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Instability regions of pneumatic artificial muscle actuator subject to direct and parametric excitations

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Abstract

The present work deals with a system attached to a mass and a Pneumatic Artificial Muscle (PAM) actuator with time-varying pneumatic pressure which results in a direct and parametrically excited system. The governing differential equation of motion is solved using the second-order method of multiple scales (MMS) and the closed-form equations are determined. With the help of these equations, the parametric instability regions have been studied for simple and principal parametric resonance conditions. The influence of different muscle parameters, damping, amplitude and frequency of the time-varying pressures on the instability regions are investigated and verify with the help of time response and phase portraits. This study can be useful for designers and researchers to get an idea about the critical values and safe operating range of different parameters of the PAM.

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References

  1. Schulte, H.: The Application of External Power in Prosthetics and Orthotics. The Characteristics of the McKibben Artificial Muscle, p. 874. National Research Council, Ottawa (1961)

    Google Scholar 

  2. Caldwell, D.G., Tsagarakis, N.: Biomimetic actuators in prosthetic and rehabilitation applications. Technol. Health Care 10(2), 107–120 (2002). https://doi.org/10.3233/THC-2002-10203

    Article  Google Scholar 

  3. Ferris, D.P., Czerniecki, J.M., Hannaford, B.: An ankle-foot orthosis powered by artificial pneumatic muscles. J. Appl. Biomech. 21(2), 189–197 (2005). https://doi.org/10.1123/jab.21.2.189

    Article  Google Scholar 

  4. Kalita, B., Narayan, J., Dwivedy, S.K.: Development of active lower limb robotic-based orthosis and exoskeleton devices: A systematic review. Int. J. Soc. Robot. (2020). https://doi.org/10.1007/s12369-020-00662-9

    Article  Google Scholar 

  5. Hannaford, B., Winters, J.M., Chou, C.P., Marbot, P.H.: The anthroform biorobotic arm: A system for the study of spinal circuits. Ann. Biomed. Eng. 23(4), 399–408 (1995). https://doi.org/10.1007/BF02584440

    Article  Google Scholar 

  6. Vermeulen, J., Verrelst, B., Vanderborght, B., Lefeber, D., Guillaume, P.: Trajectory planning for the walking biped ‘Lucy.’ Int. J. Rob. Res. 25(9), 867–887 (2006). https://doi.org/10.1177/0278364906069343

    Article  Google Scholar 

  7. Shin, D., Sardellitti, I., Park, Y.L., Khatib, O., Cutkosky, M.: Design and control of a bio-inspired human-friendly robot. Int. J. Rob. Res. 29(5), 571–584 (2010). https://doi.org/10.1177/0278364909353956

    Article  Google Scholar 

  8. Tondu, B., Ippolito, S., Guiochet, J.: A seven-degrees-of-freedom robot-arm driven by pneumatic artificial muscles for humanoid robots. Int. J. Rob. Res. 24(4), 257–274 (2005). https://doi.org/10.1177/0278364905052437

    Article  Google Scholar 

  9. Hošovský, A., Piteľ, J., Židek, K., Tóthová, M., Sárosi, J., Cveticanin, L.: Dynamic characterization and simulation of two-link soft robot arm with pneumatic muscles. Mech. Mach. Theory 103, 98–116 (2016). https://doi.org/10.1016/j.mechmachtheory.2016.04.013

    Article  Google Scholar 

  10. Robinson, R.M., Kothera, C.S., Sanner, R.M., Wereley, N.M.: Nonlinear control of robotic manipulators driven by pneumatic artificial muscles. IEEE ASME Trans. Mechatron. 21(1), 55–68 (2015). https://doi.org/10.1109/TMECH.2015.2483520

    Article  Google Scholar 

  11. De Volder, M., Moers, A.J., Reynaerts, D.: Fabrication and control of miniature McKibben actuators. Sens. Actuator A 166(1), 111–116 (2011). https://doi.org/10.1016/j.sna.2011.01.002

    Article  Google Scholar 

  12. Li, H., Kawashima, K., Tadano, K., Ganguly, S., Nakano, S.: Achieving haptic perception in forceps manipulator using pneumatic artificial muscle. IEEE ASME Trans. Mechatron. 18(1), 74–85 (2013). https://doi.org/10.1109/TMECH.2011.2163415

    Article  Google Scholar 

  13. Ashwin, K.P., Ghosal, A.: Static modeling of miniaturized pneumatic artificial muscles, kinematic analysis, and experiments on an endoscopic end-effector. IEEE ASME Trans. Mechatron. 24(4), 1429–1439 (2019). https://doi.org/10.1109/TMECH.2019.2916783

    Article  Google Scholar 

  14. Chou, C., Hannaford, B.: Measurement and modeling of McKibben pneumatic artificial muscles. IEEE ASME Trans. Robot. Autom. 12(1), 90–102 (1996). https://doi.org/10.1109/70.481753

    Article  Google Scholar 

  15. Tondu, B., Lopez, P.: Modeling and control of McKibben artificial muscle robot actuators. IEEE Control Syst. Mag. 20(2), 15–38 (2000). https://doi.org/10.1109/37.833638

    Article  Google Scholar 

  16. Hocking, E.G., Wereley, N.M.: Analysis of nonlinear elastic behaviour in miniature pneumatic artificial muscles. Smart Mater. Struct. 22(1), 1–14 (2013). https://doi.org/10.1088/0964-1726/22/1/014016

    Article  Google Scholar 

  17. Kothera, C.S., Jangid, M., Sirohi, J., Wereley, N.M.: Experimental characterization and static modeling of McKibben actuators. J. Mech. Des. 131(9), 1–10 (2009). https://doi.org/10.1115/1.3158982

    Article  Google Scholar 

  18. Aron, P.A., Anjel, M., Javier, A., Ramon, P., Joseba, L.: Modelling in Modelica and position control of a 1-DoF set-up powered by pneumatic muscles. Mechatronics 20(5), 535–552 (2010). https://doi.org/10.1016/j.mechatronics.2010.05.002

    Article  Google Scholar 

  19. Wickramatunge, K.C., Leephakpreeda, T.: Study on mechanical behaviors of pneumatic artificial muscle. Int. J. Eng. Sci. 48(2), 188–198 (2010). https://doi.org/10.1016/j.ijengsci.2009.08.001

    Article  Google Scholar 

  20. Kalita, B., Dwivedy, S.K.: Nonlinear dynamics of a parametrically excited pneumatic artificial muscle (PAM) actuator with simultaneous resonance condition. Mech. Mach. Theory 135, 281–297 (2019). https://doi.org/10.1016/j.mechmachtheory.2019.01.031

    Article  Google Scholar 

  21. Kalita, B., Dwivedy, S.K.: Dynamic analysis of pneumatic artificial muscle (PAM) actuator for rehabilitation with principal parametric resonance condition. Nonlinear Dyn. 97(4), 2271–2289 (2019). https://doi.org/10.1007/s11071-019-05122-2

    Article  Google Scholar 

  22. Kalita, B., Dwivedy, S.K.: Nonlinear dynamic response of pneumatic artificial muscle: A theoretical and experimental study. Int. J. Nonlin. Mech. 125, 103544 (2020). https://doi.org/10.1016/j.ijnonlinmec.2020.103544

    Article  Google Scholar 

  23. Kalita, B., Dwivedy, S.K.: Numerical investigation of nonlinear dynamics of a pneumatic artificial muscle with hard excitation. J. Comput. Nonlinear Dyn. 15(4), 041003 (2020). https://doi.org/10.1115/1.4046246

    Article  Google Scholar 

  24. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, Hoboken (1995)

    Book  Google Scholar 

  25. Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics—Analytical, Computational and Experimental Methods. Wiley, Hoboken (1995)

    Book  Google Scholar 

  26. Moon, F.C., Pao, Y.H.: Vibration and dynamic instability of a beam-plate in a transverse magnetic field. J. Appl. Mech. 36(1), 92–100 (1969). https://doi.org/10.1115/1.3564592

    Article  Google Scholar 

  27. Chen, C.C., Yah, M.K.: Parametric instability of a beam under electromagnetic excitation. J. Sound Vib. 240(4), 747–764 (2001). https://doi.org/10.1006/jsvi.2000.3255

    Article  Google Scholar 

  28. Pratiher, B., Dwivedy, S.K.: Parametric instability of a cantilever beam with magnetic field and periodic axial load. J. Sound Vib. 305(4–5), 904–917 (2007). https://doi.org/10.1016/j.jsv.2007.04.039

    Article  Google Scholar 

  29. Hyun, S.H., Yoo, H.H.: Dynamic modeling and stability analysis of axially oscillating cantilever beams. J. Sound Vib. 228(3), 543–558 (1999). https://doi.org/10.1006/jsvi.1999.2427

    Article  Google Scholar 

  30. Dwivedy, S.K., Sahu, K.C., Babu, S.: Parametric instability regions of three-layered soft-cored sandwich beam using higher-order theory. J. Sound Vib. 304(1–2), 326–344 (2007). https://doi.org/10.1016/j.jsv.2007.03.016

    Article  Google Scholar 

  31. Dwivedy, S.K., Mahendra, N., Sahu, K.C.: Parametric instability regions of a soft and magnetorheological elastomer cored sandwich beam. J. Sound Vib. 325(4–5), 686–704 (2009). https://doi.org/10.1016/j.jsv.2009.03.039

    Article  Google Scholar 

  32. Yang, H., Xiao, F., Xu, P.: Parametric instability prediction in a top-tensioned riser in irregular waves. Ocean Eng. 70, 39–50 (2013). https://doi.org/10.1016/j.oceaneng.2013.05.002

    Article  Google Scholar 

  33. Parker, R.G., Wu, X.: Parametric instability of planetary gears having elastic continuum ring gears. J. Vib. Acoust. 134(4), 041011 (2012). https://doi.org/10.1115/1.4005836

    Article  Google Scholar 

  34. Wu, H., Yang, J., Kitipornchai, S.: arametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates. Int. J. Mech. Sci. 135, 431–440 (2018). https://doi.org/10.1016/j.ijmecsci.2017.11.039

    Article  Google Scholar 

  35. Ashwin, K.P., Ghosal, A.: A survey on static modeling of miniaturized pneumatic artificial muscles with new model and experimental results. Appl. Mech. Rev. 70(4), 040802 (2018). https://doi.org/10.1115/1.4041660

    Article  Google Scholar 

  36. Wakimoto, S., Suzumori, K., Kanda, T.: Development of intelligent McKibben actuator. IEEE/RSJ Int. Conf. Intell. Robots Syst. (2005). https://doi.org/10.1109/IROS.2005.1545315

    Article  Google Scholar 

  37. Tondl, A., Nabergoj, R.: The effect of parametric excitation on a self-excited three-mass system. Int. J. Nonlin. Mech. 39(5), 821–832 (2004). https://doi.org/10.1016/S0020-7462(03)00057-X

    Article  MATH  Google Scholar 

  38. Nayfeh, A.H.: Perturbation Methods. Wiley, Hoboken (2008)

    Google Scholar 

  39. Luongo, A., Paolone, A.: On the reconstitution problem in the multiple time-scale method. Nonlinear Dyn. 19(2), 135–158 (1999). https://doi.org/10.1023/A:1008330423238

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank Dr. D. J. Bordoloi, Technical Officer, ME Dept., IIT Guwahati and Mr. Arunjoyti Borgohain, Yantrabot Technologies Pvt. Ltd. for their help to perform and complete the experimental work.

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  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Bhaben Kalita & Santosha K. Dwivedy

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  1. Bhaben Kalita
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Correspondence to Bhaben Kalita.

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Kalita, B., Dwivedy, S.K. Instability regions of pneumatic artificial muscle actuator subject to direct and parametric excitations. Arch Appl Mech 92, 2019–2039 (2022). https://doi.org/10.1007/s00419-022-02144-y

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