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Multibody modeling of human body for the inverse dynamics analysis of sagittal plane movements

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Abstract

A multibody methodology for systematic construction of a two-dimensional biomechanical model of a human body is presented, aimed at effective determination of the muscle forces and joint reaction forces in the lower extremities during sagittal plane movements such as vertical jump, standing long jump or jumping down from a height. While the hip, knee and ankle joints are modeled as enforced directly by the muscle forces applied to the foot, shank, thigh and pelvis at the muscle attachment points, the actuation of the other joints is simplified to the torques representing the respective muscle action. The developed formulation is applicable to both the flying and support phases, enhanced by an effective scheme for the determination of reaction forces exclusively in the lower extremity joints. The determination of reactions from the ground is also provided. The problem of muscle force redundancy in the lower extremities is solved by applying the pseudoinverse method, with post-processing procedures used to assure the muscle being tensile. Results of the inverse dynamics analysis of vertical jump are reported.

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References

  1. Seireg, A., Arvikar, R.: Biomechanical Analysis of the Musculoskeletal Structure for Medicine and Sports. Hemisphere, Washington (1989)

    Google Scholar 

  2. Tözeren, A.: Human Body Dynamics: Classical Mechanics and Human Movement. Springer, Berlin (2000)

    Google Scholar 

  3. Yamaguchi, G.T.: Dynamic Modeling of Musculoskeletal Motion. Kluwer, Dordrecht (2001)

    MATH  Google Scholar 

  4. Robertson, D.G.E., Caldwell, G.E., Hamill, J., Kamen, G., Whittlesey, S.N.: Research Methods in Biomechanics. Human Kinetics, Champaign (2004)

    Google Scholar 

  5. Winter, D.A.: Biomechanics and Motor Control of Human Movement. Wiley, New York (2005)

    Google Scholar 

  6. Amirouche, F.: Computational Methods in Multibody Dynamics. Prentice Hall, New York (1992)

    MATH  Google Scholar 

  7. Seireg, A., Arvikar, R.J.: A mathematical model for evaluation of forces in lower extremities of the musculo–skeletal system. J. Biomech. 6, 313–326 (1973)

    Article  Google Scholar 

  8. Seireg, A., Arvikar, R.J.: The prediction of muscular load sharing and joint forces in the lower extremities during walking. J. Biomech. 8, 89–102 (1975)

    Article  Google Scholar 

  9. Pandy, M.G., Anderson, F.C., Hull, D.G.: A parameter optimization approach for the optimal control of large-scale musculoskeletal systems. Trans. ASME J. Biomech. Eng. 114, 450–460 (1992)

    Google Scholar 

  10. Silva, M.P.T., Ambrósio, J.A.C., Pereira, M.S.: Biomechanical model with joint resistance for impact simulation. Multibody Syst. Dyn. 1, 65–84 (1997)

    Article  MATH  Google Scholar 

  11. Eberhard, P., Spägele, T., Gollhofer, A.: Investigations for the dynamical analysis of human motion. Multibody Syst. Dyn. 3, 1–20 (1999)

    Article  MATH  Google Scholar 

  12. Spägele, T., Kistner, A., Gollhofer, A.: Modelling, simulation and optimization of a human vertical jump. J. Biomech. 32, 521–530 (1999)

    Article  Google Scholar 

  13. Andriacchi, T.P., Alexander, E.J.: Studies of human locomotion: past, present and future. J. Biomech. 33, 1217–1224 (2000)

    Article  Google Scholar 

  14. Heller, M.O., Bergmann, G., Deuretzbacher, G., Dürselen, L., Pohl, M., Claes, L., Haas, N.P., Duda, G.N.: Musculo–skeletal loading conditions at the hip during walking and stair climbing. J. Biomech. 34, 883–893 (2001)

    Article  Google Scholar 

  15. Hatze, H.: The fundamental problem of myoskeletal inverse dynamics and its implications. J. Biomech. 35, 109–115 (2002)

    Article  Google Scholar 

  16. Pandy, M.G.: Computer modeling and simulation of human movements. Ann. Rev. Biomed. Eng. 3, 245–273 (2002)

    Article  Google Scholar 

  17. Pennestrì, E., Renzi, A., Santonocito, P.: Dynamic modeling of the human arm with video-based experimental analysis. Multibody Syst. Dyn. 7, 389–406 (2002)

    Article  MATH  Google Scholar 

  18. Chenut, X., Fisette, P., Samin, J.-Cl.: Recursive formalism with a minimal dynamic parameterization for the identification and simulation of multibody systems. Application to the human body. Multibody Syst. Dyn. 8, 117–140 (2002)

    Article  MATH  Google Scholar 

  19. Silva, M.P.T., Ambrósio, J.A.C.: Kinematic data consistency in the inverse dynamic analysis of biomechanical systems. Multibody Syst. Dyn. 8, 219–239 (2002)

    Article  MATH  Google Scholar 

  20. Blajer, W., Czaplicki, A.: Contact modeling and identification of planar somersaults on the trampoline. Multibody Syst. Dyn. 10, 289–312 (2003)

    Article  MATH  Google Scholar 

  21. Silva, M.P.T., Ambrósio, J.A.C.: Human motion analysis using multibody dynamics and optimization tools. Technical Report IDMEC/CPM—2004/001, Instituto Superior Técnico of the Technical University of Lisbon (2004)

  22. Czaplicki, A., Silva, M., Ambrósio, J., Jesus, O., Abrantes, J.: Estimation of the muscle force distribution in ballistic motion based on a multibody methodology. Comput. Methods Biomech. Biomed. Eng. 9, 45–54 (2006)

    Article  Google Scholar 

  23. Vukobratović, M., Potkonjak, V., Babković, K., Borovac, B.: Simulation model of general human and humanoid motion. Multibody Syst. Dyn. 17, 71–96 (2007)

    Article  Google Scholar 

  24. Nikravesh, P.E.: Systematic reduction of multibody equations of motion to a minimal set. Int. J. Non-Linear Mech. 25, 143–151 (1990)

    Article  Google Scholar 

  25. Blajer, W.: A geometric unification of constrained system dynamics. Multibody Syst. Dyn. 1, 3–21 (1997)

    Article  MATH  Google Scholar 

  26. Schiehlen, W.: Multibody system dynamics: roots and perspectives. Multibody Syst. Dyn. 1, 149–188 (1997)

    Article  MATH  Google Scholar 

  27. Blajer, W.: On the determination of joint reactions in multibody mechanisms. Trans. ASME J. Mech. Des. 126, 341–350 (2004)

    Article  Google Scholar 

  28. Blajer, W., Czaplicki, A.: An alternative scheme for determination of joint reaction forces in human multibody models. J. Theor. Appl. Mech. 43, 813–824 (2005)

    Google Scholar 

  29. Hardt, D.E.: Determining muscle forces in the leg during normal human walking—an application and evaluation of optimization methods. Trans. ASME J. Biomech. Eng. 100, 72–78 (1978)

    Google Scholar 

  30. Crowninshield, R.D., Brand, R.A.: A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14, 793–801 (1981)

    Article  Google Scholar 

  31. Patriarco, A.G., Mann, R.W., Simon, S.R., Mansour, J.M.: An evaluation of the approaches of optimization models in the prediction of muscle forces during human gait. J. Biomech. 14, 513–525 (1981)

    Article  Google Scholar 

  32. Yamaguchi, G.T., Moran, D.W., Si, J.: A computationally efficient method for solving the redundant problem in biomechanics. J. Biomech. 28, 999–1005 (1995)

    Article  Google Scholar 

  33. Anderson, F.C., Pandy, M.G.: Static and dynamic optimization solutions for gait are practically equivalent. J. Biomech. 34, 153–161 (2001)

    Article  Google Scholar 

  34. Pierce, J.E., Li, G.: Muscle forces predicted using optimization methods are coordinate system dependent. J. Biomech. 38, 695–802 (2005)

    Article  Google Scholar 

  35. Ben-Israel, A., Greville, T.N.E.: Generalized Inverses: Theory and Applications. Wiley, New York (1977)

    Google Scholar 

  36. Udwadia, F.E., Kalaba, R.E.: Analytical Dynamics: a New Approach. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  37. Zatsiorsky, V.M.: Kinetics of Human Motion. Human Kinetics, Champaign (2002)

    Google Scholar 

  38. Sinelnikov, R.D.: Atlas of Human Anatomy. Mir, Moscov (1989)

    Google Scholar 

  39. Yamaguchi, G.T., Sawa, A.G.U., Moran, D.W., Fessler, M.J., Winters, J.M.: A survey of human musculotendon actuator parameters. In: Winters, J.M., Woo, S.L.-Y. (eds.) Multiple Muscle Systems: Biomechanics and Movement Organization, pp. 717–773. Springer, Berlin (1990)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mechanics, Technical University of Radom, ul. Krasickiego 54, 26-600, Radom, Poland

    Wojciech Blajer, Krzysztof Dziewiecki & Zenon Mazur

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  1. Wojciech Blajer
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  2. Krzysztof Dziewiecki
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  3. Zenon Mazur
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Correspondence to Wojciech Blajer.

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Blajer, W., Dziewiecki, K. & Mazur, Z. Multibody modeling of human body for the inverse dynamics analysis of sagittal plane movements. Multibody Syst Dyn 18, 217–232 (2007). https://doi.org/10.1007/s11044-007-9090-2

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  • DOI: https://doi.org/10.1007/s11044-007-9090-2

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