The application of additive technologies, namely, fused deposition modeling, is a new reality for prototyping gripping devices of industrial robots. However, during 3D printing of holes and nozzle elements, difficulties arise with reducing their diameter. Therefore, this article conducts a comprehensive study of the Bernoulli gripping device prototype with a cylindrical nozzle, manufactured by fused deposition modeling 3D printing. The three main reasons for reducing the diameter of the gripper nozzle after printing were due to the poor-quality model, excessive extrusion of plastic in the middle of the arc printing path, and linear shrinkage of printing material after cooling. The proposed methodology consisted of determining the three coefficients that allowed the determination of the diameter of the designed nozzle. The use of air pressure distributions on the surface of the manipulation object, and lifting forces of gripping devices with different 3D printing layer heights were found. It was experimentally determined that as the height of the printing layer increased, the lifting force decreased. This was due to the formation of swirls due to the increased roughness of the grip surface. It was proven that as the height between the manipulation object and the grip increased, the effect of surface roughness on the lifting force decreased, resulting in an increase in the lifting force. Determination of the rational operating parameters of gripping devices manufactured by 3D printing from the point of view of maximum lifting force, were determined.