# Development, Experimental Assessment, and Application of a Vacuum-Driven Soft Bending Actuator
## 3 Experimental Results and Discussion
### Experimental Assessment of Angular Velocity-Bending Angle Characteristic
For the experimental assessment of the VSBA-2 with a 0.5 kg load, the maximum bending angle is \(\theta=90^{\circ}\), and a longer time was required to reach it (Figure S1b in the Supplementary Materials). For \(p=-0.8\) bar, the \(\theta=90^{\circ}\) was reached in 4.3 s, which is about 20% more time compared to the VSBA-2 without load. Additionally, at higher vacuum pressures, a linear bending angle-time relationship was observed up to approximately 66% of the maximum bending angle, with and without load. The experimental assessments for the VSBA-3, featuring larger rib spacing, are presented in Figure 6c and Table 2. The results once again confirm the advantage of larger rib spacing, which allows for a higher maximum bending angle of \(\theta=130^{\circ}\) in 2.1 s (\(p=-0.8\) bar), which is 40% shorter than the time required for the VSBA-2. Also, for vacuum pressures between \(-0.5\) and \(-0.7\) bar, shorter times were observed to reach the maximum angle in comparison with the VSBA-2. However, for vacuum pressures between \(-0.2\) and \(-0.4\) bar, the VSBA-3 was unable to reach maximum bending angle. An experimental result of the VSBA-3 with a 0.5 kg load demonstrated an operational dynamic similar to that without load. At \(p=-0.8\) bar, the same maximum bending angle of \(\theta=130^{\circ}\) was achieved after 4.5 s, which is about 55% more time compared to the case without a load (Figure S1c in the Supplementary Materials). The results of the laboratory assessments for the VSBA-4 are shown in Figure 6d and Table 2. As previously mentioned, among all the VSBAs made from heat-shrinkable material, the VSBA-4 achieves the largest bending angle of \(\theta=135^{\circ}\), taking 2.7 s to reach this angle at \(p=-0.8\) bar. Compared to the VSBA-2, the VSBA-4 achieves the maximum bending angle in 23% less time. Furthermore, it was observed that the VSBA-4 reaches 70% of its maximum bending angle in less than 0.5 s, representing performance not seen in previous actuator versions. This characteristic arises from the smaller surface area of the VSBA-4 exposed to airflow, which, according to the continuity equation, results in a higher velocity. Experimental measurements were also conducted on the VSBA-4 with a load of 0.1 kg, because the VSBA-4 could not overcome the 0.5 kg load. A similar dynamic  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{2}{c}{**VSBA-1**} & \multicolumn{2}{c}{**VSBA-2**} & \multicolumn{2}{c}{**VSBA-3**} & \multicolumn{2}{c}{**VSBA-4**} \\ \hline \(p\) (bar) & 0 (kg) & 0.5 (kg) & 0 (kg) & 0.5 (kg) & 0 (kg) & 0.5 (kg) & 0 (kg) & 0.1 (kg) \\ \hline \(-0.8\) & 140 & 135 & 120 & 90 & 130 & 110 & 135 & 90 \\ \hline \(-0.7\) & 140 & 135 & 120 & 90 & 130 & 90 & 120 & 70 \\ \hline \(-0.6\) & 140 & 135 & 120 & 75 & 130 & 70 & 100 & 60 \\ \hline \(-0.5\) & 140 & 135 & 120 & 45 as in the case without load was confirmed. At \(p=-0.8\) bar, a maximum bending angle of \(\theta=90^{\circ}\) was achieved in 2.4 s, which is about 12% more time compared to the unloaded case (Figure S1d in the Supplementary Materials). A linear angle-time relationship is observed up to an angle of \(30^{\circ}\) in both experiments, with and without load. Based on the achieved bending angle-time results, the relationship between angular velocity and bending angle was calculated. From the results obtained for the VSBA-1 (Figure 7a), it is evident that the maximum velocity of \(\omega=130^{\circ}/\)s is achieved at \(p=-0.8\) bar. Analyzing the velocity dynamics for all vacuum pressures reveals a sharp increase in velocity until it reaches its peak, after which the velocity gradually decreases as the VSBA-1 bends to its final position. For vacuum pressures ranging from \(-0.5\) bar to \(-0.8\) bar, the maximum velocities are achieved at an angle of \(\theta=30^{\circ}\), while for lower vacuum values, the maximum velocities are reached within an angle range of \(80^{\circ}\) to \(120^{\circ}\).