Abstract
A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The motion of the system is excited by two identical unbalanced rotors based on the respective bodies. Major attention is given to the steady-state motion. A nearly-resonant excitation mode, when the angular velocities of the rotor are close to the natural frequency of the system, is considered. A set of algebraic equations for determining an approximate value of the average steady-state velocity of the entire system is obtained for the case of small friction. It is shown that control of the steady-state motion can be provided by changing the phase shift between the rotations of the rotors and the sign of the resonant detuning measured by the difference between the angular velocity of the rotors and the natural frequency of the system. By varying the phase shift one can control the magnitude of the average velocity, and varying the detuning enables one to change the direction of the motion.
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References
Chernousko, F.L.: The motion of a multilink system along a horizontal plane. J. Appl. Math. Mech. 64(1), 5–15 (2000)
Chernousko, F.L.: The wave-like motion of a multilink system on a horizontal plane. J. Appl. Math. Mech. 64(4), 497–508 (2000)
Chernousko, F.L.: The motion of a flat linkage over a horizontal plane. Dokl. Phys. 45(1), 42–45 (2000)
Chernousko, F.L.: The motion of a three-link system along a plane. J. Appl. Math. Mech. 65(1), 13–18 (2001)
Chernousko, F.L.: Controllable motions of a two-link mechanism along a horizontal plane. J. Appl. Math. Mech. 65(4), 665–677 (2001)
Smyshlyaev, A.S., Chernousko, F.L.: Optimization of the motion of multilink robots on a horizontal plane. J. Comput. Syst. Sci. Int. 40(2), 340–348 (2001)
Chernousko, F.L.: Snake-like locomotions of multilink mechanisms. J. Vib. Control 9(1–2), 237–256 (2003)
Sobolev, N.A., Sorokin, K.S.: Experimental investigation of snakelike motions of a three-link mechanism. J. Comput. Syst. Sci. Int. 45(5), 841–849 (2006)
Saito, M., Fukaya, M., Iwasaki, T.: Modeling, analysis, and synthesis of serpentine locomotion with a multilink robotic snake. IEEE Control Syst. Mag. 22(1), 64–81 (2002)
Figurina, T.Yu.: Quasi-static motions of a two-member linkage along a horizontal plane. Mech. Solids 38(1), 24–32 (2003)
Figurina, T.Yu.: Controlled quasistatic motions of a two-link robot on a horizontal plane. J. Comput. Syst. Sci. Int. 43(3), 481–496 (2004)
Figurina, T.Yu.: Quasi-static motion of a two-link system along a horizontal plane. Multibody Syst. Dyn. 11, 251–272 (2004)
Figurina, T.Yu.: Controlled slow motions of a three-link robot on a horizontal plane. J. Comput. Syst. Sci. Int. 44(3), 473–480 (2005)
Chernousko, F.L.: The optimum rectilinear motion of a two-mass system. J. Appl. Math. Mech. 66(1), 1–7 (2002)
Li, H., Furuta, K., Chernousko, F.L.: Motion generation of the capsubot using internal force and static friction. In: Proc. 45th. IEEE Conf. on Decision and Control, San Diego, CA, USA, pp. 6575–6580 (2006)
Vartholomeos, P., Papadopoulos, E.: Dynamics, design and simulation of a novel microrobotic platform employing vibration microactuators. Trans. ASME J. Dyn. Syst. Meas. Control 128, 122–133 (2006)
Breguet, J.-M., Clavel, R.: Stick and slip actuators: design, control, performances and applications. In: Proc. Int. Symp. on Micromechatronics and Human Science, Nagoya, Japan, pp. 89–95 (1998)
Schmoeckel, F., Worn, H.: Remotely controllable mobile microrobots acting as nano-positioners and intelligent tweezers in scanning electron microscopes (SEMs). In: Proc. IEEE Int. Conf. on Robotics and Automation, Seoul, Korea, pp. 3903–3913 (2001)
Chernousko, F.L.: On the motion of a body containing a movable internal mass. Dokl. Phys. 50(11), 593–597 (2005)
Chernousko, F.L.: Analysis and optimization of the motion of a body controlled by means of a movable mass. J. Appl. Math. Mech. 70(6), 819–842 (2006)
Chernousko, F.L.: Optimal periodic motions of a two-mass system in a resistive medium. J. Appl. Math. Mech. 72(2), 202–215 (2008)
Chernousko, F.L.: On the optimal motion of a body with an internal mass in a resistive medium. J. Vib. Control 14(1–2), 197–208 (2008)
Figurina, T.Yu.: Optimal control of the motion of a two-body system along a straight line. J. Comput. Syst. Sci. Int. 46(2), 227–233 (2007)
Bolotnik, N.N., Zeidis, I., Zimmermann, K., Yatsun, S.F.: Dynamics of controlled motion of vibration-driven systems. J. Comput. Syst. Sci. Int. 45(5), 831–840 (2006)
Sobolev, N.A., Sorokin, K.S.: Experimental investigation of a model of a vibration-driven robot with rotating masses. J. Comput. Syst. Sci. Int. 46(5), 826–835 (2007)
Bolotnik, N.N., Figurina, T.Yu.: Optimal control of the rectilinear motion of a rigid body on a rough plane by means of the motion of two internal masses. J. Appl. Math. Mech. 72(2), 126–135 (2008)
Zimmermann, K., Zeidis, I., Steigenberger, J., Huang, J.: An approach to the modelling of worm-like motion systems with a finite number of degrees of freedom. First Steps in Technical Realization. In: Proc. of the 4th International Conference of Climbing and Walking Robots, Karlsruhe, Germany, pp. 561–568 (2001)
Zimmermann, K., Zeidis, I., Pivovarov, M., Abaza, K.: Forced nonlinear oscillator with nonsymmetric dry friction. Arch. Appl. Mech. 77, 353–362 (2007)
Zimmermann, K., Zeidis, I., Steigenberger, J.: Mathematical model of worm-like motion systems with finite and infinite numbers of degrees of freedom, Theory and Practice of Robots and Manipulators. In: Proceedings of the 14th CISM–IFToMM Symposium (RoManSy 14), pp. 507–516 (2002)
Zimmermann, K., Zeidis, I., Naletova, V.A., Turkov, V.A.: Modelling of worm-like motion systems with magneto-elastic elements. Phys. Status Solidi 1(12), 3706–3709 (2004)
Zimmermann, K., Zeidis, I.: Worm-like locomotion as a problem of nonlinear dynamics. J. Theor. Appl. Mech. 45(1), 179–187 (2007)
Miller, G.: The motion dynamics of snakes and worms. Comput. Graph. 22(4), 169–173 (1988)
Steigenberger, J.: On a class of biomorphic motion systems. Faculty of Mathematics and Natural Sciences, Technische Universitaet Ilmenau, Preprint M 12/99 (1999)
Zimmermann, K., Zeidis, I., Behn, C.: Mechanics of Terrestrial Locomotion with a Focus on Nonpedal Motion Systems. Springer, Heidelberg (2009)
Zimmermann, K., Zeidis, I.: Locomotion systems based on vibration. In: RoManSy 17, Robot Design, Dynamics, and Control, Tokyo, Japan, pp. 51–59 (2008)
Bogolyubov, N.N., Mitropolski, Yu.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Gordon and Breach Science, New York (1961)
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This study was partly supported by the German Research Society (DFG) (projects Zi 540-12/1 and SFR 622) and the Russian Foundation for Basic Research (project 09-01-91330).
An erratum to this article can be found at http://dx.doi.org/10.1007/s11044-009-9166-2
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Zimmermann, K., Zeidis, I., Bolotnik, N. et al. Dynamics of a two-module vibration-driven system moving along a rough horizontal plane. Multibody Syst Dyn 22, 199–219 (2009). https://doi.org/10.1007/s11044-009-9158-2
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DOI: https://doi.org/10.1007/s11044-009-9158-2