# NURSE-2 DoF Device for Arm Motion Guidance: Kinematic, Dynamic, and FEM Analysis
## 5 FEM Analysis  
Since the proposed mechanism should assist arm exercises that are normally performed over a work table, proper commercial spherical wheels have been added in the mechanical design in order to give stiffness to the linkage structure and use a work table as support (See Figure 6). Furthermore, an ergonomic interface has been studied and added to the structure to allow the patient to lean the arm and distribute its weight. The mechanism structure has also been attached to a fixed frame with \"T\" shape for a portable design that can be installed on a table or a flat plate. The fixed frame allows also to use flat motor or other rotational motors. A linear static FEM (Finite Element Method) analysis has been performed to test the feasibility of the prototype and to check the response of the proposed structure to the considered applied forces. All the device components have been considered as made of aluminium 1060 alloy with linear elastic isotropic properties as in Table 2. A soil has been considered during the FEM analysis in order to simulate the work table support for mechanism operation. Gravity force has been considered acting along the Z axis. The average weight of the arm has also been assumed as 37 N for the force acting on the mechanism end-effector during the simulation considering the average weight of the upper limb [25; 33]. The horizontal forces that can come from the human arm have been considered negligible for the current static analysis. However, they can be considered in a future work using a dynamic FEM analysis. To analyse the model using the proper criteria a mesh is needed. Table 6 shows the mesh information. Figure 6: A CAD design of the proposed mechanism including a mechanical interface and wheels. As Stress Analysis criterion, Von Mises stress function has been used as a measure of all stress components of a general 3-D state of stress. Von Mises stress function \(\sigma_{\text{vm}}\), can be expressed by stress components in the form [34]:  
\[\sigma_{Von\ Mises}=\sqrt{\frac{\left(\sigma_{1}-\sigma_{2}\right)^{2}+\left( \sigma_{2}-\sigma_{3}\right)^{2}+\left(\sigma_{3}-\sigma_{1}\right)^{2}}{2}}, \tag{20}\]  
where \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are the three principal stresses acting on X, Y, and Z-axes of the body. Von Mises stress is a non-negative scalar stress measure that evaluates elasto-plastic properties. This number function represents a stress magnitude, which can be compared against the yield strength of the material in order to determine whether or not failure by yielding is predicted. Using the maximum Von Mises stress criteria, [34], the condition of safe design can be expressed as:  
\[\frac{\sigma_{Von\ Mises}}{\sigma_{limit}}<1. \tag{21}\]  
If the Factor Of Safety (FOS) is 0 we are in a critical condition and if it is \(<\)1 the material failed. Displacement along Z, stress and FOS of the proposed mechanism have been obtained from the FEM analysis. Figure 7a shows the mechanism displacement along Z axis that has a minimum value \(-\)1.60 mm and a maximum value of 0.73 mm. Therefore, the reached displacement along Z can be considered negligible. \begin{table}
\begin{tabular}{c c} \hline \hline
**Mesh Type** & **Solid Mesh** \\ \hline Mesh type & Solid Mesh \\ Mesher Used & Curvature-based mesh \\ Jacobian points & 4 Points \\ Maximum element size & 36.376 mm \\ Minimum element size & 7.275 mm \\ Total Nodes & 552,744 \\ Total Elements & 355,186 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mesh information for FEM (Finite Element Method) analysis. Figure 7: _Cont._  
Figure 7b shows the computed stress that has a range between \(6.39\times 10^{-7}\) N/m\({}^{2}\) and \(4.45\times 10^{6}\) N/m\({}^{2}\). Therefore, the stress is very far from the yield limit of the material reported in Table 2. The stress results show that the structure is stiff and it can support the applied forces using light bars. Figure 7c shows the computed Factor Of Safety (FOS) check. The FOS values reach a minimum of 6.19 that can be seen in the red zones.