## 2 Materials and Methods
### Kinematics Definition
#### 2.1.1 Cross-Body Adduction Test  
The CBA test was completed in 5 steps, starting from an anatomical position, as listed in Table 1.  
In OpenSim, the first step of a 90\({}^{\circ}\) internal rotation about the glenohumeral joint was achieved by setting the shoulder_rot coordinate to 90\({}^{\circ}\). The second step was to perform a pronation of 20 degrees, which was done by setting the pro_sup coordinate to 20\({}^{\circ}\). This will place the arm so that the thumb is facing forward. The third step was to have a shoulder flexion of 60\({}^{\circ}\), which was done by first setting an elv_angle to 90\({}^{\circ}\) and shoulder_elv to 60\({}^{\circ}\). Elv_angle sets the plane of motion and can change from \(-100^{\circ}\) to 135\({}^{\circ}\). Elv_angle of 0\({}^{\circ}\) means the frontal or coronal plane where the abduction/adduction motion occurs, and 90\({}^{\circ}\) means the sagittal plane where flexion/extension of the shoulder occurs. Suppose we increase the elv_angle from 90\({}^{\circ}\). In that case, it will move the plane of motion towards the medial end of the body, and the arm movement occurs on that plane. At the same time, the negative value sets the plane of motion in the posterior direction of the body. The fourth step is 10\({}^{\circ}\) adduction, which was achieved by increasing the elv_angle by 10\({}^{\circ}\) from step three so that the arms will move toward the center. Finally, an elbow flexion of 90\({}^{\circ}\) is set to achieve the final resting position for the CBA in OpenSim, as shown in Figure 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Step**} & \multicolumn{3}{c}{**AnyBody Modeling SystemTM**} & \multicolumn{3}{c}{**OpenSim**} \\ \cline{2-7}  & **Angle** & **Joint** & **Rotation** & **Angle** & **Joint** & **Rotation** \\ \hline
1 & 90\({}^{\circ}\) & GH & Internal Humeral & 90\({}^{\circ}\) & GH & Internal Humeral \\ \hline
2 & 20\({}^{\circ}\) & Elbow & Pronation & 20\({}^{\circ}\) & Elbow & Pronation \\ \hline
3 & 60\({}^{\circ}\) & GH & Flexion & 60\({}^{\circ}\) & GH & Flexion \\ \hline
4 & 24\({}^{\circ}\) & GH & Adduction & 10\({}^{\circ}\) & GH & Adduction \\ \hline
5 & 90\({}^{\circ}\) & Elbow & Flexion & 90\({}^{\circ}\) & Elbow & Flexion \\ \hline \hline \end{tabular} Note: GH: glenohumeral.  
\end{table}
Table 1: Joint angles required to obtain the final resting posture for the cross-body adduction test using AnyBody Modeling SystemTM and OpenSim.  
Figure 1: Final resting posture for the cross-body adduction test using OpenSim: (**a**) front view and (**b**) sagittal view.  
In the AnyBody Modeling SystemTM, the joint angles are applied using the man-nequin.any file, which takes both the joint positions and joint velocity as an input. Since this study focuses only on the static cases, the joint angles summarized in Table 1 were changed in the mannequin.any file, using the corresponding joint names. Additionally, joint velocities were set to the default zero value to achieve the final resting posture for the CBA test. The only difference was in the adduction angle, which was set to 24\({}^{\circ}\) in the AnyBody Modeling SystemTM to match the final resting position of the CBA test obtained from OpenSim, as shown in Figure 2.