Abstract
In rectilinear locomotion, snakes propel themselves by extending or contracting parts of the body. It is interesting that some large snakes will lift the activated part of the body during rectilinear motion. We hypothesize that snakes use this unique strategy named “lifting behavior" to improve the performance of rectilinear motion on a rough horizontal surface. The purpose of this paper is to examine our hypothesis by examining whether rectilinear motion benefits from lifting behavior. In this study, we derive equations to estimate the energy consumption of rectilinear motion on a simplified 4-link snake robot model. We consider not only mechanical energy dissipation but also heat energy loss during motion. A criterion of minimum energy loss is used as a candidate for the strategy to show how much lifting behavior improves energy efficiency. Our analysis provides a framework for theoretical analysis of the energy cost of rectilinear locomotion for snakes, which can help biologists to further understand the behaviors of snakes. This study also provides some new insights into rectilinear locomotion.
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References
Alexander, R., Jayes, A., Ker, R.: Estimates of energy cost for quadrupedal running gaits. J. Zool. 190(2), 155–192 (1980)
Arroyo, M., Heltai, L., Millán, D., DeSimone, A.: Reverse engineering the euglenoid movement. Proc. Natl. Acad. Sci. 109(44), 17874–17879 (2012)
Benham, P.P., Crawford, R.J., Armstrong, C.G.: Mechanics of Engineering Materials. Longman Harlow, Essex (1996)
Bogert, C.M.: Rectilinear locomotion in snakes. Copeia 4, 253–254 (1947)
Chernous’ ko, F.: The optimum rectilinear motion of a two-mass system. J. Appl. Math. Mech. 66(1), 1–7 (2002)
Chernousko, F.: Analysis and optimization of the rectilinear motion of a two-body system. J. Appl. Math. Mech. 75(5), 493–500 (2011)
Childress, S., Hosoi, A., Schultz, W.W., Wang, Z.J.: Natural Locomotion in Fluids and on Surfaces. Springer, Berlin (2012)
Cogger, H.G., Cameron, E., Sadlier, R., Eggler, P.: The action plan for Australian reptiles. Australian Nature Conservation Agency, Canberra (1993)
Curtin, N., Woledge, R.: Efficiency of energy conversion during shortening of muscle fibres from the dogfish scyliorhinus canicula. J. Exp. Biol. 158(1), 343–353 (1991)
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)
DeSimone, A., Tatone, A.: Crawling motility through the analysis of model locomotors: two case studies. Eur. Phys. J. E 35(9), 1–8 (2012)
DeSimone, A., Teresi, L.: Elastic energies for nematic elastomers. Eur. Phys. J. E 29(2), 191–204 (2009)
Erkmen, I., Erkmen, A.M., Matsuno, F., Chatterjee, R., Kamegawa, T.: Snake robots to the rescue!. IEEE Robot. Autom. Mag. 9(3), 17–25 (2002)
Figurina, T.Y.: Optimal motion control for a system of two bodies on a straight line. J. Comput. Syst. Sci. Int. 46(2), 227–233 (2007)
Gray, J.: The mechanism of locomotion in snakes. J. Exp. Biol. 23(2), 101–120 (1946)
Hatze, H., Buys, J.: Energy-optimal controls in the mammalian neuromuscular system. Biol. Cybern. 27(1), 9–20 (1977)
Hu, D.L., Nirody, J., Scott, T., Shelley, M.J.: The mechanics of slithering locomotion. Proc. Natl. Acad. Sci. 106(25), 10081–10085 (2009)
Kassim, I., Phee, L., Ng, W.S., Gong, F., Dario, P., Mosse, C., et al.: Locomotion techniques for robotic colonoscopy. IEEE Eng. Med. Biol. Mag. 25(3), 49–56 (2006)
Lissmann, H.: Rectilinear locomotion in a snake (Boa occidentalis). J. Exp. Biol. 26(4), 368–379 (1950)
Marvi, H., Bridges, J., Hu, D.L.: Snakes mimic earthworms: propulsion using rectilinear travelling waves. J. R. Soc. Interface 10(84), 20130, 188 (2013)
Marvi, H., Hu, D.L.: Friction enhancement in concertina locomotion of snakes. J. R. Soc. Interface 9(76), 3067–3080 (2012)
Mosauer, W.: On the locomotion of snakes. Science 76(1982), 583–585 (1932)
Nanua, P., Waldron, K.: Energy comparison between trot, bound, and gallop using a simple model. J. Biomech. Eng. 117(4), 466–473 (1995)
Nishii, J.: An analytical estimation of the energy cost for legged locomotion. J. Theor. Biol. 238(3), 636–645 (2006)
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)
Qiao, J., Shang, J., Goldenberg, A.: Development of inchworm in-pipe robot based on self-locking mechanism. IEEE/ASME Trans. Mechatron. 18(2), 799–806 (2013)
Secor, S.M., Jayne, B.C., Bennett, A.F.: Locomotor performance and energetic cost of sidewinding by the snake Crotalus cerastes. J. Exp. Biol. 163(1), 1–14 (1992)
Tanaka, Y., Ito, K., Nakagaki, T., Kobayashi, R.: Mechanics of peristaltic locomotion and role of anchoring. J. R. Soc. Interface 9(67), 222–233 (2012)
Zhou, X., Majidi, C., O’Reilly, O.M.: Energy efficiency in friction-based locomotion mechanisms for soft and hard robots: slower can be faster. Nonlinear Dyn. 78(4), 2811–2821 (2014)
Zimmermann, K., Zeidis, I.: Worm-like locomotion as a problem of nonlinear dynamics. J. Theor. Appl. Mech. 45(1), 179–187 (2007)
Zimmermann, K., Zeidis, I., Behn, C.: Mechanics of Terrestrial Locomotion: With a Focus on Non-pedal Motion Systems. Springer, Berlin (2009)
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This work were supported by the National Natural Science Foundation of China (No. 61233010), and the Shanghai Municipal Science & Technology Commission Project (No. 14DZ1110900, 15XD1501800).
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Tang, W., Xie, S., Li, H. et al. The influence of lifting behavior on energy efficiency in rectilinear locomotion. Arch Appl Mech 87, 1–13 (2017). https://doi.org/10.1007/s00419-016-1167-z
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DOI: https://doi.org/10.1007/s00419-016-1167-z