## 2 Materials and Methods  
### Actuator Design and Fabrication  
PneuNets actuators belong to the bellows actuator category, in which the specific bending movement is achieved by the deformation of the inner cavities. The actuator used benefits from a uniform bending movement over the entire surface, and it generally possesses the advantage of a fast response when pressurized, usually at low actuating pressure values. To achieve uniform deformation, the existing inextensible layer limits axial expansion during pressurization. Therefore, the bending motion is actively controlled during actuator pressurization. The internal pressures cause bending and lead to the production of mechanical energy while also accumulating elastic energy. As for the extension movement, it is passively controlled by different levels of pressurization as well as by the elastic energy accumulated by the actuator through bending movement, more precisely at the moment of pressurization. The choice of this type of actuator with this geometry was based on a number of advantages related to the simplicity of construction, low cost of realization, and meeting the needs of force and range of movement in the case of finger actuation, where the forces are relatively small. In addition, this type of configuration has proven over time to be the appropriate variant for such cases, receiving validation from the scientific community. The 3D design of the actuators was carried out in the SolidWorks 2021 software in two different lengths. The actuators were chosen to be made in two different lengths due to the different anatomical dimensions of the human fingers. The main dimensions of the actuator and its components can be found in Figure 2.  
The four elements that make up the actuator are the main body, through which the specific bending movement is achieved; two layers of silicone that enclose the main body;  
Figure 1: Principle diagram of actuation using PneuNets actuators. Figure 2: Cross-section with main dimensions of the actuator. and between these two 3 mm thick layers of silicone, there is an inextensible layer of paper inserted to limit the axial extension, helping to achieve the bending movement. The dimensions of the main body are l--8 mm, d--2 mm, t--2.5 mm, and b--15 mm. These sizes were determined by numerical and experimental finite element modelling in the section below. They are identical for all 5 actuators and, in addition to these dimensions, the actuators have a width of 20 mm, while the lengths are 95 mm for fingers 2 (index), 3 (middle), and 4 (ring), and 75 mm for fingers 1 (thumb) and 5 (little), respectively. These dimensions were determined experimentally, encompassing the DIP, PIP, and MCP joints at which the flexion/extension movement is performed. In the field of soft robotics, the most commonly used manufacturing processes are casting and 3D printing. In most situations, these two techniques are used collectively, with 3D printing being the technology for producing molds [29]. In this case, too, we have used casting as the main process to manufacture the actuators, and the molds were fabricated by 3D printing technology using polylactic acid (PLA) as the material. The 3 component molds needed to make the actuators were previously 3D modeled and 3D made using a Craft-Bot printer with a single extruder. The material from which the actuators were made is a two-component RTV ZA 22A silicone with a Shore hardness of A 22, composed of two elements A and B (base and catalyst), which are dosed in equal quantities. The specifications of this material are given in Table 1.  
The manufacturing process by casting is based on a rigorous realization process. Following the mixing of the two components, which have been weighed beforehand, in equal quantities, a series of air bubbles accumulate in the material, which, once they enter the actuator, can alter its behavior or, worse still, cause it to break during pressurization. Therefore, an intermediate process was carried out to remove the air bubbles utilizing a vacuum system.