## 3 Results
### Trajectory Deviations  
To numerically evaluate the similarity of the trajectories of the selected MF and PF joints across different protocols, we calculated the deviation of trajectories from a base-line joint's trajectory, obtained during P2 protocol. The yellow lines in Figure 8 depict the base-line trajectories of the MF for one of the subjects during the P2 protocol; however, Figure 9 shows graphs with the normalised results, averaged across all subjects, for the MF's and PF's MCP joint and the fingertip. Graphs in Figure 9 titled MF MCP and PF MCP show deviations in the movement of the MF's and PF's MCP joint, and graphs titled MF tip and PF tip show deviations in the MF's and PF's fingertip movements. The blue colour represents the P0, and the red represents the P1 protocol. Whiskers were added to the graphs to help visualise the standard deviation (SD) of the data. Both protocols were compared to the P2 protocol--yellow, which represents the baseline and can be barely seen, as its values are close to zero. Figure 8: The MF joints’ trajectories in the sagittal plane for one of the subjects and all three experimental protocols: P0—blue, P1—red, and P2—yellow. The deviations in the MCP joints can be interpreted as a base error since the trajectories of the MCP joints stem directly from the wrist flexion and extension and are, as such, not directly impacted by the device. The base error can be attributed to movements of the markers due to the skin's elasticity. To estimate how well the device mimics the movement of the unconstrained wrist and fingers of the healthy subjects, we can use the fingertip deviations. The normalised motion starts in the flexed position, at the left of the \(x\)-axis. The deviations in both graphs, _MF tip_ and _PF tip_, show a considerable difference between the P0 and P2 protocols and also between the P0 and P1 protocols in the first half of the normalised motion, i.e., flexion; however, this was expected because, as stated before, during the P0, the subjects were able to move through their entire ROM, flexing their fingers into a fist. At the same time, that could not be performed during the P1 and P2 protocol, as the device has a limited ROM when moving into flexion, from both safety and mechanical standpoints. The normalised motion ends in the extended position, at the right of the \(x\)-axis, where the results are within the base error, indicating sufficient similarity of the trajectories between the P0 and P2 protocols, as well as the P1 and P2 protocols, meaning that the device adequately mimics the movement of the wrist and fingers into extension. To further analyse the deviations of the trajectories for the MF, we computed the root-mean-square deviation (RMSD) of the deviation values between the P0 and P2 protocol for each of the subjects. We computed the RMSD values for the movement into flexion and the extension separately. Table 2 presents the obtained RMSD values and the SD for the MCP joint and the fingertip deviations. Figure 9: Deviation of the finger joints’ trajectories from their base-line trajectory. The results from Table 2 are consistent with the results shown in Figure 9. Except for the subject B, the MF MCP deviations are within reasonable levels of error for both flexion and extension. Their cumulative average across the subjects, excluding the subject B, gives us a value of 0.5 cm, which most likely stems from an error due to skin elasticity, which is present in every measurement. The same can be observed from the MF tip RMSD values during extension. The values are again within reasonable error levels, with most of them close to the 0.5 cm mark. That is, if we take that into account, the part of the RMSD values is probably a consequence of skin deformations due to finger fixations. Namely, Figure 9 shows that towards the extension, there are no major differences in the amplitude of the deviations for the P0 and P1 protocol, meaning that only the measurement error remains.