Problem statement. Mobile robotic systems are widely used in various fields of industry and social life: from small household appliances to large-size road-building machinery. Specific attention of scientists and designers is paid to the vibration-driven locomotion systems able to move in the environments where the use of classical wheeled and caterpillar robots is impossible or inefficient. Purpose. The main objective of this paper consists in generalizing the actual research results dedicated to various design diagrams and mathematical models of suspension systems of mobile vibration-driven robots. Methodology. The differential equations describing the robot motion are derived using the Lagrange-d'Alembert principle. The numerical modeling is carried out in the Mathematica software by solving the derived system of differential equations with the help of the Runge-Kutta methods. The verification of the obtained results is performed by computer simulation of the robot motion in the SolidWorks and MapleSim software. Findings (results). The time dependencies of the basic kinematic parameters (displacement, velocity, acceleration) of the robot’s vibratory system are analyzed. The possibilities of maximizing the robot translational velocity are considered. Originality (novelty). The paper generalizes the existent designs and mathematical models of the mobile vibration-driven robots’ suspensions and studies the combined four-spring locomotion system moving along a rough horizontal surface. Practical value. The obtained results can be effectively used by researchers and designers of vibration-driven locomotion systems while improving the existent designs and developing the new ones. Scopes of further investigations. While carrying out further investigations on the subject of the paper, it is necessary to solve the problem of optimizing the robot’s oscillatory system parameters in order to maximize its translational velocity.
[1] L. Jaulin, Mobile Robotics, 2nd ed. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2019. https://doi.org/10.1002/9781119663546
[2] 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, September 12–16, 2011, pp. 1–6.
[3] 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, Jun. 2018. https://doi.org/10.1007/S11012-017-0801-3
[4] I. Loukanov, V. Vitliemov, S. Stoyanov, and S. Stoyanov, “Design developments of vibration-driven robots,” in Proc. 56th Science Conference of Ruse University, Ruse, Bulgaria, 2017, pp. 50–59.
[5] R. M. Morariu-Gligor, A. V. Crişan, and F. M. Şerdean, “Optimal design of an one-way plate compactor,” ACTA TECHNICA NAPOCENSIS, vol. 60, no. 4, pp. 557–564, Nov. 2017.
[6] L. Crisóstomo, N. F. Ferreira, and V. Filipe, “Robotics services at home support,” International Journal of Advanced Robotic Systems, vol. 17, no. 4, pp. 1–11, 2020. https://doi.org/10.1177/1729881420925018
[7] K. Ragulskis et al., “Investigation of dynamics of a pipe robot with vibrational drive and unsymmetric with respect to the direction of velocity of motion dissipative forces,” Agricultural Engineering, vol. 52, pp. 1–6, 2020. https://doi.org/10.15544/ageng.2020.52.1
[8] Y. Yan, Y. Liu, L. Manfredi, and S. Prasad, “Modelling of a vibro-impact self-propelled capsule in the small intestine,” Nonlinear Dynamics, vol. 96, no. 1, pp. 123–144, 2019. https://doi.org/10.1007/s11071-019-04779-z
[9] B. Guo, Y. Liu, R. Birler, and S. Prasad, “Self-propelled capsule endoscopy for small-bowel examination: Proof-of-concept and model verification,” International Journal of Mechanical Sciences, vol. 174, Article ID 105506, 2020. https://doi.org/10.1016/j.ijmecsci.2020.105506
[10] V. 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, vol. 52, pp. 16–31, 2018. https://doi.org/10.23939/istcipa2018.52.016
[11] M. Schulke, L. Hartmann, and C. Behn, “Worm-like locomotion systems: development of drives and selective anisotropic friction structures,” in Proc. 56th International Scientific Colloquium “Innovation in Mechanical Engineering – Shaping the Future”, Ilmenau, Germany, September 12–16, 2011, pp. 1–21.
[12] V. Korendiy, “Dynamics of two-mass mobile vibratory robot with electromagnetic drive and vibro-impact operation mode,” Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 4, no. 2, pp. 80–93, 2018. https://doi.org/10.23939/ujmems2018.02.080
[13] V. Du Nguyen and N. T. La, “An improvement of vibration-driven locomotion module for capsule robots,” Mechanics Based Design of Structures and Machines, vol. 49, no. 7, pp. 1–15, 2020. https://doi.org/10.1080/15397734.2020.1760880.
[14] O. Lanets, O. Kachur, V. Korendiy, and V. Lozynskyy, “Controllable crank mechanism for exciting oscillations of vibratory equipment,” in Lecture Notes in Mechanical Engineering, pp. 43–52, 2021. https://doi.org/10.1007/978-3-030-77823-1_5
[15] V. Korendiy, V. Gursky, O. Kachur, V. Gurey, O. Havrylchenko, and O. Kotsiumbas, “Mathematical modeling of forced oscillations of semidefinite vibro-impact system sliding along rough horizontal surface,” Vibroengineering Procedia, vol. 39, pp. 164–169, 2021. https://doi.org/10.21595/vp.2021.22298
[16] G. Cicconofri, F. Becker, G. Noselli, A. Desimone, and K. Zimmermann, “The inversion of motion of Bristle Bots: analytical and experimental analysis,” in Parenti-Castelli V., Schiehlen W. (eds), ROMANSY 21 – Robot Design, Dynamics and Control. CISM International Centre for Mechanical Sciences (Courses and Lectures), vol. 569, Springer, Cham., 2016, pp. 225–232. https://doi.org/10.1007/978-3-319-33714-2_25
[17] D. Kim, Z. Hao, A. R. Mohazab, and A. Ansari, “On the forward and backward motion of milli-bristle-bots,” International Journal of Non-Linear Mechanics, vol. 127, Article ID 103551, 2020. https://doi.org/10.1016/j.ijnonlinmec.2020.103551
[18] D. W. Choi, C. W. Lee, D. Y. Lee, D. W. Lee, and H. U. Yoon, “A hybrid soft actuator inspired by grass-spike: Design approach, dynamic model, and applications,” Applied Sciences (Switzerland), vol. 10, no. 23, pp. 1–15, 2020. https://doi.org/10.3390/app10238525
[19] C. Hastings, K. Mischo, and M. Morrison, Hands-on Start to Wolfram Mathematica and Programming with the Wolfram Language, 2nd ed. Champaign, IL, USA: Wolfram Media, Inc., 2016.
[20] R. Müller, Modellierung, Analyse und Simulation Elektrischer und Mechanischer Systeme mit Maple und MapleSim [Modeling, Analysis and Simulation of Electrical and Mechanical Systems with Maple and MapleSim], 2nd ed. Wiesbaden, Germany: Springer Vieweg, 2020, (in German). https://doi.org/10.1007/978-3-658-29131-0
[21] K.-H. Chang, Motion Simulation and Mechanism Design with SOLIDWORKS Motion 2021. Mission, KS, USA: SDC Publications, 2021.