# A Parallel Robot with Torque Monitoring for Brachial Monoparesis Rehabilitation Tasks
## 2 Materials and Methods
### The Dynamic Analysis of ASPIRE  
As stated in the first section of the paper, a robotic system for physical rehabilitation should undergo a dynamic analysis to determine the behavior of the robotic structure during the rehabilitation procedure, hence this section extends the dynamic analysis previously presented in [37], with a series of properties regarding the components of the robotic structure. Each motion module of ASPIRE (the module for flexion/extension, the one for adduction/abduction and the one for pronation supination) is analyzed with respect to the composing components. By studying the dynamic behavior of each module using virtual simulation the required torque to perform different rehabilitation scenarios can be computed. Figure 3 presents the ASPIRE structure divided into rehabilitation modules. The mass of each module was computed using Siemens NX; the adduction-abduction module weighs 25.39 kg, the flexion-extension module weighs 18.25 kg, and the pronation-supination module weighs 1.29 kg. To analyze the dynamic behavior of each rehabilitation module a harmonic motion was used as input for each active revolute joint (Amplitude: 50\({}^{\circ}\), Frequency: 100 \({}^{\circ}\)/s) and the recorded torques of each joint are graphically represented. To achieve more accurate results, a simulated manikin was used during the simulation. For computing the biomechanical model of the patient Plagenhoef model [38] was used which defines standard man and women limb segments weights. The values for the upper limb extracted from [38] are given in Table 2. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Risk Factor** & **Associated Risk** & **Risk Overcome Measure** \\ \hline Wounds Skin diseases & Cannulas or wounds in anchor points may create discomfort during the rehabilitation & When the patient presents wounds over the anchor zones, bandage must be applied before attaching the rehabilitation device \\ \hline Overall poor health state & Pulmonary, respiratory, cardiovascular diseases may influence the effects of the rehabilitation. & When enrolling the physical rehabilitation, the patient must not have diseases that may obstruct the physical therapy. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 3: ASPIRE rehabilitation modules. For the virtual simulation max value of segments weights was used for each upper-limb segment (0.526 kg for hand weight, 1.519 kg for forearm segment, and 2.633 kg for upper arm segment); the virtual setup is displayed in Figure 4.  
The virtual manikin was defined using the above data and the position of the patient during the procedure was simulated. For the flexion-extension module, a 25-s simulation was carried on and the max torque obtained was 127.202 Nm while the minimum value was \(-\)13.231 Nm. Figure 5 represents the time-based torque variation during the simulation. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Segment** & \multicolumn{2}{c}{**Segment Weight**} \\ \hline  & Men & Woman \\ Hand & 0.526 kg & 0.306 kg \\ Forearm & 1.519 kg & 0.965 kg \\ Upper arm & 2.633 kg & 1.777 kg \\ \hline \end{tabular}
\end{table} 
Table 2: Weight of upper-limb segment according to Plagenhoef [39]. Figure 4: Virtual setup for simulation. Figure 5: Torques recorded during the flexion-extension module simulation. For the adduction-abduction module also a 25-s simulation was carried on and the max torque obtained was 5.040 Nm while the minimum value was \(-\)4.81 Nm. Figure 6 represents the time-based torque variation during the simulation. For the pronation-supination module the max torque obtained was 1.91 Nm while the minimum value was \(-\)1.89 Nm. Figure 7 represents the time-based torque variation during the simulation. The results obtained during the virtual simulation imply the use of quite big motors to perform the rehabilitation motion; to overcome this problem, gearboxes were used.