## 4 System Implementation and Experimental Results
### Elbow Joint Flexion-Extension Exercise  
During this exercise session, the subject performs flexion and extension of the elbow. This exercise is repeated a few times and the sensor measurements of the node, which is attached to the subject's forearm, are recorded and processed. This results to the estimation of the node's orientation angles \(\phi\), \(\theta\) and \(\psi\). Using the node's orientation angles, we can estimate the elbow DoF angles. Comparison between the proposed custom-made sensor node and the Shimmer3 sensor unit for the estimated angles \(\theta_{4}\) and \(\theta_{5}\) are shown in Figures 3 and 4, respectively. The trajectories of the shoulder, the elbow, the wrist joints and the tip of the hand in \(x,y\), and \(z\) axes are presented in Figure 5. The distances between the segments joints, as shown in this figure, are in accordance with the corresponding fractions of human's height. The motion takes place in the \(y-z\) plane and the value of \(x\) component for each joint is constant and equal to the \(l_{c}\), due to the dependence of the segments' position only by the angle \(\theta_{4}\). In this case, the position of the forearm is calculated by the transformation matrix \(T_{4}^{6}\), which depends only on the variable \(\theta_{4}\). The angle \(\theta_{5}\) affects only the orientation of the forearm and not its position. Furthermore, the hand is supposed to be aligned with the forearm, thus angles \(\theta_{6}\) and \(\theta_{7}\) of the wrist joint are zeroed. Figure 4: Elbow rotation angle \(\theta_{5}\)—Pronation-Supination DoF. Figure 3: Elbow rotation angle \(\theta_{4}\)—Flexion-Extension DoF. The resulted joints' trajectories, as extracted by the upper limb model presented in Section 2, for the calculated elbow DoF angles, are illustrated in Figure 6. The trajectories, as extracted for the case of the custom-made sensor node, are noted with the 'o' symbol and represent the exercise that the patient has performed. The upper limb segments' trajectories for the case of the Shimmer3 sensor unit's measurements are also presented in the same figure. Deviations between the trajectories, especially in the upper and lower limit of the motion range, are identified in this figure. In the case of Shimmer3, the trajectories are more limited (noted with deep purple and deep red color). This is resulted by the elbow DoF angle \(\theta_{4}\) that ranges from \(13^{\circ}\) to \(85^{\circ}\) approximately, while the corresponding angle calculated by the measurements of the proposed sensor node ranges between \(8^{\circ}\) to \(88^{\circ}\), as shown in Figure 3.  
The processing and filtering methodology, described in Section 3.1, were followed for the IMU measurements of both sensor nodes. The nodes were calibrated before the capturing session. It was noticed that the differences in the elbow angles' ranges, which were observed along a series of experiments, were related to the calibration accuracy of the sensors. Moreover, it was noticed that the forearm configuration during the exercise execution does not account for the gimbal lock problem. Finally, the points that are visualized in the trajectories' 3D plots correspond to the total number of the exercise's repetitions and not to only one. Figure 5: Joints trajectories coordinates in \(x\), \(y\), \(z\) axes for elbow flexion-extension exercise—Custom-made sensor node.