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Dynamic analysis of impact in swing-through crutch gait using impulsive and continuous contact models

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Abstract

The dynamics associated with the impact of the crutch with the ground is an important topic of research, since this is known to be the main cause of mechanical energy loss during swing-through gait. In this work, a multibody system representing a subject walking with crutches is used to investigate the behavior of two different contact models, impulsive and continuous, used for impact analysis. In the impulsive (discrete) approach, the impact interval is considered to be negligible and, therefore, the system configuration is constant. The postimpact state is directly obtained from the preimpact one through algebraic equations. In the continuous approach, the stiffness and dissipation characteristics of the contact surfaces are modeled through nonlinear springs and dampers. The equations of motion are integrated during the impact time interval to obtain the postimpact state, which, in principle, can differ from that obtained by means of the impulsive approach. Although both approaches have been widely used in the field of biomechanics, we have not found any comparative study in the existing literature justifying the model chosen for impact analysis. In this work, we present detailed numerical results and discussions to investigate several dynamic and energetic features associated with crutch impact. Based on the results, we compare the implications of using one contact model or the other.

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References

  1. Jaspers, P., Peeraer, L., Van Petegem, W., Van der Perre, G.: The use of an advanced reciprocating gait orthosis by paraplegic individuals: A follow-up study. Spinal Cord 35, 585–589 (1997)

    Article  Google Scholar 

  2. Noreau, L., Richards, C.L., Comeau, F., Tardif, D.: Biomechanical analysis of swing-through gait in paraplegic and non-disabled individuals. J. Biomech. 28, 689–700 (1995)

    Article  Google Scholar 

  3. Requejo, P.S., Wahl, D.P., Bontrager, E.L., Newsam, C.J., Gronley, J.K., Mulroy, S.J., Perry, J.: Upper extremity kinetics during Lofstrand crutch-assisted gait. Med. Eng. Phys. 27, 19–29 (2005)

    Article  Google Scholar 

  4. Slavens, B.A., Bhagchandani, N., Wang, M., Smith, P.A., Harris, G.F.: An upper extremity inverse dynamics model for pediatric Lofstrand crutch-assisted gait. J. Biomech. 44, 2162–2167 (2011)

    Article  Google Scholar 

  5. Thys, H., Willems, P.A., Saels, P.: Energy cost, mechanical work and muscular efficiency in swing-through gait with elbow crutches. J. Biomech. 29, 1473–1482 (1996)

    Article  Google Scholar 

  6. Waters, R.L., Lunsford, B.R.: Energy cost of paraplegic locomotion. J. Bone Jt. Surg., Am. Vol. 67, 1245–1250 (1985)

    Google Scholar 

  7. Shoup, T.E., Fletcher, L.S., Merril, B.R.: Biomechanics of crutch locomotion. J. Biomech. 7, 11–19 (1974)

    Article  Google Scholar 

  8. Opila, K.A., Nicol, A.C., Paul, J.P.: Upper limb loadings of gait with crutches. J. Biomech. Eng. 109, 285–290 (1987)

    Article  Google Scholar 

  9. Malkan, D.H.: Bilateral ulnar neuropraxia: a complication of elbow crutches. Injury: The British Journal of Accident. Surgery 23, 426 (1992)

    Google Scholar 

  10. Donelan, J.M., Kram, R., Kuo, A.D.: Simultaneous positive and negative external mechanical work in human walking. J. Biomech. 35, 117–124 (2002)

    Article  Google Scholar 

  11. Kuo, A.D., Donelan, J.M., Ruina, A.: Energetic consequences of walking like an inverted pendulum: Step-to-step transitions. Exerc. Sport Sci. Rev. 33, 88–97 (2005)

    Article  Google Scholar 

  12. Adamczyk, P.G., Collins, S.H., Kuo, A.D.: The advantages of a rolling foot in human walking. J. Exp. Biol. 209, 3953–3963 (2006)

    Article  Google Scholar 

  13. Van der Spek, J.H., Veltink, P.H., Hermens, H.J., Koopman, B.F.J.M., Boom, H.B.K.: A model-based approach to stabilizing crutch supported paraplegic standing by artificial hip joint stiffness. IEEE Trans. Neural Syst. Rehabil. Eng. 11, 443–451 (2003)

    Article  Google Scholar 

  14. Gilardi, G., Sharf, I.: Literature survey of contact dynamics modelling. Mech. Mach. Theory 37, 1213–1239 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  16. Cuadrado, J., Pàmies-Vilà, R., Lugrís, U., Alonso, F.J.: A force-based approach for joint efforts estimation during the double support phase of gait. Proc. IUTAM 2, 26–34 (2011)

    Article  Google Scholar 

  17. Kecskemethy, A.: A novel cylinder-plane foot contact model for human gait motion reproduction. In: Proc. ECCOMAS Thematic Conf. on Multibody Dynamics, Brussels, Belgium (2011)

    Google Scholar 

  18. Millard, M., McPhee, J., Kubica, E.: Multi-step forward dynamic gait simulation. In: Bottasso, C.L. (ed.) Multibody Dynamics: Computational Methods and Applications, pp. 25–43. Springer, Berlin (2009)

    Google Scholar 

  19. Argatov, I.: Development of an asymptotic modeling methodology for tibio-femoral contact in multibody dynamic simulations of the human knee joint. Multibody Syst. Dyn. (2011, in press). doi:10.1007/s11044-011-9275-6

    Google Scholar 

  20. Machado, M., Flores, P., Pimenta Claro, J.C., Ambrósio, J., Silva, M., Completo, A., Lankarani, H.M.: Development of a planar multibody model of the human knee joint. Nonlinear Dyn. 60, 459–478 (2010)

    Article  MATH  Google Scholar 

  21. Bei, Y., Fregly, B.J.: Multibody dynamic simulation of knee contact mechanics. Med. Eng. Phys. 26, 777–789 (2004)

    Article  Google Scholar 

  22. Silva, P.C., Silva, M.T., Martins, J.M.: Evaluation of the contact forces developed in the lower limb/orthosis interface for comfort design. Multibody Syst. Dyn. 24, 367–388 (2010)

    Article  MATH  Google Scholar 

  23. McGeer, T.: Passive dynamic walking. Int. J. Robot. Res. 9, 62–82 (1990)

    Article  Google Scholar 

  24. Collins, S.H., Wisse, M., Ruina, A.: A three-dimensional passive dynamic walking robot with two legs and knees. Int. J. Robot. Res. 20, 607–615 (2001)

    Article  Google Scholar 

  25. Kuo, A.D.: Energetics of actively powered locomotion using the simplest walking model. J. Biomech. Eng. 124, 113–120 (2002)

    Article  Google Scholar 

  26. Tlalolini, D., Aoustin, Y., Chevallereau, C.: Design of a walking cyclic gait with single support phases and impacts for the locomotor system of a thirteen-link 3D biped using the parametric optimization. Multibody Syst. Dyn. 23, 33–56 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hurmuzlu, Y.: Dynamics of bipedal gait: Part I – Objective functions and the contact event of a planar five-link biped. J. Appl. Mech. 60, 331–336 (1993)

    Article  Google Scholar 

  28. Kövecses, J., Kovács, L.L.: Foot impact in different modes of running: mechanisms and energy transfer. Proc. IUTAM 2, 101–108 (2011)

    Article  Google Scholar 

  29. Font-Llagunes, J.M., Kövecses, J.: Dynamics and energetics of a class of bipedal walking systems. Mech. Mach. Theory 44, 1999–2019 (2009)

    Article  MATH  Google Scholar 

  30. Carpentier, C., Font-Llagunes, J.M., Kövecses, J.: Dynamics and energetics of impacts in crutch walking. J. Appl. Biomech. 26, 473–483 (2010)

    Google Scholar 

  31. Gilchrist, L.A., Winter, D.A.: A two-part, viscoelastic foot model for use in gait simulations. J. Biomech. 29, 795–798 (1996)

    Article  Google Scholar 

  32. Kaplan, M.L., Heegaard, J.H.: Energy-conserving impact algorithm for the heel-strike phase of gait. J. Biomech. 33, 771–775 (2000)

    Article  Google Scholar 

  33. Winter, D.A.: Biomechanics and Motor Control of Human Movement. Wiley, Hoboken (2005)

    Google Scholar 

  34. Batlle, J.A.: Termination conditions for three-dimensional inelastic collisions in multibody systems. Int. J. Impact Eng. 25, 615–629 (2001)

    Article  Google Scholar 

  35. Modarres Najafabadi, S.A., Kövecses, J., Angeles, J.: A comparative study of approaches to dynamics modeling of contact transitions in multibody systems. In: Proc. ASME Int. Design Eng. Tech. Conferences IDETC’05, Long Beach, CA, USA (2005)

    Google Scholar 

  36. Agulló Batlle, J., Barjau Condomines, A.: Rough collisions in multibody systems. Mech. Mach. Theory 26, 656–677 (1991)

    Article  Google Scholar 

  37. Batlle, J.A.: The sliding velocity flow of rough collisions in multibody systems. J. Appl. Mech. 63, 804–809 (1996)

    Article  MATH  Google Scholar 

  38. Kövecses, J.: Dynamics of Mechanical Systems and the Generalized Free-Body Diagram-Part I: General Formulation. J. Appl. Mech. 75(061012), 1–12 (2008)

    Google Scholar 

  39. Goldsmith, W.: Impact: The Theory and Physical Behaviour of Colliding Solids. Arnold, London (1960)

    MATH  Google Scholar 

  40. Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42, 440–445 (1975)

    Article  Google Scholar 

  41. Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)

    Google Scholar 

  42. Flores, P., Machado, M., Silva, M.T., Martins, J.M.: On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst. Dyn. 25, 357–375 (2011)

    Article  MATH  Google Scholar 

  43. Gonthier, Y., McPhee, J., Lange, C., Piedbœuf, J.C.: A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody Syst. Dyn. 11, 209–233 (2004)

    Article  MATH  Google Scholar 

  44. Dopico, D., Luaces, A., Gonzalez, M., Cuadrado, J.: Dealing with multiple contacts in a human-in-the-loop application. Multibody Syst. Dyn. 25, 167–183 (2011)

    Article  MathSciNet  Google Scholar 

  45. Johnson, K.L.: Contact Mechanics, 6th edn. Cambridge University Press, Cambridge (1996)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the Spanish Ministry of Science and Innovation under the project DPI2009-13438-C03-03 and the Natural Sciences and Engineering Research Council of Canada (NSERC). The support is gratefully acknowledged.

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Correspondence to Josep M. Font-Llagunes.

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Font-Llagunes, J.M., Barjau, A., Pàmies-Vilà, R. et al. Dynamic analysis of impact in swing-through crutch gait using impulsive and continuous contact models. Multibody Syst Dyn 28, 257–282 (2012). https://doi.org/10.1007/s11044-011-9300-9

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  • DOI: https://doi.org/10.1007/s11044-011-9300-9

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