# Soft Robotic Gripper with Chambered Fingers for Performing In-Hand Manipulation
## 2 Analysis of the Soft Actuator
As previously mentioned, inflating the middle chamber will be used for grasping. We compared every model's bending angle around the \(Y\)-axis at given pressures from 25 kPa to 85 kPa. As the comparison plot indicates, the symmetrically located chambers led to a larger bending angle at a given pressure. Among all the models, the round cross-section finger with chamber distances of 0.01 m achieved the highest deformation. It started to bend from \(8^{\circ}\) at 25 kPa. For the asymmetrically located chambers, the round cross-section finger with chambers distance of 0.012 m and 0.02 m displayed the largest deformation. However, when the models with the asymmetric chambers are compared, it can be seen that those models have small differences from each other. These facts imply that if the finger is only used for grasping or bending along one axis, the finger with symmetrically located chambers is the most applicable. However, our final goal is to make a gripper for grasping and twisting, and for this reason, we had to investigate the effect of the side chamber's inflation. Next, we compared each model's deformation when the side chamber was inflated. As shown in Figure 3, when we applied pressure to the side chamber, the bending direction was different in each model depending on the cross-section shape and the location of chambers. The side chamber's inflation will be used for twisting motion, thus bending around the \(X\)-axis is the most crucial part in this part. With the round cross-section, the finger bent in the direction away from the inflated chamber. This shows that the round cross-section shape does not produce any obstacle to movement. But in the case of the trapezoidal cross-section, the bending direction differed in each case, based on the chambers' locations. In more detail, when the chambers in the trapezoid finger were located symmetrically around the central axis, most of the bending occurred around the Y-axis. In contrast, in the trapezoidal-shaped finger with asymmetric chambers, rotation occurred around the \(X\)-axis. The comparison plot of bending angle for every model's side chambers inflation determined that the \begin{table}
\begin{tabular}{c c} \hline
**Name** & **Coefficient Value (MPa)** \\ \hline C10 & 0.04 \\ C01 & \(-\)0.033 \\ C11 & \(1.2\times 10^{-3}\) \\ sse & \(8.26\times 10^{-3}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The incompressible hyperelasticity of the silicone, which is determined to be a third-order Mooney–Rivlin model. round cross-section with asymmetric chambers, which were separated by 0.012 m and 0.02 m, and the trapezoidal cross-section with chamber distances of 0.012 m and 0.02 m, exhibited the highest bending around the \(X\)-axis, as shown in Figure 4b. Regarding the distance from middle chamber to neutral axis, the deformation of the finger is formed. From the comparison plot of the middle chamber's inflation shown in Figure 4a, we conclude that the distance from the middle chamber to the neutral axis does not directly affect the bending performance. From Table 2, the distance of the round cross-section with symmetric chambers of 0.01 m showed the largest bending, which is the longest distance from the neutral axis among the round cross-section. Also, if we consider only the symmetric styles, the trapezoid cross-section with the shortest distance to the neutral axis performed the least bending. However, among the asymmetric styles, the round cross-section with distances of 0.006 m and 0.01 m from a neutral axis to the middle chamber and side chamber, respectively, showed the highest bending performance. Meanwhile, for the round cross-section with distances of 0.006 m and 0.008 m from a neutral axis to the middle chamber and side chamber, respectively, the finger bent with the smallest angle, as can be seen in Figure 4a. Figure 4: Comparison of finite element method (FEM) models: (**a**) Plot showing a comparison of the bending along the \(X\)-axis for each model, when the middle chamber was inflated.