## 2 Mechanism
### Principle of the 3-DOF Upper-limb Exoskeleton  
The 5-DOF upper-limb exoskeleton has characteristics of flexibility due to the multiple degrees of freedom, but too many degrees of freedom will lead to a complex structure, which increases the self-weight. Therefore, the degrees of freedom of the 5-DOF upper-limb exoskeleton are analyzed and optimized. The function of the degrees of freedom of the 5-DOF upper-limb exoskeleton is shown in Table 3.  
The shoulder flexion/extension \(\left(\theta_{2}^{5}\right)\), elbow flexion/extension \(\left(\theta_{4}^{5}\right)\) and shoulder adduction/abduction \(\left(\theta_{1}^{5}\right)\) are significant for performing tasks. The shoulder internal/external-rotation \(\left(\theta_{3}^{5}\right)\) and elbow pronation/supination \(\left(\theta_{5}^{5}\right)\) are mainly used to increase workspace and flexibility. The weights of these two joints and the corresponding actuators account for 24% of the total weight of the 5-DOF upper-limb exoskeleton. In order to simplify the structure and reduce weight, the shoulder internal/external-rotation \(\left(\theta_{3}^{5}\right)\), elbow pronation/supination \(\left(\theta_{5}^{5}\right)\) and their actuators are removed, which will cause the problem of a smaller workspace. To solve this problem, internal-rotation of the elbow flexion/extension by 90\({}^{\circ}\) around the upper-arm will create a new degree of freedom: elbow external-flexion/internal-extension (Elbow EF/IE) \(\left(\theta_{3}^{3}\right)\). The problem of flexibility in the end-effector is solved by the tools designed for different loads. Based on the results of the above analysis, a non-anthropomorphic 3-DOF upper-limb exoskeleton with an internally rotated elbow joint is proposed. The 3 DOFs include the following: shoulder flexion/extension \(\left(\theta_{1}^{3}\right)\), shoulder adduction/abduction \(\left(\theta_{2}^{3}\right)\) and elbow external-flexion/internal-extension \(\left(\theta_{3}^{3}\right)\), as shown in Figure 3. Different from the 5-DOF upper-limb exoskeleton, when the upper-limb of the human body performs elbow flexion/extension in the sagittal plane, the 3-DOF upper-limb exoskeleton performs elbow external-flexion/internal-extension in the plane of the vertical sagittal plane; the exoskeleton and the human arm are not fully attached together. According to the motion range of human joints and the motion range of the 5-DOF upper-limb exoskeleton, the motion range of the 3-DOF upper-limb exoskeleton is determined, as shown in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Configuration** & **Motion** & **Range** \\ \hline \multirow{3}{*}{3-DOF} & Shoulder Flex./Ext. \(\left(\theta_{1}^{3}\right)\) & 180\({}^{\circ}\)/50\({}^{\circ}\) \\  & Shoulder Add./Abd. \(\left(\theta_{2}^{3}\right)\) & 180\({}^{\circ}\)/30\({}^{\circ}\) \\  & Elbow EF/IE \(\left(\theta_{3}^{3}\right)\) & 118\({}^{\circ}\)/0\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Motion range of the 3-DOF upper-limb exoskeleton. \begin{table}
\begin{tabular}{c c} \hline \hline
**Motion** & **Function** \\ \hline Shoulder Flex./Ext. \(\left(\theta_{2}^{5}\right)\) & Complete lifting, pull down, etc., which require the upper-limb to swing back and forth. \\ Shoulder Add./Abd. \(\left(\theta_{1}^{5}\right)\) & Complete side lifting, etc., which require the upper-limb to swing lateral. \\ Shoulder Int./Ext. Rot \(\left(\theta_{3}^{5}\right)\) & Increase the workspace of the upper-limb. \\ Elbow Flex./Ext. \(\left(\theta_{4}^{5}\right)\) & Complete lifting, pull down, etc., which require the upper-limb to swing back and forth. \\ Elbow Pron./Sup. \(\left(\theta_{5}^{5}\right)\) & Increase the flexibility of the end-effector. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Function of the DOFs of the 5-DOF upper-limb exoskeleton. As described in Figure 2, the 5-DOF upper-limb exoskeleton is an anthropomorphic structure.