# Soft Robotic Gripper with Chambered Fingers for Performing In-Hand Manipulation
## 2 Analysis of the Soft Actuator
In this stage, we optimized the most effective model for making bending and twisting motions. In this paper, a twisting motion is considered to be grasping the object and rotating it by a certain angle by inflating the side chambers. Therefore, we examined the bending angle during each chamber's inflation. We named the chamber that was equidistant from the other two chambers the middle chamber, and the other two chambers were designated side chambers, because those two chambers have the same performance on bending. We assumed that the middle chamber would be used for grasping and that the side chambers would be used for the twisting motion. Thus, to optimize the differences between the symmetric location and asymmetric location of the chambers and to check how it affected the finger's motion, we investigated the middle chamber's inflation and the side chamber's inflation, respectively. In this part, we focused on analyzing the geometry of the finger using the FEM method. To understand the behavior of the soft actuator, eight different models were analyzed and compared, based on the relationship between pressure and bending angle, by observing the effects of cross-sectional  
Figure 3: Top view showing the deformation results in ANSYS when a side chamber was inflated: Round cross-section with symmetrically located chambers, with chamber distance values of 0.01 m and 0.014 m (**A**) in the figure; round cross-section with asymmetric locations, with chamber distance values of 0.008 m, 0.016 m, 0.012 m, and 0.02 m (**a,b**) in the figure; trapezoidal cross-section with symmetrically located chambers, with chamber distance values of 0.01 m and 0.014 m (**A**) in the figure; trapezoidal cross-section with asymmetrically located chambers, with chamber distance values of 0.008 m, 0.016 m, 0.012 m, and 0.02 m (**a,b**) in the figure. The figure contains the base dimensions of each cross-section. All the round cross-sectioned models have a diameter of 0.026 m (**d**) and finger height of 0.12 m, while all the trapezoidal cross-sectioned fingers have a big base length of 0.035 m (**L**), a small base length of 0.025 m (**l**), and a leg length of 0.02 m (**h**). The deformation of each model is shown in the dark part and the dashed line represents the initial position of each finger. shape, the location of chambers, and the distance between chambers. As mentioned previously, we chose two different distance sizes for symmetric and asymmetric styles on each cross-sectional shape: 0.01 m and 0.014 m for symmetrically located chambers and the asymmetric chambers involves 0.008 m, 0.016 m, 0.012 m, and 0.02 m. The space of 0.014 m and 0.012-0.02 m was selected due to the minimum wall size of 0.0024 m. If the wall size was smaller than the minimum value, the finger will be easily damaged during high pressure. Also, the difference between each space distance is 0.004 m. The finger's bending motion started to be varied only when we change distance size by 0.004 m. Therefore, we chose the chamber distance sizes with wall size of 0.0024 m (at minimum) and by variance of 0.004 m.  
Figure 2 shows the deformations of all the models, which were formulated in ANSYS Workbench 19.2. In the finite element model, material nonlinearities must be considered in addition to geometry, especially for large deformations of a soft actuator. In the simulation, the material properties were set to be the same as Dragon skin 10 (Smooth-On Inc.), which was later used to make our proposed finger. According to the literature, the incompressible hyperelasticity of Dragon skin 10 is determined to be a third-order Mooney-Rivlin model with coefficients, as shown in Table 1[26]. Firstly, we investigated the middle chamber's inflation. Figure 2 shows the deformation results for all models when the middle chamber was inflated, which resulted in all fingers bending around the \(Y\)-axis. In other words, when we pressurized the middle chamber, all of the finger models bent in the opposite direction of inflated chamber.