# The Enhanced Adaptive Grasping of a Soft Robotic Gripper Using Rigid Supports
## 3 Design and Grasping Principles of the Proposed Gripper
### Soft Fingers  
Each chamber expands like a balloon. Large deformation of the chamber requires silicones that can withstand high stress, and Ecoflex-0030 and Ecoflex-0050 are applied in this work. The fabric at the bottom of the soft finger limits the stretching in the tangential and axial directions, which makes the upper side of the chamber grow longer in the axial direction than the lower side after the expansion in order to make the soft finger bend. FEM simulations are conducted to verify the grasping principle using the database of silicone materials [19]. Three groups of different distributions of silicones on one soft finger in 20 kPa (Table 1) are designed to show the effect of intrinsic mechanical properties of silicones on different parts of the soft gripper to improve the wrapping performance of the soft gripper. Figure 2: Designed soft robotic gripper with rigid supports. (**a**): The structure of the designed rigid supports; (**b**): released soft robotic gripper with rigid supports. The \"head\" part and the \"tail\" part are indicated in Figure 3(b1). The junctions between the fingers are selected as the zero point of the \(x\)-axis and the lowest point of the bending curve as the zero point of the \(y\)-axis to analyze the FEM results. The governing equations of the relative curvature value in Figure 3 are as follows:  
\[y=f(x) \tag{1}\]  
\[f^{\prime}=\frac{dy}{dx} \tag{2}\]  
\[f^{\prime\prime}=\frac{d^{2}y}{dx^{2}} \tag{3}\]  
\[K=\frac{\left|f^{\prime\prime}\right|}{\left(1+f^{\prime}\right)^{\frac{3}{2}}} \tag{4}\]  
where \(x\) and \(y\) are the relative displacement value from point \(O\) (Figure 3(a1,b1,c1)), and \(f\) is the fitting function between \(x\) and \(y\), and \(K\) is the relative curvature value. The original curve and the fitting curve are highly coincident (Figure 3(a2,b2,c2)). The governing equations of the relative curvature's variance in Table 1 are as follows:  
\[var=\frac{\sum_{j=0}^{n}\left|y_{j}-\frac{1}{n}\sum_{i=0}^{n}y_{i}\right|^{2}} {n} \tag{5}\]  
\[D_{max}=\max_{0\leq i\leq n}\left(\sqrt{D_{x}^{2}+D_{y}^{2}+D_{z}^{2}}\right) \tag{6}\]  
where \(var\) is the variance of relative curvature value, and \(D_{max}\) is the maximum total deformation in FEM. It is demonstrated in Table 1 that the silicone with a lower Young's Modulus contributes to wider range deformation, which makes the soft fingers have stronger wrapping ability but weaker strength. From Table 1, the variance of relative curvature value for the gripper with mixed silicones is the greatest, showing that applying different silicones in different parts of the gripper has a large impact on the deformation of the gripper. Comparing a1, b1, and c1 in Figure 3, it is obvious that the deformation in the x axis and the y axis are all different due to different values of Young's Modulus. The inflation of the \"head\" part (using rigid Ecoflex-0050) is smaller than that in the soft \"tail\" (Ecoflex-0030). The bending of the Ecoflex0050 part of group 2 is smaller than the same part of group 3, while it is larger than that of group 1, which is also reflected in the curvature (Figure 3(a3,b3,c3)). When applying different silicones in one finger, the intrinsic mechanical properties will be enhanced. The deformation of silicone with a smaller Young's Modulus is greater than usual, while the deformation of silicone with the greater Young's Modulus is smaller than usual, which has been verified in the following experiment (Section 3.3. Bending Performance Comparison). Therefore, by using Ecoflex-0050 in the \"head\" part and Ecoflex-0030 in the \"tail\" part, although the maximum total deformation is smaller, the contact area and the bending degree at the fingertip increase, which means more adaptive grasping.