## 4 Dynamics Analysis
### Dynamics  
The upper-arm and the forearm of the 5-DOF upper-limb exoskeleton are 330 mm and 370 mm, and the upper-arm and the forearm of the 3-DOF upper-limb exoskeleton are 328 mm and 372 mm, respectively. The load capacity of the upper-limb exoskeleton for material hanging is heavy, and the design index of the 5-DOF upper-limb exoskeleton lifting capacity is 50 kg. In order to compare the characteristics of the two exoskeletons with a heavy load, the load on both end-effectors is 50 kg. The load on the end-effector is much heavier than the upper arm and the forearm of the 5-DOF upper-limb exoskeleton; therefore, the exoskeleton is considered as a 0 mass in the dynamic analysis. The time for raising up and lateral lifting is 5 s and 3 s, respectively, which refers to the rounded time of the human body to perform the actual actions. The dynamic equations of motion for the two exoskeletons are derived using the Lagrange method, and joint torques can be solved [27]. Figures 10-13 show the joint torque curves. Because shoulder flexion/extension (\(\theta_{1}^{3}\), \(\theta_{1}^{5}\)) of the two exoskeletons does not work during lateral-lifting, the joint torques and power consumption of the two joints will not be considered in the process. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Action** & **Parameters** & **Data** \\ \hline \multirow{3}{*}{Raising up} & \(O_{0}G_{0}\) & 1500 mm \\  & \(B_{0}B_{0}^{\prime}\) & 883 mm \\  & \(B_{1}B_{1}^{\prime}\) & 1931 mm \\ \hline \multirow{3}{*}{Lateral lifting} & \(O_{0}B_{0}^{\prime}\) & 1500 mm \\  & \(B_{0}^{\prime}B_{1}^{\prime}\) & 350 mm \\ \cline{1-1}  & \(\angle B_{0}O_{0}B_{1}\) & 30\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters of the end-effector trajectory. Figure 9: End-effector trajectory: (**a**) Raising-up; and (**b**) Lateral-lifting. Figure 11: Joint torque curves of raising up for the 5-DOF exoskeleton. Figure 12: Joint torque curves of lateral lifting for the 3-DOF exoskeleton. Figure 10: Joint torque curves of raising up for the 3-DOF exoskeleton. Figure 13: Joint torque curves of lateral lifting for the 5-DOF exoskeleton. Since elbow torque is mainly borne by structural components during raising up, the maximum elbow joint torque of the 3-DOF upper-limb exoskeleton is significantly reduced. According to the simulation results, the maximum joint torques in the two exoskeletons are obtained during the process of raising up and lateral lifting (Table 9). From Table 9, the maximum joint torques of shoulder flexion/extension and shoulder addduction/abduction for the two exoskeletons are identical during the process of raising up and lateral lifting, but compared with elbow flexion/extension \(\left(\theta_{4}^{5}\right)\) of the 5-DOF upper-limb exoskeleton, the maximum joint torque of elbow external-flexion/internal-extension \(\left(\theta_{3}^{3}\right)\) for the 3-DOF upper-limb exoskeleton was reduced by approximately 50%. According to the joint torque curves and angular velocity \(\dot{q}\) obtained by kinematics, the joint power consumption curves can be further obtained (Figures 14-17). Figure 14: Joint power consumption curves of raising up for the 3-DOF exoskeleton. Figure 15: Joint power consumption curves of raising up for the 5-DOF exoskeleton. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Configuration** & **Motion** & **Maximum Joint Torque (Nm)** \\ \hline \multirow{4}{*}{5-DOF} & Shoulder Flex./Ext. \(\left(\theta_{1}^{5}\right)\) & 295 \\  & Shoulder Add./Abd. \(\left(\theta_{2}^{5}\right)\) & 185 \\  & Shoulder Int./Ext. Rot \(\left(\theta_{3}^{5}\right)\) & 0 \\  & Elbow Flex./Ext. \(\left(\theta_{4}^{5}\right)\) & 192 \\  & Elbow Pron./Sup. \(\left(\theta_{5}^{5}\right)\) & 0 \\ \hline \multirow{4}{*}{3-DOF} & Shoulder Flex./Ext. \(\left(\theta_{1}^{3}\right)\) & 295 \\  & Shoulder Add./Abd. \(\left(\theta_{2}^{3}\right)\) & 185 \\  & Elbow EF/IE \(\left(\theta_{3}^{3}\right)\) & 96 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Maximum joint torques.