*The purpose of research.* Substantiation of inertial, stiffness and excitation parameters of mechanical oscillatory system of mobile vibratory robot in order to maximize its motion speed. *Methodology.* The technique of the research is based on fundamental concepts of engineering mechanics and theory of mechanical vibrations. In order to deduce the differential equations of motion of the mechanical system of mobile vibratory robot the Lagrange second order equations were used. The computation modelling of the system’s motion caused by periodic excitation forces was carried out using MathCAD software. *Results.* The design diagram (model) of the two-mass mobile vibratory system with electromagnetic drive was constructed. The mathematical model of its motion was developed and the parameters of the resonance vibro-impact mode of its operation were substantiated. The steady-state and transient conditions of operation of the system under the influence of periodic excitation force of various magnitude were investigated. *Scientific novelty.* The structure of mobile vibratory device designed on the basis of two-mass oscillatory system with vibro-impact operation mode was substantiated. The differential equations of motion of the proposed system were set up taking into account the nonlinear stiffness characteristic of the elastic element connecting two oscillating bodies. The influence of the system’s excitation parameters on its motion speed was analysed. This allows to substantiate the rational magnitude and frequency of the excitation force. *Practical value.* The results of the carried-out investigations can be used while designing and developing control systems of mobile vibratory transporting and robotic devices in order to ensure the possibility of changing the speed of their motion without changing the inertial and stiffness parameters of their mechanical oscillating systems. *Scopes of further investigations.* While carrying out further investigations it is necessary to study the possibility of changing the nonlinearity of stiffness characteristic of the elastic element in order to change the kinematic parameters of the system’s motion. In addition, it is necessary to substantiate the mechanisms of changing the direction of motion of mobile vibratory robot.

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