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Worm-like motion enabled by changing the position of mass center in the anisotropic environment

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Abstract

The directional motion of a continuous worm induced by travelling the mass center of its body is studied in this paper. To this end, a new locomotion gait is constructed to derive the condition that the worm can move forward in one period. The interaction force between the worm body and environment is an anisotropic dry friction. The governing equation describing worm-like motion is firstly considered as a quasi-static case for a slow actuation history or for a larger friction. Then the solution of this equation is derived based on the specific form of the tension and its continuous distribution along the worm body. Furthermore, through the method of piecewise analysis of the motion, the expressions of the tension and the displacement along its body in each stage are specifically calculated. The net displacement over one period is further obtained. As a result, the condition that the directed motion of the worm can be effectively achieved. The results show that the worm can keep the body length unchanged by means of the given locomotion gait during the motion process.

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References

  1. Tanaka, Y., Ito, K., Nakagaki, T., Kobayashi, R.: Mechanics of peristaltic locomotion and role of anchoring. J. R. Soc. Interface 9, 222–233 (2012)

    Article  Google Scholar 

  2. DeSimone, A., Tatone, A.: Crawling motility through the analysis of model locomotors: two case studies. Eur. Phys. J. E 35(9), 1–8 (2012)

    Article  Google Scholar 

  3. DeSimone, A., Guarnieri, F., Noselli, G., Tatone, A.: Crawlers in viscous environments: linear vs non-linear rheology. Int. J. Non Linear Mech. 56, 142–147 (2013)

    Article  Google Scholar 

  4. Gidoni, P., Noselli, G., DeSimone, A.: Crawling on directional surfaces. Int. J. Non Linear Mech. 61, 65–73 (2014)

    Article  Google Scholar 

  5. Noselli, G., Tatone, A., DeSimone, A.: Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost. Mech. Res. Commun. 58, 73–81 (2014)

    Article  Google Scholar 

  6. Bolotnik, N., Pivovarov, M., Zeidis, I., Zimmermann, K.: On the motion of lumped-mass and distributed-mass self-propelling systems in a linear resistive environment. Zamm Z. Angew. Math. Mech. 96(6), 747–757 (2016)

    Article  MathSciNet  Google Scholar 

  7. Chernousko, F.L.: The optimal periodic motions of a two-mass system in a resistant medium. J. Appl. Math. Mech. 72(2), 116–125 (2008)

    Article  MathSciNet  Google Scholar 

  8. 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)

    Article  MathSciNet  Google Scholar 

  9. Bolotnik, N.N., Zeidis, I.M., Zimmermann, K., Ystsun, S.F.: Dynamics of controlled motion of vibration-driven system. J. Comput. Syst. Sci. Int. 45(5), 831–840 (2006)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Sorokin, K.S.: Motion of a mechanism along a rough inclined plane using the motion of internal oscillating masses. J. Comput. Syst. Sci. Int. 48(6), 993–1001 (2009)

    Article  MathSciNet  Google Scholar 

  12. Li, H., Furuta, K., Chernousko, F.L.: A pendulum-driven cart via internal force and static friction. In: Proceeings of Intermational Conference on Physics and Control, St.Petersburg, Russia, pp. 15–17 (2005)

  13. Fang, H.B., Xu, J.: Controlled motion of a two-module vibration-driven system induced by internal acceleration-controlled masses. Arch. Appl. Mech. 82(4), 461–477 (2012)

    Article  Google Scholar 

  14. Zimmermann, K., Zeidis, I., Pivovarov, M., Abaza, K.: Forced nonlinear oscillator with nonsymmetric dry friction. Arch. Appl. Mech. 77, 353–362 (2007)

    Article  Google Scholar 

  15. Zimmermann, K., Zeidis, I., Pivovarov, M.: Dynamics of two interconnected mass points in a resistive medium. Differ. Equ. Dyn. Syst. 21(1–2), 21–28 (2013)

    Article  MathSciNet  Google Scholar 

  16. Zimmermann, K., Zeidis, I., Pivovarov, M., Behn, C.: Motion of two interconnected mass points under action of non-symmetric viscous friction. Arch. Appl. Mech. 80(11), 1317–1328 (2010)

    Article  Google Scholar 

  17. Niebur, E., Erdös, P.: Theory of the locomotion of nematodes: dynamics of undulatory progression on a surface. Biophys. J. 60(5), 1132–1146 (1991)

    Article  Google Scholar 

  18. DeSimone, A., Gidoni, P., Noselli, G.: Liquid crystal elastomer strips as soft crawlers. J. Mech. Phys. Solids 84, 254–272 (2015)

    Article  MathSciNet  Google Scholar 

  19. Jiang, Z.W., Xu, J.: Analysis of worm-like locomotion driven by the sine-squared strain wave in a linear viscous medium. Mech. Res. Commun. 85, 33–44 (2017)

    Article  Google Scholar 

  20. Cochet-Escartin, O., Mickolajczyk, K.J., Collins, E.M.S.: Scrunching: a novel escape gait in planarians. Phys. Biol. 12(5), 056010 (2015)

    Article  Google Scholar 

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Acknowledgements

This project is supported by the Key Program of the National Natural Science Foundation of China under Grant No. 11932015. High-Level Personal Foundation of Henan University of Technology in No. 2019BS006 and Key Scientific Research Foundation of the Higher Education Institutions of Henan Province in No. 20B416001.

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Ziwang Jiang & Jian Xu

  2. Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai, 200092, China

    Jian Xu

  3. College of Science, Henan University of Technology, Zhengzhou, 450001, China

    Ziwang Jiang

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  1. Ziwang Jiang
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  2. Jian Xu
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Correspondence to Jian Xu.

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Jiang, Z., Xu, J. Worm-like motion enabled by changing the position of mass center in the anisotropic environment. Arch Appl Mech 90, 1059–1071 (2020). https://doi.org/10.1007/s00419-020-01661-y

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