they are grouped around the programmed value. A very sharp bell indicates that the values are very close to the programmed value and a flatter bell indicates that values far from the programmed value are presented. The graphs correspond to each of the axes. Figure 7a corresponds to the \(x\)-axis, Figure 7b corresponds to the \(y\)-axis, and Figure 7c corresponds to the \(z\)-axis. Table 5 shows the representative values of the difference between the real value and the one obtained through the absolute error in the trajectories analyzed without a load. The values are represented concerning each coordinate axis of the inertial system of the anthropomorphic mechanism. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Movement** & **Time (s)** \\ \hline Case 1—Series of excluding exercises by joint. & 24 \\ \hline Case 3—Activation of muscle memory through trajectory tracking. & 45.5 \\ \hline Shoulder abduction–adduction & 16 \\ \hline Shoulder flexion–extension & 14 \\ \hline Internal and external shoulder rotation & 14 \\ \hline Arm flexion–extension & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time per work cycle. Figure 6: Trajectories of case 3-Activation of muscle memory through trajectory tracking. Figure 8 shows the trajectories corresponding to the flexion-extension movement of the shoulder, whose reading was performed under load conditions of 2.2 kg. Figure 9 shows the position distribution of one of the upper limb movements corresponding to shoulder abduction-adduction with a load of 2.2 kg. The graphs correspond to each of the axes. Figure 9 concerns the \(x\)-axis, Figure 9 concerns the \(y\)-axis, and Figure 9 concerns the \(z\)-axis. Table 6 shows the values corresponding to the absolute error of the movements analyzed with the load. These values compared to those taken in the no-load readings show an increase in the variation. Table 7 shows the root mean square (RMS) values that indicate the amount of error in the position of the ERMIS exoskeleton. Two values are shown, the first corresponds to the programmed value, and the second is the RMS value, which compares the programmed value with the obtained values. It functions as an estimate of positional accuracy.