## 3 Results and Discussion
### Impact of Internal Fitting Diameter on BGD Power Characteristics  
Since one of the main parameters affecting the power characteristics of a Bernoulli gripping device is its flow characteristics (L/min) [91], the internal diameter of the fittings, which throttle flow, can affect this particular indicator. Therefore, to investigate the effect of the inner diameter of the fitting on the power characteristics of a BGD, the main threaded connections used in the manufacture of BGDs are defined as 1/8, 1/4, 3/8, 1/2, M5, and M7. Usually, collet pneumatic fittings, which are manufactured by various companies, are used to supply compressed air (Metal Work [92], Camozzi Automation [93], Festo [94], SMC [95] and others). For all the above-mentioned companies, the collet fittings have a similar structure (Figure 9) in the given range of threads, and it is possible to use different pipe thicknesses (4, 6, 8, 10, and 12 mm) with different flow sections. As can be seen from the design of collet fittings (Figure 9), the smallest diameter of the through section is located at the place of twisting the fitting with a hexagon (SW1 (Figure 9a), H (Figure 9b), 1 (Figure 9c), and CH 4 (Figure 9d)). For different fitting threads, the diameter of the taper varies (2.5, 4, 5, 6, 7, and 8 mm), and they have an average length of 5 mm. As this narrowing can lead to throttling of the stream of compressed air, research on the influence of the parameters of narrowing the fitting on the power characteristics of a Bernoulli gripping device is carried out. The gap between the BGD and the OM at \(h_{c}\) = 0.25 mm ensures the maximum lifting force, with the system parameters \(r_{1}\) = 30 mm, \(r_{0}\) = 15 mm, \(\alpha\) = 15 deg, and \(h_{0}\) = 0.06 mm. To begin with, the influence of the input geometry on the power characteristics of a BGD is considered as follows: narrowing the fitting with a round diameter of 6 mm and a length of 5 mm, narrowing the fitting with a transition from 8 to 6 mm with a length of 5 mm, and narrowing the fitting with a transition from 8 to a hexagon with a diameter of 6 mm and a length of 5 mm (Figure 10). Figure 9: Designs of pneumatic collet fittings: (**a**) Camozzi Automation [93]; (**b**) SMC [95]; (**c**) Festo [94]; and (**d**) Metal Work [92]. From the graph shown in Figure 10, it is clear that the pressure distribution on the surface of the object of manipulation changes only in the range of 13 to 18 mm on the supply side of compressed air (Figure 11). The pressure jump on the surface of an OM (Figure 11) is presented at a radius of 15.5 mm due to an uneven supply of compressed air to the gripping device chamber. The lifting force of a BGD for narrowing the fitting of a round diameter of 6 mm results in 38.2892 N; for narrowing the fitting with a transition from 8 to 6 mm, it results in 38.281 N; and for narrowing the fitting with a transition from 8 to a hexagon with a diameter of 6 mm, it results in 38.2388 N. The difference in the lifting force of a BGD, which is dependent on the geometry of the narrowing of the fitting, is due to this jump in front of the nozzle on the supply side of compressed air. However, the difference in the lifting force for the narrowing in the form of a hexagon and a circle with a radius of 6 mm is 0.05 N, which can be neglected, and further research was done for a fitting with a narrowing of the cylindrical inlet from 8 mm to \(d\). Subsequently, we conducted a study of the effect of a diameter of \(d\) (2.5, 4, 5, 6, 7, or 8) mm narrowing of the fitting (with a  
Figure 11: Dependence of air pressure distribution on the surface of an OM at different parameters of the geometry of the narrowing of the fitting. Figure 10: Dependence of air pressure distribution on the surface of an OM at different parameters of the geometry of the narrowing of the fitting. horizontal inlet) for the supply of compressed air into the chamber of the gripping device at different inlet pressures (Figure 12).