# Validation of Cable-Driven Experimental Setup to Assess Movements Made with Elbow Joint Assistance
## 3 Results
Hence, for the range of flexion or extension between \(80^{\circ}\leq\theta\leq 120^{\circ}\), the effect of the joint position is minimal. Furthermore, the plots in Figure 4e,f have a load of 1 kg and 2 kg at \(\theta=120^{\circ}\), and reported an increase in the cable tension value due to the increase in mass. The discrete points shown in blue on the surface plots are the experimental cable tension values. Figure 5 shows the surface plot of the magnitude of the reaction force at the joint, \(F\), with the anchor point positions \(d_{1}\) and \(d_{2}\). Figure 5a represents the surface plot of the reaction force at the joint for the joint position, \(\theta=90^{\circ}\), and a load of 0.5 kg. The reaction force at the joint is calculated using the known cable tension values with Equation (7). As \(F_{x}\) and \(F_{y}\) are proportional to the cable tension--refer to Equation (7)--and the surface plot of reaction force, it can be seen that Figure 5 has a similar gradient as the surface plot of the cable tension--refer to Figure 4. Figure 5b,c show the surface plots of the reaction force at the joint at \(\theta=90^{\circ}\) for a load of 1 kg and 2 kg, respectively. The value of the reaction force increases with an increase in the load. Figure 5d-f are the surface plots of the reaction force at the joint for the joint position \(\theta=120^{\circ}\), with loads of 0.5 kg, 1 kg, and 2 kg, respectively. The surface plots at \(120^{\circ}\) exhibit the same trend as the surface plots at \(90^{\circ}\). Figure 4: (**a–f**) Surface plots of simulated tension, \(T_{s_{min}}\), with variations in anchor positions \(d_{1}\) and \(d_{2}\), at joint positions \(90^{\circ}\) and \(120^{\circ}\), and masses 0.5 kg, 1 kg, and 2 kg. Discrete dots along the surface plot represent the experimentally recorded tension, \(T_{s_{exp}}\) values. Figure 5: (**a–f**) Surface plots of the simulated reaction force at the elbow, with the variation in anchor position \(d_{1}\) and \(d_{2}\) at joint positions \(90^{\circ}\), and \(120^{\circ}\) and masses 0.5 kg, 1 kg, and 2 kg. Discrete dots along the surface plot represent the reaction force calculated using the experimentally recorded tension. Figure 6 shows the surface plot of the moment generated, \(M_{A}\), at the anchor point attachment \(A\) on the lower bar--refer to Figure 3--with the anchor point positions \(d_{1}\) and \(d_{2}\). Figure 6a is the surface plot of the moment at the anchor point attachment \(A\), with \(M_{A}\) at the joint position, \(\theta\) = 90\({}^{\circ}\), and a load of 0.5 kg. It is observed that \(M_{A}\) decreases along \(d_{2}\) and remains nearly similar along \(d_{1}\). From Equation (16), \(M_{A}\) depends on cable tension \(T_{s}\) and the attachment point \(A\). For the case of \(d_{2}\) = 0.05 m, the direction of \(\overrightarrow{DE}\) is nearly parallel to the lower bar and nearly perpendicular to \(AD\), for any value of \(d_{1}\)--refer to Figure 3--thus, the maximum moment is observed at this configuration. Now, \(\overrightarrow{DE}\) becomes steeper when \(d_{2}\) is moved from 0.05 m towards 0.15 m, for any \(d_{1}\), resulting in a decreasing moment. Figure 6b,c are the plots of the moment, \(\overrightarrow{M_{A}}\), at \(\theta\) = 90\({}^{\circ}\), and loads of 1 kg and 2 kg. With the increase in mass, \(T_{S}\) increases but the configuration will remain similar; thus, we observe an increase in \(M_{A}\) with a similar gradient. Figure 6d is surface plot for \(M_{A}\) at \(\theta\) = 120\({}^{\circ}\) for a load of 0.5 kg. Unlike Figure 6a, we observed a change in gradient along \(d_{1}\) also. The reason for this is that the \(\overrightarrow{DE}\) is always steeper for all possible \(d_{2}\)s as compared with the case of \(\theta\) = 90\({}^{\circ}\). Figure 6e,f are the surface plots of \(M_{A}\), at \(\theta\) = 120\({}^{\circ}\) and the loads of 1 kg and 2 kg, respectively. We observe a similar behavior in gradient as reported in Figure 6d.