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.
 N. Bolotnik, I. Zeidis, K. Zimmermann, and S. Yatsun, "Vibration driven robots", in Proc. 56th International Scientific Colloquium “Innovation in Mechanical Engineering – Shaping the Future”, Ilmenau University of Technology, Ilmenau, Germany, 12–16 September 2011, pp. 1-6.
 I. Loukanov, V. Vitliemov, S. Stoyanov, and S. Stoyanov, “Design developments of vibration-driven robots,” in Proceedings of 56th Science Conference of Ruse University, 2017, pp. 50–59.
 T.-H. Duong, V.-D. Nguyen, and N.-T. La, “A new autogenous mobile system driven by vibration without impacts, excited by an impulse periodic force,” MATEC Web Conf., vol. 148, p. 04005, 2018.
 N. N. Bolotnik, I. M. Zeidis, K. Zimmermann, and S. F. Yatsun, “Dynamics of controlled motion of vibration-driven systems,” J. Comput. Syst. Sci. Int., vol. 45, no. 5, pp. 831–840, 2006.
 S. F. Yatsun, A. V. Razinkova, and A. N. Grankin, “Issledovanie dvizheniia vibrorobota s elektromagnitnym privodom” [“Investigation of the movement of a vibro-robot with an electromagnetic drive”], Izvestiia vysshikh uchebnykh zavedenii. Mashinostroenie [Proceedings of higher educational institutions. Mechanical Engineering], no. 10, pp. 53–64, 2007.
 A. N. Grankin and S. F. Yatsun, “Investigation of vibroimpact regimes of motion of a mobile microrobot with electromagnetic drive,” J. Comput. Syst. Sci. Int., vol. 48, no. 1, pp. 155–163, 2009.
 A. N. Grankin and S. F. Yatsun, “Issledovanie vibroudarnykh rezhimov dvizheniia mobilnogo mikrorobota s elektromagnitnym privodom” [“Study of vibro-impact movement modes of a mobile microrobot with an electromagnetic drive”]” Izvestiia Rossiiskoi akademii nauk. Teoriia i sistemy upravleniia [Proceedings of the Russian Academy of Sciences. Theory and systems of control], no. 1, pp. 163–171, 2009.
 K. A. Sapronov, A. A. Cherepanov, and S. F. Yatsun, “Investigation of motion of a mobile two-mass vibration-driven system,” J. Comput. Syst. Sci. Int., vol. 49, no. 1, pp. 144–151, 2010.
 Y. Yan, Y. Liu, J. Páez Chávez, F. Zonta, and A. Yusupov, “Proof-of-concept prototype development of the self-propelled capsule system for pipeline inspection,” Meccanica, vol. 53, no. 8, pp. 1997–2012, 2018.
 Y. Yan et al., “Optimization and experimental verification of the vibro-impact capsule system in fluid pipeline,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 233, no. 3, pp. 880–894, 2019.
 V. M. Korendiy, “Substantiation of parameters and motion modelling of two-mass mobile vibratory system with two unbalanced vibration exciters”, Avtomatizacìâ virobničih procesìv u mašinobuduvannì ta priladobuduvannì [Industrial Process Automation in Engineering and Instrumentation], no. 52, p. 71-80, 2018.
 V. Gursky, I. Kuzio, and V. Korendiy, “Optimal Synthesis and Implementation of Resonant Vibratory Systems,” Univers. J. Mech. Eng., vol. 6, no. 2, pp. 38–46, 2018.