Aim. The simulation of work for gear transmission with variable gear ratio for machines with technological purpose, which are consist of established spur gear with an eccentricity. Method. The investigations were carried out by the kinematic analysis methods of classical mechanics, analytic geometry, and the theory of the gearing. Results. There were obtained the correlations that present the functioning of the spur gear with variable gear ratio, in which cylindrical wheels are used. Moreover, these cylindrical wheels are established with an eccentricity. There were designed the mathematic models of the influence for the angle of rotation for driving gear wheel to the change the angle of rotation and the angular velocity of the output gear for the multi-pair gear transmission of variable gear ratio. There were proposed to use two identical cylindrical gears with eccentricity, which are established in pairs, instead of elliptical wheels, to increase the technological level of production for the gears with variable gear ratio. Furthermore, there were proposed to use the cylindrical gear wheels that were manufactured with displacement, to ensure the efficiency of the gear transmission. Normal coefficient of profile shift must be identical for the gear wheels of the transmission and it has to have a negative value. The gear wheels should be used with an odd number of teeth. Scientific novelty. There were carried out that the cylindrical gear wheels in gear transmission, which are eccentrically established, have elliptical centroids. There were determined an important characteristic of the gear transmission that is consist of two identical eccentrically mounted cylindrical gear wheels. It is that in any angular position of gear wheels, a straight line, which connects the centers of pitch diameters for gear wheels pass through the point that divides the centerline of the gear transmission in half. There were proposed to use the procedure of differentiation of implicit functions to determine the ratio between the input and output angular velocities. There were obtained the mathematical models that determine the variable angle of rotation of the output gear wheel, variable gear ratio of multi-pair transmission and an equation of elliptical centroids of eccentrically mounted cylindrical gear wheels in parametric and canonical forms. Practical significance. The developed scientifically-reasonable recommendations for the practical use of gear transmission with variable gear ratio, which are composed of one or more pairs of identical cylindrical gear wheels that are mounted in transmission with an eccentricity, for full realization of the functional capabilities of machines of technological purpose that appears in work cycles with uneven movements of their actuators.
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