# Research on Bifurcated Origami Hydraulic Dampers for Real Road Vibration Loads
## 2 Materials and Methods
### Bifurcated Origami Hydraulic Damper  
To efficiently apply origami hydraulic dampers in compact spaces, we propose a bifurcated origami hydraulic damper, as shown in Figure 3. A tube connects the main and branch origami dampers, allowing hydraulic oil to flow back and forth between them. Figure 3: Inner workings of bifurcated origami hydraulic damper. Figure 2: Conceptual diagram of the origami hydraulic damper. In addition, an orifice hole is placed at the end of the bifurcated origami hydraulic damper. Accompanying the expansion and contraction changes in the cylindrical origami structure, the origami hydraulic damper induces a damping effect when the hydraulic oil passes through the orifice hole. The damping effect of the origami hydraulic damper can be adjusted by changing the size of the orifice holes. In this study, we used polyethylene materials, which can be easily and quickly produced in the laboratory. The flat expansion view of the origami structure is shown in Figure 4. To achieve folding along the axial direction into a cylindrical origami structure with a closed circumference, it is essential to identify the inclination angles \(\theta_{1}\), \(\theta_{2}\), \(\theta_{3}\), and \(\theta_{4}\) of the folds based on the number of segments \(n\) in the origami structure, as shown in Figure 4. The subsequent segments are arranged in an equal isosceles trapezoid array. Given that all the angles are the same, we only need to determine the appropriate size of one angle. The conditions for folding are expressed by the following equation. \[\theta_{1}=\theta_{2}=\theta_{3}=\theta_{4}=\frac{\pi}{n} \tag{1}\]  
The one unit of origami structure folded is shown in Figure 5.  
To verify the characteristics of the bifurcated origami hydraulic damper depicted in Figure 3, an experimental setup was developed and analyzed, as shown in Figure 6. This validation setup included the main origami damper, the bifurcated origami damper, an elastic spring, a mass block, a frame, and a fixed plate. The validation experimental setup was structured as follows: First, in order to be easily and quickly produced, we used the transparent polyethylene cylinder sheet with a thickness of approximately 0.1 mm, as shown in Figure 6a, folded along the printing line to form a cylindrical origami structure. Moreover, the manufacturing process of the bifurcated origami hydraulic damper is the same as that in reference [28]. A trapezoidal acrylic sheet was attached to the side of the origami structure with an adhesive to further increase its rigidity. The finished origami structure damper film is shown in Figure 6b. An aluminum connector was attached to the end face of the collapsed polyethylene cylinder, as shown in Figure 6c, to obtain the origami hydraulic damper set. Furthermore, as shown in Figure 6d, the assembled hydraulic damper set was attached to a frame with  
Figure 4: Closing the one unit of cylindrical origami structure. Figure 5: The folded one unit of origami structure. four elastic springs to obtain a vibration model with elastic springs and the main origami hydraulic damper (Figure 6e). As shown in Figure 7, by fabricating bifurcated origami hydraulic tanks (Figure 7a) and mounting them on the frames of the bifurcated tanks (Figure 7b), a bifurcated origami hydraulic tank system (Figure 7c) was created by combining the two bifurcated hydraulic tanks. Figure 3:0 Main origami hydraulic damper device. (**a**) Polyethylene cylindrical tube. (**b**) Origami damper film. (**c**) Mian origami damper. (**d**) Spring frame. (**e**) Vibration test device. Figure 3:1 _Cont._  
Finally, As shown in Figure 7d, a fixed base was connected to the lower end of the assembled main origami hydraulic damper vibration model, an oil tube was connected to the lower end, and a bifurcated hydraulic oil tank was connected to the other end to validate the experimental system of the bifurcated origami hydraulic damper. In the actual measurement experiment, hydraulic oil was injected into the bifurcated origami hydraulic damper.