# Pneumatic Soft Actuator with Anisotropic Soft and Rigid Restraints for Pure in-Plane Bending Motion
## 2 Design, Material, and Fabrication  
### Structural Design and Analysis  
The in-plane bending actuator with anisotropic soft and rigid restraints (2D-PSA) was composed of two parts, as shown in Figure 1. One part included the anisotropic soft and rigid restraints, which consisted of intertwining fiber and a 2D-following chain. The other part was the soft matrix, which was made of a rubber compound named Ecoflex 0030 (Smooth-On Inc., Macungie, PA, USA).  
A soft matrix has an air cavity enveloped by expanding and non-expanding layers to fulfill the requirements for a common bending motion [12, 19, 20]. However, a common bending motion can be distorted when out-of-plane forces are applied. With the aim of achieving pure in-plane bending motion, a previously-published mechanical programming design method [20, 21] is referenced and improved in this study.  
First, the pure in-plane bending motion was specified by two norms.  
Norm I: Pure in-plane bending without out-of-plane distortion external to the plane, such as twisting;  
Norm II: Only axial, but non-radial inflation of the soft matrix is allowed.  
To meet Norm I, a serial 2D-following chain, which consisted of a set of rigidly-connected hinges, was buried inside the non-expanding layer matrix. The 2D-following chain acted as a rigid restraint for 2D-PSA, as shown in Figure 2. Each section of the 2D-following chain had three degrees of freedom: translations along the x- and y-axes and rotation around the z-axis. In other words, translation along the z-axis and rotations around the x- and y-axes were restrained. The mechanism of the 2D-following chain reserved certain degrees of freedom for in-plane bending and restrained other degrees of freedom to avoid out-of-plane distortion. Furthermore, the inextensibility of the 2D-following chain restrained elongation of the soft matrix to form a non-expanding layer.  
To meet Norm II, intertwining fiber was buried inside the expanding layer matrix. The intertwining fiber acted as a soft restraint for 2D-PSA. It was a 3D structure that was woven as an intertwining net, whose pattern was a compressed rhombus along the axial direction. Then, the intertwining net allowed the expanding layer to elongate in the axial direction, but restrained the expanding layer from enlarging in the radial direction. There was still some slight enlarging  
Figure 1: Conceptual diagram of a smart soft actuator with anisotropic soft and rigid restraints.  
in the radial direction, but we neglected it. As shown in Figure 3, the structure of the intertwining fiber maintained all DOFs except for elongation in the tangent direction of the lines. The dense grids ensured that the matrix in the expanding layer did not easily burst when it was inflated. As a result, the actuator was able to tolerate higher air pressure so that a larger bending angle and greater force could be realized.  
Two air cavities that were symmetrical with respect to the 2D-following chain were included in the design to achieve in-plane bidirectional bending. When one air cavity was inflated and the other was not, 2D-PSA was able to bend to one side. It bent to the other side when the second cavity was inflated and the first one was deflated.  
Overall, because of the 2D-following chain, intertwining fiber, and symmetrical soft matrix, 2D-PSA gained an anisotropic structural feature (as shown in Figure 1) to achieve pure in-plane bending.