The differential equation, obtained as a result of the theoretical study of the movement of the bare seed on the surface of the grate of the saw gin, made it possible to determine the trajectory of the movement of the seed. The rib is one of the main working bodies of the saw gin. It serves for the free passage of the saw blades through it into the working chamber, for the withdrawal of the fiber caught on the saw teeth after separating it from the seed. A number of studies have been carried out to improve the working elements of the saw gin. The purpose of the research is to create the possibility of timely withdrawal of bare seeds from the working chamber of the saw gin by creating a concavity on the working surface of the grate. The use of the Euler equation for the movement of bare cotton seed along the grate contour, taking into account its speed V, density ρ , pressure P, made it possible to obtain a graph of seed distribution along the grate contour. An experimental 30-saw gin was developed and manufactured, the research carried out on it allowed to determine the rational parameters of new grates, which are recommended for introduction into production. The dependence of the location of the rectilinear part of the general contour on the shape of its convexity and concavity is determined. Based on the above equations, using separate functions, we present the view of the grate profile in the coordinate system modeled on the MAPLE-17 program.