Acta Mechanica

, Volume 230, Issue 1, pp 105–120 | Cite as

Transient characteristics of a straight tube actuated by viscous compressible flow with consideration of large axisymmetric deformation

  • Min Zhang
  • Kai FengEmail author
  • Kai Zhang
  • Zilong Zhao
  • Yuanlong Cao
Original Paper


Advancements in soft materials and advantages brought by unlimited degrees of freedom have led to the wide acceptance of soft robotics in medical and military fields. Gas actuation has been widely adopted in soft robotics due to its low gas viscosity, high power density, and rapid response capability. Many researchers have developed kinematic models to investigate its free-form deformation. Nevertheless, serious challenges still remain. These challenges are related to the transient characteristics of a gas actuator subjected to inner fluid and external force. This paper presents a numerical study on the transient characteristics of a straight tube actuated with viscous compressible flow by taking compressibility of gas and large deformation of the tube wall into account. The equation governing compressible flow is coupled with equations governing wall elasticity deformation to generate an integrodifferential equation. The equation is solved with finite difference and Newton–Raphson methods to obtain the transient properties. The effect of fluid and structure parameters on the transient properties under sudden inlet pressure and external force is investigated. Predictions show that the propagation speed with the consideration of large tube deformation is larger than that without the consideration of large tube deformation. In addition, the propagation speed of pressure decreases as the tube wall thickness increases, while the radial impact and axial compression on tube help in the propagation speed of fluid pressure. These findings can lead to improved applications of gas actuation in soft robotics.


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  1. 1.
    Drossel, W.-G., Schlegel, H., Walther, M., Zimmermann, P., Bucht, A.: New concepts for distributed actuators and their control. In: Soft Robotics, pp. 19–32. Springer, New York (2015)Google Scholar
  2. 2.
    Marchese, A.D., Katzschmann, R.K., Rus, D.: A recipe for soft fluidic elastomer robots. Soft Robot 2(1), 7–25 (2015)CrossRefGoogle Scholar
  3. 3.
    Rus, D., Tolley, M.T.: Design, fabrication and control of soft robots. Nature 521(7553), 467–475 (2015)CrossRefGoogle Scholar
  4. 4.
    Park, Y.L., Chen, B.R., Majidi, C., Wood, R.J.: Active modular elastomer sleeve for soft wearable assistance robots. In: IEEE/RSJ International Conference on Intelligent Robots and Systems 2012, pp. 1595–1602. (2012)Google Scholar
  5. 5.
    Cianchetti, M., Ranzani, T., Gerboni, G., Nanayakkara, T., Althoefer, K., Dasgupta, P., Menciassi, A.: Soft robotics technologies to address shortcomings in today’s minimally invasive surgery: the STIFF-FLOP approach. Soft Robotics 1(2), 122–131 (2014)CrossRefGoogle Scholar
  6. 6.
    Park, Y.-L., Chen, B.-R., Pérez-Arancibia, N.O., Young, D., Stirling, L., Wood, R.J., Goldfield, E.C., Nagpal, R.: Design and control of a bio-inspired soft wearable robotic device for ankle-foot rehabilitation. Bioinspiration Biomim. 9(1), 016007 (2014)CrossRefGoogle Scholar
  7. 7.
    Kanno, T., Haraguchi, D., Yamamoto, M., Tadano, K., Kawashima, K.: A forceps manipulator with flexible 4-DOF mechanism for laparoscopic surgery. IEEE/ASME Trans. Mechatron. 20(3), 1170–1178 (2015)CrossRefGoogle Scholar
  8. 8.
    Mosadegh, B., Polygerinos, P., Keplinger, C., Wennstedt, S., Shepherd, R.F., Gupta, U., Shim, J., Bertoldi, K., Walsh, C.J., Whitesides, G.M.: Soft robotics: pneumatic networks for soft robotics that actuate rapidly. Adv. Funct. Mater. 24(15), 2109–2109 (2014)CrossRefGoogle Scholar
  9. 9.
    Marchese, A.D., Katzschmann, R.K., Rus, D.: Whole arm planning for a soft and highly compliant 2D robotic manipulator. In: IEEE/RSJ International Conference on Intelligent Robots and Systems 2014, pp. 554–560. (2014)Google Scholar
  10. 10.
    Vikas, V., Cohen, E., Grassi, R., Sözer, C., Trimmer, B.: Design and locomotion control of a soft robot using friction manipulation and motor-tendon actuation. IEEE Trans. Robotics 32(4), 949–959 (2016)CrossRefGoogle Scholar
  11. 11.
    Cao, Y., Shang, J., Liang, K., Fan, D., Ma, D., Tang, L.: Review of soft-bodied robots. Jixie Gongcheng Xuebao (Chin. J. Mech. Eng.) 48(3), 25–33 (2012)CrossRefGoogle Scholar
  12. 12.
    Polygerinos, P., Lyne, S., Wang, Z., Nicolini, L.F., Mosadegh, B., Whitesides, G.M., Walsh, C.J.: Towards a soft pneumatic glove for hand rehabilitation. IEEE Int. Conf. Intell. Robots Syst. 8215(2), 1512–1517 (2013)Google Scholar
  13. 13.
    Burgner-Kahrs, J.: Task-Specific Design of Tubular Continuum Robots for Surgical Applications. Springer, Berlin (2015)CrossRefGoogle Scholar
  14. 14.
    Shin, S.J., Chang, C.B., Sung, H.J.: Simulation of a valveless pump with an elastic tube. Int. J. Heat Fluid Flow 38(12), 13–23 (2012)CrossRefGoogle Scholar
  15. 15.
    Heil, M., Pedley, T.J.: Large axisymmetric deformation of a cylindrical shell conveying a viscous flow. J. Fluids Struct. 9(3), 237–256 (1995)CrossRefGoogle Scholar
  16. 16.
    Grotberg, J.B., Jensen, O.E.: Biofluid mechanics in flexible tubes. Ann. Rev. Fluid Mech. 36(1), 121–147 (2004)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Venkatesan, M., Ponnusamy, P.: Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section immersed in a fluid. Int. J. Mech. Sci. 49(6), 741–751 (2007)CrossRefGoogle Scholar
  18. 18.
    Djordjevic, V.D., Vukobratovic, M.: On a steady, viscous flow in two-dimensional collapsible channels. Acta Mech. 163(3), 189–205 (2003)CrossRefGoogle Scholar
  19. 19.
    Tuema, E.V., Ilegbusi, O.: Unsteady integrodifferential equation of fluid-structure interaction in constricted collapsible tube model of diseased human coronary artery. Int. J. Differ. Equ. 2012, 1687–9643 (2012)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Elbaz, S.B., Gat, A.D.: Dynamics of viscous liquid within a closed elastic cylinder subject to external forces with application to soft robotics. J. Fluid Mech. 758, 221–237 (2014)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Elger, D.F., Roberson, J.A.: Engineering Fluid Mechanics. Wiley, Hoboken (2013)Google Scholar
  22. 22.
    Elbaz, S.B., Jacob, H., Gat, A.D.: Transient gas flow in elastic microchannels. J. Fluid Mech. 846, 460–481 (2018)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers, vol. 2. McGraw-Hill, New York (1998)Google Scholar
  24. 24.
    Brown, F.T.: The transient response of fluid lines. J. Fluids Eng. 84(4), 547 (1962)Google Scholar
  25. 25.
    White, F.M.: Fluid Mechanics. McGraw-Hill Education, New York (2015)Google Scholar
  26. 26.
    Elbaz, S.B., Gat, A.D.: Axial creeping flow in the gap between a rigid cylinder and a concentric elastic tube. Physics 65, 580–602 (2015)zbMATHGoogle Scholar
  27. 27.
    Mollmann, B.: Introduction to the Theory of Thin Shells. Wiley, Hoboken (1981)zbMATHGoogle Scholar
  28. 28.
    Timoshenko, S.P., Woinowsky-Krieger, S.: Theory of Plates and Shells. McGraw-Hill, New York (1959)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaPeople’s Republic of China
  2. 2.State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanPeople’s Republic of China

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