# NURSE-2 DoF Device for Arm Motion Guidance: Kinematic, Dynamic, and FEM Analysis
## 4 Dynamic Analysis  
The feasibility of the suggested linkage mechanism was evaluated by a dynamic analysis using ADAMS solver within SolidWoks software (version 2018, Dassault Systemes, S.A., Suresnes, Francia) simulating the mechanism performs the exercise path showed in Figure 2 in Section 2. In the simulation setting, a 1060 aluminium alloy has been used for the mechanism links. Table 2 shows the assumed characteristics of the chosen material. The parameters of friction and gravity force are shown in Table 3. The simulation considers an integrator step size of \(1.0\times 10^{-4}\), with a maximum value of \(1.0\times 10^{-1}\) and a minimum value of \(1.0\times 10^{-11}\), 800 frames per seconds and an accuracy of \(1.0\times 10^{-9}\). A time of 8 seconds is required to perform the selected exercise path as reported in [24]. Considering the average weight of the upper limb [25,33], a force of 37 N has been applied in the amplified tracing point of the mechanism (Point \(F\) in Figure 3 in Section 3) perpendicular to the working plane (Z axis). It is important to note that the amplified tracing point of the mechanism (Point \(F\) in Figure 3 in Section 3) must track the desired exercise path showed in Figure 2, Section 2. It is important to note that in this dynamic analysis the motors of the mechanism are simulated using the trend of velocities required to perform the trajectory to trace the number 8 as the input parameter, see Figure 5a. The dynamic analysis outcomes are the torque, angular displacement, and angular acceleration required by the simulated motors to perform the prescribed trajectory. Angular displacement, angular acceleration and torque obtained from the dynamic analysis are shown in Figure 5b-d, respectively. Table 4 shows the results for motor 1 obtained from the dynamic analysis as well as the maximum and minimum velocity used as input for motor 1. Table 5 shows the results for motor 2 obtained from the dynamic analysis as well as the maximum and minimum velocity used as input for motor 2. The dynamic simulation outcomes allow to choose the motors for the mechanism construction and to check the efficient operation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Value** & **Units** \\ \hline Elastic Modulus & \(6.90\times 10^{10}\) & N/m\({}^{2}\) \\ Poisson’s Ratio & 0.33 & N/A \\ Shear Modulus & \(2.70\times 10^{10}\) & N/m\({}^{2}\) \\ Mass Density & 2 700 & kg/m\({}^{3}\) \\ Tensile Strength & \(6.89\times 10^{7}\) & N/m\({}^{2}\) \\ Yield Strength & \(2.76\times 10^{7}\) & N/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of 1060 Aluminum alloy. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Description** & **Value** & **Units** \\ \hline \(\
u_{k}\) & Dynamic friction velocity & 10.16 & mm/s \\ \(\mu_{k}\) & Dynamic friction coefficient & 0.20 & N/A \\ \(\
u_{s}\) & Static friction velocity & 0.10 & mm/s \\ \(\mu_{s}\) & Static friction coefficient & 0.25 & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Body contact parameters for the simulation. Referring to Figure 5, and the numerical values reported in Tables 4 and 5, the angular displacements present a symmetric mechanism performance and the computed accelerations and torques values confirm the possibility to use inexpensive commercial motors. The proposed mechanism has a satisfactory behaviour in achieving the desired objective since it presents a smooth motion and limited torque (referring to plots in Figure 5). Therefore, according to the design and operations requirements, the proposed mechanism can be considered a feasible design to assist the human arm exercises.