## 1 Introduction  
The current stage of robotics and gripping device development has led to an increase in the parameters that need to be considered when building handling operations [1; 2; 3; 4; 5; 6; 7]. A gripping device is one of the main components that depends on the type of object of manipulation [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 35; 36]. Some papers [9; 14; 16; 17; 20; 24; 26; 27; 28; 31; 35; 36] present methods of creating gripping devices for specific types of objects. In [10; 15; 18; 21; 22; 25; 29; 30; 31; 35; 37], work is widely carried out under the classification of gripping devices of industrial robots. The methods of recognition [19; 23], grasping [13; 18; 32; 33], and manipulation [8; 11; 12; 34] for different gripping devices vary greatly and depend on the object. Among all the gripping devices of industrial robots, pneumatic jet grippers have the greatest dependence on the input parameters of their power characteristics, which are not specified in their technical characteristics. The wrong choice in input parameters for capturing systems can critically influence the power characteristics and energy efficiency of the whole system. In addition, devices that use the power effect of a jet of air emanating from a shielded nozzle [38; 39; 40; 41; 42; 43; 44; 45; 46] are found in the automated production systems of a wide variety of applications. The nature of the interaction of the air jet with the load depends on many parameters, and the positive effects of such an interaction can be leveraged for various tasks, such as holding loads due to aerodynamic attraction and the contactless transportation of loads on an air cushion. Jet gripping devices using the aerodynamic attraction effect are becoming increasingly common, and hence these grippers are usually called Bernoulli gripping devices (BGD) [47]. In the designs of Bernoulli gripping devices of various companies (Festo, Aventies, Schmalz, SMC, and others), it is possible to supply pressure from two directions: vertically parallel to the gripping axis and horizontally perpendicular to the gripping axis (Figure 1). In addition, it is possible to connect fittings with different thicknesses of the hose and flow section, which will affect the flow and power characteristics of the BGD. However, the current literature about the performance of the BGD does not in any way describe the change in the characteristics of the gripping devices due to the parameters relating the compressed air inlet structures to the gripping chamber. Most studies conducted about grips of this type are associated with the optimization of parameters of the active surface and nozzle elements of Bernoulli gripping devices [40; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57]. Paper [48] identifies the need for a new range of end effectors suitable for non-rigid products, and it introduces a novel non-contact gripping device. Another area of research on Bernoulli gripping devices is the substantiation of modeling methods in different software environments [50; 51; 52; 53; 54] with changed parameters for the objects of manipulation. Such objects of manipulation include food [40; 54; 55] and organ tissue during laparoscopy [57]. This researched has allowed for an understanding a wide range of applications of gripping devices of this type. In [49], the advantages of the use of Bernoulli gripping devices in the transport and loading systems of automated production are discussed. The modeling of the dynamics of air flow in a nozzle and in a radial interval between the interacting surfaces of a Bernoulli gripper and an object of transportation is carried out. For this purpose, we use an average of a RANS equation of dynamics of viscous gas, an SST-model of turbulence, and a \(\gamma\)-model of laminar and turbulent transition. Options for the constructive improvement of a form of nozzle and conditions for the analysis of the energy efficiency of a Bernoulli gripper are offered.