## 2 Materials and Methods
### Structure Design: Hydraulic Pressure Group  
A hydraulic system pumps oil to the hydraulic cylinders of the bench. In contains two gear pumps, with a nominal working pressure of 140 bar, and a maximal pressure of 180 bar. This hydraulic system allows a variation in the rotation speed of the mobile platform of the testing bench. The hydraulic system has been depicted in Figure 5a.  
Figure 4: Von [PERSON] stress on upper subset of the test bench.  
Figure 5: Hydraulic system installed in the test bench. (**a**) Complete system. (**b**) Detail of the hydraulic system, while a test of its correct operation is being carried out.  
Figure 3: Total deformation on upper subset of the test bench.  
The hydraulic cylinders that have been installed, model DGN250, present a rod diameter of 30 mm, a piston diameter of 50 mm, and a stroke length of 1000 mm. They have been installed with an angle of 10.3\({}^{\circ}\). These cylinders provide a net force of 27,480 N each, with a working pressure of 140 bar. The motion speed of the piston can be modified. The correct operation of the hydraulic system has been verified by a standard procedure. A picture of the hydraulic system checking is shown in Figure 5b.  
The thrust force (\(F_{t}\)) and the traction pressure (\(P_{t}\)) of each one of the hydraulic cylinders have been calculated as follows:  
\[F_{t}[\text{kg}]=A_{piston}[\text{cm}^{2}]\cdot P_{working}[\text{bar}]=\pi \cdot(2.5\text{ cm})^{2}\cdot 140\text{ bar}=2.75\;tn \tag{2}\]  
\[P_{t}[\text{kg}]=[A_{piston}[\text{cm}^{2}]-A_{rad}[\text{cm}^{2}]]\cdot P_{working }[\text{bar}]=\pi\cdot[(2.5\text{ cm})^{2}-(1.5\text{ cm})^{2}]\cdot 140\text{ bar}=1.75\;tn \tag{3}\]  
Both hydraulic cylinders produce a thrust force of 2.75 \(\times\) 2 = 5.5 \(tn\), which is enough to support the loads of the own weight of the upper platform, ATV-Quad and dummy (estimated at around 250-350 kg). A study of moments has been carried out for the validation of hydraulic cylinders. Figure 6 shows the acting forces and their point of application.  
Notice that \(F_{m}\) is the force applied by the ATV-Quad with the dummy mass, \(F_{t}\) is the thrust force exerted by the hydraulic cylinder, and \(F_{t,x}\) and \(F_{t,y}\) and their horizontal and vertical components, respectively. The variables \(dm\), \(dx\) and \(dy\) are the distances from the point of application of the forces to the pivot point of the platform. All these parameters have been depicted in Figure 6.  
Performing the balance of moments at the pivot point, it has been obtained Figure 7, where it can be observed that if the ATV-Quad (together with the dummy) is located at a distance \(dm\) = 2100 mm, the maximum mass that the latter could have it is 760 kg, and if it were located at the end of the platform (worst case), that is, \(dm\) = 3000 mm, the maximum mass of the ATV-Quad and dummy set could be up to 530 kg.  
Figure 6: Static analysis of moments at the pivot point.  
Figure 7: Maximum admissible mass of the ATV-Quad, dummy and upper platform as a function of the distance \(dm\).  
As the maximum mass of an ATV-Quad with the dummy and the upper platform is within the range of 530-760 kg, much more than the mass of ATV-Quad+dummy system, the hydraulic cylinders for this application are validated.