# Validation of Cable-Driven Experimental Setup to Assess Movements Made with Elbow Joint Assistance
## 3 Results
### Optimization of Anchor Positions
#### 3.1.1 Case 1: Performance of the Exosuit  
In a cable-driven exosuit, the anchor positions are typically embedded on a fabric-based structure worn by the user. Thus, the moments generated at the anchor positions essentially result in wear and tear of the fabric. Further, it causes deflections in anchor positions, leading to unbalanced forces during actuation. Therefore, it is crucial to minimize the resulting moments to improve the performance of the exosuit. So, we defined a minimization problem to reduce moments \(M_{A}\) and \(M_{C}\), with respect to anchor positions \(d_{1}\) and \(d_{2}\) as presented in Equation (17). It should be noted that the function of the exosuit is also affected by the wear and tear of cable along with anchor point attachments [42,43]. From the results presented in Figure 2b, the chosen cable is a nylon-braided cable, which has a longer lifespan among the tested cables. Hence, the failure of anchor point attachments alone is the considered parameter for studying the performance of the device. For optimization, at each joint position, using a gradient descent algorithm, the optimal \(d_{1}\) and \(d_{2}\) are identified  
Figure 7: (a–f) Surface plots of the simulated moment at the anchor position \(C\), by varying \(d_{1}\) 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 moment at \(C\) calculated using the experimentally recorded tension.  
between the bounds of 0.05 m and 0.15 m. Although, for a typical rehabilitation paradigm, the elbow range of motion varies from 80\({}^{\circ}\) to 120\({}^{\circ}\), the optimization is carried out for a full range of motion of a healthy individual, i.e., between 52\({}^{\circ}\) and 180\({}^{\circ}\)[38].  
\[\min\left(\left\|\overrightarrow{M_{A}}^{\rightarrow}\right\|+\left\| \overrightarrow{M_{C}}^{\rightarrow}\right\|\right)\right|_{(d_{1},d_{2})} \tag{17}\]  
Figure 8a shows the optimum positions of \(d_{1}\) and \(d_{2}\) for the chosen joint range of motion. It is observed that \(d_{2}\) converges towards the upper bound, implying the farthest position on the upper arm from the elbow joint for the complete range of motion. Additionally, \(d_{1}\) varies within the bounds. To comprehend the behavior of \(d_{1}\), we presented three schematics--refer to Figure 8b--which represents three different joint positions 55\({}^{\circ}\), 90\({}^{\circ}\), and 120\({}^{\circ}\). The green-colored cable in each schematic represents the optimal position of \(d_{1}\) on the forearm, while the red-colored cable represents non-optimal positions. From Figure 8b(I), at the optimal position, the cable and anchor point are aligned, resulting in a minimal moment at \(A\), which is not the case for the other two positions. At a 90\({}^{\circ}\) joint position, as shown in Figure 8b(II), at the optimal position, the cable becomes steeper when \(d_{1}\) is closest to the elbow, and hence, generates a lesser moment at anchor position \(A\), which is not the case for the other two positions. Further, at 120\({}^{\circ}\), as shown in Figure 8b(III), at the optimal position \(d_{1}\) which is farthest from the elbow, the minimum moment at \(A\) is reached as the cable tension is at its lowest--refer to Equation (10). This optimization was performed with a 0.5 kg load, and the trend remains consistent for other loads.