## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Wrapping Surface**} & \multicolumn{3}{c}{**Local Position Vector**} & \multicolumn{3}{c}{**Local Orientation**} & **Geometry** \\ \cline{2-9}  & \(\overline{\mathbf{u}}_{w,x}\) **[m]** & \(\overline{\mathbf{u}}_{w,y}\) **[m]** & \(\overline{\mathbf{u}}_{w,z}\) **[m]** & \(\mathbf{\theta}_{w,x}\) **[rad]** & \(\mathbf{\theta}_{w,y}\) **[rad]** & \(\mathbf{\theta}_{w,z}\) **[rad]** & **[mm]** \\ \hline Ground cylinder & \(-0.0439\) & \(-0.0039\) & \(0.1478\) & \(1.3753\) & \(-0.2946\) & \(2.4360\) & \(\begin{array}{c}r=3\\ h=30\end{array}\) \\ \hline Shoulder ellipsoid \(1\) & \(-0.0078\) & \(-0.0041\) & \(-0.0014\) & \(3.0016\) & \(-0.8535\) & \(2.5742\) & \(\begin{array}{c}s_{x}=35\\ s_{y}=20\end{array}\) \\ \hline Shoulder ellipsoid \(2\) & \(0.0033\) & \(0.0073\) & \(0.0003\) & \(-2.0043\) & \(-1.0016\) & \(0.9755\) & \(\begin{array}{c}s_{x}=25\\ s_{y}=20\end{array}\) \\ \hline Elbow cylinder & \(0.0028\) & \(-0.2919\) & \(-0.0069\) & \(-0.1402\) & \(-0.0063\) & \(0.1550\) & \(\begin{array}{c}r=16\\ h=50\end{array}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Wrapping surfaces location and orientation with respect to the reference joints and geometry. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Joint**} & \multicolumn{3}{c}{**Unit Vector Axis**} \\ \cline{2-5}  & \(\hat{\
u}_{x}\) & \(\hat{\
u}_{y}\) & \(\hat{\
u}_{z}\) \\ \hline Shoulder & \(-0.0589\) & \(0.0023\) & \(0.9983\) \\ Elbow & \(0.0494\) & \(0.0366\) & \(0.9981\) \\ \hline \end{tabular}
\end{table} 
Table 4: Joints’ rotation axed with respect to the parent bodies. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Muscle**} & \multicolumn{3}{c}{**Unit Vector Axis**} \\ \cline{2-5}  & \(\hat{\
u}_{x}\) & \(\hat{\
u}_{y}\) & \(\hat{\
u}_{z}\) \\ \hline Shoulder & \(-0.0589\) & \(0.0023\) & \(0.9983\) \\ Elbow & \(0.0494\) & \(0.0366\) & \(0.9981\) \\ \hline \end{tabular}
\end{table} 
Table 4: Joints’ rotation axed with respect to the parent bodies. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Muscle**} & \multicolumn{3}{c}{**Maximum**} & **Optimal** & **Slack** & **Optimal** & **Maximum** \\  & **Isometric** & **Muscle Fibre** & **Tendon** & **Pennation** & **Pennation** \\  & **Force** & **Length** & **Length** & **Angle** & **Velocity** \\  & \(F_{0}\) **[N]** & \(I_{0}\) **[m]** & \(I_{t}\) **[m]** & \(\mathbf{\alpha}_{0}\) **[rad]** & \(\mathbf{v}_{max}\) **[\(I_{0}\)/s]** \\ \hline Long triceps & 798.52 & \(0.1340\) & \(0.1430\) & \(0.209\) & \(10\) \\ Lateral triceps & 624.30 & \(0.1138\) & \(0.0980\) & \(0.157\) & \(10\) \\ Medial triceps & 624.30 & \(0.1138\) & \(0.0908\) & \(0.157\) & \(10\) \\ Long biceps & 624.30 & \(0.1157\) & \(0.2723\) & \(0\) & \(10\) \\ Short biceps & 435.56 & \(0.1321\) & \(0.1923\) & \(0\) & \(10\) \\ Brachialis & 987.26 & \(0.0858\) & \(0.0535\) & \(0\) & \(10\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Muscles’ properties. In order to prove the reliability of the kinematical analysis, Figure 8; Figure 9 show the comparison between the system configuration (the position of the bodies with their mass centre, the muscles and the wrapping surfaces) in the OpenSim model and in the Matlab model, in correspondence of the first and the last time instants. The kinematical analysis can be viewed in Supplementary Materials--Video S1. Figure 8: Kinematics first time instant in (**a**) OpenSim and (**b**) Matlab. Figure 7: Arm26 degrees of freedom over time. The long biceps wrapped on the ellipsoid keeps its path on the surface during the simulation because the shoulder angle is constant; it is shown in Figure 10.  
Figure 10: Shoulder wrapping. Figure 9: Kinematics last time instant in (**a**) OpenSim and (**b**) Matlab. The wrapping muscles on the cylinder close to the elbow are viewed in Figure 11 at the start and at the end of the analysis time period, in order to show the brachialis wrapping on the cylinder front and the triceps wrapping on the cylinder back.