# Validation of Cable-Driven Experimental Setup to Assess Movements Made with Elbow Joint Assistance
## 3 Results  
The variation in cable tension, \(\overrightarrow{T_{s}}\), reaction force at the joint, \(\overrightarrow{F}\), and the perceived moment at anchor points, \(\overrightarrow{M_{A}}\) and \(\overrightarrow{M_{C}}\), with respect to changes in the \(d_{1}\) and \(d_{2}\), are presented as surface plots in Figures 4-7. These plots are generated using Equations (7), (10) and (16), presented in the static model. Notably, \(d_{1}\) and \(d_{2}\) vary from 0.05 to 0.15 m, with two choices of joint angles, \(90^{\circ}\) and \(120^{\circ}\), and three choices of mass, \(m\), 0.5 kg, 1 kg, and 2 kg, which are considered while generating these surface plots. From the anthropometric data [38], the length of the upper arm and lower arm for an adult is between 0.27 m and 0.30 m. Considering the width of the arm, the closest position possible to attach an anchor point is 0.05 m from the elbow. Although the farthest position can be at the end of the arm, we have chosen a mid-way position of 0.15 m. Hence, the choice of the bounds of \(d_{1}\) and \(d_{2}\) are selected as 0.05 m and 0.15 m. [PERSON] et al. [41] showed that during the range of motion exercises in rehabilitation, the initial range of the exercises was limited to avoid extreme flexion or extension positions typically in the range of \(80^{\circ}\leq\theta\leq 120^{\circ}\). For the current experiment, \(90^{\circ}\) becomes the first point of interest as forces due to gravity are at a maximum and \(120^{\circ}\) becomes the second point of interest for safe flexion during rehabilitation [41]. Also, from the anthropometric data, the mass of the forearm for an adult (90 percentile) is about 2 kg [38], i.e., for most of the population, the weight of the forearm is less than 2 kg. Thus, the efforts in the experiment were studied at 0.5 kg, 1 kg, and 2 kg to simulate varying levels of forearm weight. The experiment is conducted at \(90^{\circ}\) and \(120^{\circ}\)--refer to Figure 1--with the loads of 0.5 kg, 1 kg, and 2 kg at various anchor positions, i.e., \(d_{1}\) and \(d_{2}\in\ [0.05,\ 0.15]\). The values of tension in the cable are recorded from the load cell display. The experimental values of the distances are \(AD=0.01\) m and \(CE=0.015\) m, and the masses are \(m_{f}=0.135\) kg and \(m_{lc}=0.015\) kg. The experimentally measured cable tension values, \(T_{sexp}\), and the simulated cable tension values, \(T_{s_{sim}}\), calculated using the static model, are compared and the corresponding % deviations are presented in Table 1. Evidently, both \(T_{s_{exp}}\) and \(T_{s_{sim}}\) are in close agreement. Figure 4 shows the surface plot of the magnitude of the cable tension, \(T_{s}\), with anchor point positions, \(d_{1}\) and \(d_{2}\). Figure 4a represents the tension plot at the joint position, \(\theta=90^{\circ}\), and a load of 0.5 kg. The tension in the cable, \(T_{s}\), is observed to be less when the anchor points; \(d_{1}\) and \(d_{2}\) are 0.15 m from the joint. This is because 0.15 m is the farthest position where the desired moment to hold the joint position can be generated with minimal cable tension. Furthermore, the plots in Figure 4b,c are in the same joint position, \(\theta=90^{\circ}\), but with an increased load of 1 kg and 2 kg, respectively. Noting that the tension value is proportional to the mass--refer to Equation (10)--we observe an increase in cable tension values in Figure 4b,c. Figure 4d shows the tension plot at joint position, \(\theta=120^{\circ}\) and a load of 0.5 kg. In particular, at \(\theta=120^{\circ}\), the surface plot follows a similar trend but with minor variations in tension values compared to the surface plot at \(90^{\circ}\). This is because the cable tension is the function of sine--refer to Equation (10)--in both \(90^{\circ}\) and \(120^{\circ}\) positions; we observe the corresponding variation in simulated and experimental tension values--refer to Table 1--as well as surface plots.