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The article describes the areas of application of roller machines, trends in the development of their designs, research work on the modernization and creation of new roller machines. Special attention given to the roller machines with a variable center distance of the working shafts. The descriptions of the gear-lever differential transmission mechanisms created by authors are given. In particular, the correct applications of the created mechanisms in roller machines of six types are shown; they are 1. One of the working shafts has the ability to rotate around its own axis, and the second working shaft, in addition to rotation around its own axis, moves relative to the first working shaft along the line, passing through the center of the axes of rotation of both working shafts; 2. Both working shafts have the ability to rotate around their own axes and move symmetrically along a line passing through the same axes of rotation relative to each other; 3. One of the working shafts has the ability to rotate around its own axis, and the second working shaft, in addition to rotation around its own axis, moves relative to the first working shaft along an arc with a certain radius of curvature; 4. Both working shafts can rotate around their own axes and move symmetrically relative to each other along an arc with some symmetrical centers of rotation; 5. One of the working shafts has the ability to rotate around its own axis, and the second working shaft, in addition to rotation around its own axis, moves relative to the first working shaft along a complex trajectory; 6. Both working shafts can rotate around their own axes and move symmetrically relative to each other along a complex trajectory.

This article deals with the synthesis of a ten-link tooth-lever differential transmission mechanism. The article contains an analytical review of modern scientific research on the synthesis of tooth-lever differential transmission mechanisms of roller machines with a variable center distance of the working shafts; a method for the synthesis of toothlever differential transmission mechanisms of roller machines with a variable center distance of the working shafts described on the example of a ten-link tooth-lever differential transmission mechanism; the conditions for the synthesis of the mechanism given and substantiated when this mechanism is used in a roller machine; one of its working shafts has the ability to rotate about its own axis, and the second working shaft, in addition to rotation about its own axis, has the ability to move relative to the first working shaft along a line passing through the center the axes of rotation of both working shafts; the geometric synthesis of the tooth and lever contours of the mechanism, the dynamic synthesis of the mechanism, taking into account the angles of pressure between the lever link of the lever contour of the mechanism, which allows us to determine the optimal working position of the mechanism where the angles of pressure are within acceptable limits; the graphs of changes in the angles of pressure between the links of the lever contour of the mechanism, plotted depending on its position.