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The article substantiates the rational design of the crank mechanism of a wheel-step mover. Kinematics analysis of a prototype of the wheel-step mover revealed the presence of oscillations in the vertical coordinate of the central axis during movement. To eliminate this drawback, differential geometry methods were used, thanks to which a method for calculating the non-circular profile of support shoes was created. Studies of the dynamics of the crank mechanism of the wheel-step mover showed that even in a steady state of motion, periodically acting inertial forces arise. To reduce their effect, non-circular gears should be used in the mover power drive. The dimensions of the crank mechanism links have been calculated, at which the cross-country ability of the running system, its kinematics and dynamics characteristics are improved, energy costs when laying a track are reduced, as well as the negative impact of the machine on the fertile soil layer. The polar coordinates of the involute points have been calculated. They are needed to construct the tooth profiles of non-circular gears. As the power drive of the crank mechanism, non-circular gears have symmetrical geometric parameters along two axes and provide a constant movement speed. Thus, the wheel-step running system can be used in agriculture, the timber industry, mining, and when working in emergency situations. The mover design being developed is intended for unmanned ground vehicles. This type of unmanned vehicles is at the initial stage of its development, inferior in frequency to air and marine unmanned vehicles. A targeted concentration of production and financial resources is necessary to ensure that domestic industry has a leading position in the production and sale of unmanned ground vehicles.