## 6 Experimental Tests
### Experimental Results and Discussion
As can be observed in Figure 12(a),b the end-user performed flexion and wrist extension gestures. From Figure 12(a),b we can see; (1) the desired workspace trajectories of the wrist F/E demonstrate black curve demonstrates the workspace trajectories (without FWRMS); (2) the actual motion of the wrist F/E workspace trajectories (with FWRMS) which indicated by the blue curve. In regards, the yellow highlighted value presents the current position of the wrist in the predefined coordinate frame. We can also observe that the two trajectories are relatively identical towards one another, and the participant has confirmed that there is no movement discomfort of the device. Furthermore, we can observe the actual (with FWRMS) ROMs of the wrist F/E are (0\({}^{\circ}\)-71\({}^{\circ}\)/0\({}^{\circ}\)-57\({}^{\circ}\)). We applied the same previous approach in the finger F/E; to create a graphical representation for wrist F/E ROM. Figure 13(a) plots a comparative analysis between the desired and actual ROMs angle of the wrist F/E during the experiment's execution. It is straightforward to observe that the end-user is performing a single F/E wrist. The vertical axis stands for the wrist's angle, while the horizontal axis stands for the execution time. The graph consists of two curves: the solid blue curve demonstrates the desired (without FWRMS) ROM angle. While the orange dash curve illustrates the actual (with FWRMS) ROM angle of the wrist F/E. It is possible to note the similarities between the two ROMs. However, from Figure 12(a),b and Figure 13(a) we can find an observable error between the two ROMs and the workspace trajectories; the sum measured by root means square error RMSE of 1.14 mm. Figure 13: The real-time experiments of wrist joints workspace trajectories. (**a**), the actual ROM angle of the wrist fixing, the workspace trajectory, and the position caused by FWRMS. (**b**), actual wrist extension (blue curve) and desired (black curve) workspace trajectory and position. (**c**), the actual radial deviation of the wrist (blue curve) and the desired (black curve) workspace trajectory. (**d**), the actual wrist ulnar deviation ROM angle, workspace trajectory, and position caused by FWRMS. Like previous tests, we conducted an experiment to evaluate the wrist R/U joint's functional region with and without the FWRMS machine. In this experiment, we selected the desired R/U ROM (0\({}^{\circ}\)-24\({}^{\circ}\)/0\({}^{\circ}\)-38\({}^{\circ}\)). Once the therapy was executed, the end-user performed wrist R/U motion, as shown in Figure 13c,d which indicates; (1) the black curve which describes the workspace trajectories without FWRMS; (2) the blue curve which describes the workspace trajectories induced by FWRMS. Moreover, Figure 14b plots a graphical analysis that indicates a comparison study between the desired and actual ROM angles of the wrist R/U during the experiment's execution. The solid blue curve is plotting the desired ROM angles. While the dashed orange curve is plotting the actual ROM angles. Although comparatively both trajectories in Figure 13c and ROM angles in Figure 14b are functionally matching towards each other, but it is slightly observable that there is a significant difference in the overall performance of the proposed approach. Figure 14: Continuous passive motion rehabilitation experiment of s typical; (**a**) wrist flexion/ extension joint; (**b**) wrist radial/ulnar deviation joint. a slight error between them; it is worth nothing as an error; the sum calculated RMSE was 0.984 mm. Eventually, after the repeatable tests, the differences between the actual and the desired ROM were just a few millimeters for the finger's F/E and few degrees for the wrist F/E, R/U. The disparity in each measurement occurred primarily due to the mechanical frictions and vibrations caused by the mechanical coupling. However, as we have briefly explained, these differences do not affect the proposed system's training characteristics.