## 3 Results and Discussion  
### Influence of Compressed Air Supply Direction on BGD Power Characteristics  
We considered the default design of [PERSON] gripping devices with an arc nozzle (Figure 3) for the subsequent study. In the default design, with a vertical supply, compressed air passes through a conical insert and, through radial holes, enters the chamber of the gripping device, and with a horizontal supply, the compressed air directly enters the chamber of the gripper through the body of the gripper. In this study, we fixed certain parameters as constants: the radius of the gripping devices as \(r_{1}=30\) mm, the radius of the conical insert as \(r_{0}=15\) mm, the angle of the conical insert as \(\alpha=15\) deg, the width of the nozzle as \(h_{0}=0.06\) mm, and the diameter of the inlet hole of the fittings as \(d=8\) mm. We carried out numerical modelling in the environment of computing hydro- and gas-dynamics using Ansys-CFX with use of the SST of the \(\gamma\)-model of turbulence. To solve the problem of numerical modeling, final and differential grids were built in this software environment (Figure 4). The total number of nodes in the design area depends on the outer grip radius \(r_{1}\) and the height of the gap between the manipulation object and the grip \(h_{c}\). In order to ensure the adequate operation of the SST model and to simulate wall air flows, it is necessary that the minimum number of elements between the walls of the model is three. Therefore, the number of nodes lies within 0.9-3 million and the number of elements lies between 4.5 and 12 million for the range of distances between the BGD and OM \(h_{c}=0.1\) and 0.5 mm. The ideal gas from the program library is used during the simulation. The boundary conditions for two models of air flow are presented in Figure 5.  
Figure 4: Scheme follows the same formatting settlement grid of the final elements of the air flow at \(h_{c}=0.4\) mm. Figure 3: Diagram of compressed air supply directions through BGD chambers. Using the SonicTurbFoam solver (for turbulent streams of the compressed gases moving with sound and supersonic speeds), one can obtain the value of the distribution of teak, speed, and force over the surfaces of the studied model. For further analysis of the obtained results of modeling and theoretical research, the results of the pressure distribution on the surface of the object manipulation are shown in Figure 6.  
As seen in Figure 6, the vacuum in the area below the conical insert is greater for the horizontal pressure supply. The theoretical results of calculating the pressure distribution on the surface of the object under the conical insert are 2% less than the method obtained using the finite element (FEM), in which the gas-dynamic problems indicate their reliability. However, the mathematical model presented does not take into account the methods of supplying air to the chamber of the gripping devices, and so FEM in the Ansys-CFX software environment is later applied for research. In general, the Ansys-CFX tool has determined that the lifting force for a vertical supply of compressed air is 36.6 N and for horizontal, 37.7 N. To analyze the reason for the differences in lifting force in different directions of  
Figure 5: Extreme conditions for air flow models: (a) vertical inlet; (b) horizontal inlet. Figure 6: Pressure distribution on the surface of the object of manipulation in different directions of compressed air supply. supply of compressed air, the pressure distribution along the plane of symmetry of the gripping device in Figure 7 is considered. By observing the pressure distribution over the BGD symmetry plane, it is obvious that at in a vertical inlet (Figure 7a), the compressed air loses some of its energy in the act of leaking from the conical insert into the chamber of the gripping device. But, with a horizontal inlet (Figure 7b), the compressed air enters directly into the chamber of the gripping device and thereby provides more pressure inside.