# Soft Robotic Gripper with Chambered Fingers for Performing In-Hand Manipulation
## 2 Analysis of the Soft Actuator  
In this section, we have analyzed the influences of the longitudinal chamber's location and distance apart. Because the deformation characteristics of the actuator depends on the shape of the cross-section, the length of the actuator, and the elastic characteristic of the soft material, the non-linear finite element model is the most effective way to analyze the soft actuator [22]. As can be seen in Figure 1, we considered two different cross-section shapes: Round and trapezoid. The round cross-section is one of the common cross-sectional shape among soft actuators. The studies used round cross-section for their finger, when the finger consisted of a longitudinal single chamber or the chambers are located symmetrically around the central axis [13,23,24]. For the finger with a single chamber, the round cross-section is chosen, because the chambers are round themselves. When the chamber is inflated, it extracts the whole outer layer (finger wall) as well as the chamber wall inside layer of the finger. This removes the motion obstacle from the outer layer of finger. We chose the round cross-section as representative of the common shape of soft finger. The trapezoidal cross-section is chosen, assuming the larger contact surface with the object by making a flat surface on each side of the finger. Also, from the studies about the soft finger's cross-sectional shape, it is shown that the finger with a sharp edge performs the highest bending compared to the round cross-sectional shape [16,25]. Therefore, we selected the round and trapezoidal cross-sectional shape to investigate the most flexible motion when chambers are located asymmetrically. In each cross-section model, the chambers were located in two different styles: Equally separated from each other (symmetric) and unequally from each other (asymmetric). Each cross-section-shaped finger is investigated under four different distance sizes, including two different distance sizes on both symmetric and asymmetric locations. In total, eight different models are analyzed in this section. All eight models that are compared in FEM analysis have a height of 0.12 m and the base dimension, wall thickness are changed regarding different distances between the chambers, as shown in Figures 1-3. Figure 1: Cross-sectional views of the models and distances between chambers. Figure 2: Top view of the deformation results in ANSYS when the middle chamber is inflated: Round cross-section with symmetrically located chambers, with chamber distance values of 0.01 m and 0.014 m (**A value** 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 values** in the figure); trapezoidal cross-section with symmetrically located chambers, with chamber distance values of 0.01 m and 0.014 m (**A value** 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 values** in the figure). The figure contains the base dimensions of each cross-section. All the round cross-section 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. Every model has three longitudinal chambers. By inflating these three chambers in combination, the finger is able to make motions such as bending, grasping, and twisting, either sequentially or at the same time. But depending on the cross-section shape, the locations of the chambers, and the distance between chambers, the deformation direction and bending angle are all different. In our paper, we focused on the bending angle, which is the angle between the center of a fingertip and its initial position during inflation.