# 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
\begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter**Component** & **Joint R1** **Fx** & **Joint R1** **Fy** & **Joint R1** **Fz** & **Joint R1** **MAG** \\ \hline Min & \(-0.6321\) & \(-94.2472\) & \(-69.4304\) & 58.9881 \\ Max & 26.2981 & \(-54.6674\) & 8.8217 & 116.7565 \\ Avg & 11.9904 & \(-72.4773\) & \(-23.7857\) & 81.0712 \\ RMS & 15.3428 & 73.2824 & 34.1712 & 82.3006 \\ \hline \end{tabular}
\end{table} 
Table 13: Joint R1 connection force components. Figure 17: Connecting forces in rotational Joint R1: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Table 14 shows the values of the components of the connection forces as well as the resulting reaction in the kinematic joint R2 for the second case study. For the situation when the ParReEx robot is used by a patient and we consider the frictional forces in the kinematic joints, the following results are obtained for connecting forces in Joint C, as presented in Figure 19. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ParameterComponent** & **Joint R2 Fx** & **Joint R2 Fy** & **Joint R2 Fz** & **Joint R2 MAG** \\ \hline Min & \(-27.1507\) & \(44.5072\) & \(-34.8471\) & \(57.757\) \\ Max & \(10.8219\) & \(115.4258\) & \(31.153\) & \(119.6574\) \\ Avg & \(-9.6479\) & \(77.8998\) & \(-5.9878\) & \(83.4607\) \\ RMS & \(16.3354\) & \(79.8368\) & \(23.0639\) & \(84.6918\) \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Joint R2 connection force components. Figure 18: Connecting forces in rotational Joint R2: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. Table 15 shows the values of the components of the connection forces as well as the resulting reaction in the kinematic joint C for the second case study. For Joint A, the maximum RMS values increase from 108.2345 N in Case 1 (no joint friction) to 153.1624 N in Case 2 (with joint friction). Numerical simulation in ADAMS is performed for the manikin-robot rehabilitation assembly considering friction in the rotating joints. The connection forces in the joints have obvious increases compared to the previously studied cases because friction plays an important role in the real operation of the robot. Dynamic Analysis in MSC_ADAMS of the ParReEx-Wrist Robot Considering Flexible Elements and Joint Friction  
This subchapter is dedicated to the virtual dynamic study in ADAMS of the actuation moments and the connection forces in kinematic joints A, B, C, R1 and R2 considering \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ParameterComponent** & **Joint C** **Fx** & **Joint C** **Fy** & **Joint C** **Fz** & **Joint C** **MAG** \\ \hline Min & \(-\)38.152 & \(-\)226.9065 & 18.9705 & 39.0085 \\ Max & \(-\)2.303 & \(-\)32.8579 & 131.0045 & 264.6976 \\ Avg & \(-\)18.3145 & \(-\)101.217 & 58.4376 & 118.4064 \\ RMS & 21.8939 & 114.4402 & 66.0721 & 133.9455 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Joint C connection force components. Figure 19: Connecting forces in rotational Joint C: (**a**) in the x-direction; (**b**) in the y-direction; (**c**) in the z-direction; and (**d**) the resultant. friction in the kinematic joints and element flexibility, a case that simulates the real situation and is different from the first one, in which simplifying hypotheses have been used. This simulation assumption is necessary because, in operation, the robot elements deform, and this influences the dynamic operating parameters. The way to transform a rigid body into a deformable one in ADAMS involves:  
* Discretizing the body into finite elements and performing modal dynamics analysis, in which vibration modes are calculated based on modal superposition;
* Dynamic analysis considering the solid deformable body;
* Determination of torsional and flexural deformations of the flexible body. Table 16 shows the vibration modes of the flexible element, namely the circular guide.