# Analysis of Dynamic Behavior of ParReEx Robot Used in Upper Limb Rehabilitation
## 3 Dynamic Analysis in MSC.ADAMS of ParReEx-Wrist Robot
### Dynamic Analysis in MSC.ADAMS of the ParReEx-Wrist Robot Considering Joint Friction
Figure 22: Connecting forces in rotation Joint A computed with friction and flexible links: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Figure 23: Connecting forces in Joint B calculated assuming friction and flexible links: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Figure 24: Connecting forces in rotational Joint R1 in Case 3: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Table 20 shows the numerical results obtained for the components of the forces and the resulting reaction in joint R1 for simulation case 3. Figure 25 shows the laws of variation for the components of the connection forces in coupling R2 as well as for the resultant reaction, for the third simulation case. Table 21 shows the numerical results obtained for the components of the forces and the resulting reaction in joint R2 for simulation case 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter**Component** & **Joint R1 Fx** & **Joint R1 Fy** & **Joint R1 Fz** & **Joint R1 MAG** \\ \hline Min & \(-0.6319\) & \(-94.247\) & \(-69.4296\) & \(59.116\) \\ Max & \(26.2983\) & \(-54.7853\) & \(8.8217\) & \(116.7565\) \\ Avg & \(11.2983\) & \(-72.4702\) & \(-23.7732\) & \(81.0625\) \\ RMS & \(15.3456\) & \(73.4702\) & \(34.1647\) & \(82.2926\) \\ \hline \hline \end{tabular}
\end{table} 
Table 20: Joint R1 connection force components. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter**Component** & **Joint R2 Fx** & **Joint R2 Fy** & **Joint R2 Fz** & **Joint R2 MAG** \\ \hline Min & \(-27.1509\) & \(44.6085\) & \(-34.8469\) & \(57.8858\) \\ Max & \(10.8215\) & \(115.425\) & \(31.1528\) & \(119.6571\) \\ Avg & \(-9.6539\) & \(77.8865\) & \(-5.9965\) & \(83.4504\) \\ RMS & \(16.3394\) & \(79.8258\) & \(23.066\) & \(84.6827\) \\ \hline \hline \end{tabular}
\end{table} 
Table 21: Joint R2 connection force components. Figure 25: Connecting forces in rotational Joint R2 in Case 3: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Figure 28: Deformation of the center of mass of the circular guide: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Figure 27: Displacement of the center of mass of the circular guide: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Table 23 shows the numerical results obtained for the components and the resulting displacement of the marker attached to the center of mass of the circular guide. Table 24 shows the numerical results obtained for the components and the resulting deformations of the marker attached to the center of mass of the circular guide. A map of the specific strain distribution of the robot's circular guide is shown in Figure 29. These deformations have very small values, so this guide is designed with sufficient stiffness. Its mass can be reduced by structural stiffening, which will be discussed in the next paragraph.