In this article, the problem of mutual coverage between pairs of axes in improving the mechanical machining process in semi-finished machine axes is studied. In the research work, the movement of the base plate on which the semi-finished product is suspended at a constant speed was studied theoretically to operate a vertical shaft machine that mechanically handles the semi-finished product to the required standards.. In the article, the next process, i.e. the semi-finished hanging base plate, leaves the coverage area of the working axis pairs covered with the first elastic material and reaches the coverage area of the working axis pairs covered with a second elastic material, assuming that the forces acting on shafts capable of rapid movement, are to be taken into account. The problem posed in the thesis was solved by using Lagrange equations of the 2nd type and building differential equations based on the necessary parameters. The practical significance of the research is that vertical shaft machines serving mechanical processing of semi-finished products ensure the movement of support plates at a constant speed. In fact, the movement of the base plates at a constant speed will achieve high efficiency in the moisture compression process of semi-finished products.