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A compact smoothing-differentiation and projection approach for the kinematic data consistency of biomechanical systems

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Abstract

The estimation of the skeletal motion obtained from marker-based motion capture systems affects the results of the kinematic and dynamic analysis of biomechanical systems. The main source of error is the inaccuracy of velocities and accelerations derived from experimentally measured displacements of markers placed on the skin of joints. This error is mainly due to the amplification of high-frequency low-amplitude noise introduced by the motion capture system when the raw displacement signals are differentiated. Another source of error is the skin motion artifact that produces violations of the kinematic constraint equations of the multibody system. An integrated smoothing-differentiation-projection approach to ensure the kinematic data consistency in the context of the analysis of biomechanical systems is presented. The raw data differentiation problem is solved by applying a single-step smoothing-differentiation technique based on the Newmark integration scheme. A systematic multibody procedure is proposed based on the projection of the positions and its smoothed derivatives into their corresponding constraint manifolds to ensure the kinematic data consistency. Several benchmark kinematic signals that include an acquired nonstationary mono-dimensional motion of biomechanical origin and computer generated data of a four-bar mechanism were processed using the proposed method to study its performance.

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References

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

    Article  Google Scholar 

  2. Chiari, L., Della Croce, U., Leardini, A., Cappozzo, A.: Human movement analysis using stereophotogrammetry. Part 2: Instrumental errors. Gait Posture 21, 197–211 (2005)

    Article  Google Scholar 

  3. Leardini, A., Chiari, L., Della Croce, U., Cappozzo, A.: Human movement analysis using stereophotogrammetry. Part 3: Soft tissue artifact assessment and compensation. Gait Posture 21, 212–225 (2005)

    Article  Google Scholar 

  4. Capello, A., Capozzo, A., La Palombara, P.F., Luchetti, L., Leardini, A.: Multiple anatomical landmark calibration for optimal bone pose estimation. Hum. Mov. Sci. 16, 259–274 (1997)

    Article  Google Scholar 

  5. Lu, T.W., O’Connor, J.J.: Bone position estimation from skin marker co-ordinates using global optimisation with joint constraints. J. Biomech. 32, 129–134 (1999)

    Article  Google Scholar 

  6. Cerveri, P., Pedotti, A., Ferrigno, G.: Kinematical models to reduce the effect of skin artifacts on marker-based human motion estimation. J. Biomech. 38, 2228–2236 (2005)

    Article  Google Scholar 

  7. Silva, M.P.T., Ambrosio, 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 

  8. Ackermann, M., Schiehlen, W.: Dynamic analysis of human gait disorder and metabolical cost estimation. Arch. Appl. Mech. 75, 569–594 (2006)

    Article  MATH  Google Scholar 

  9. Silva, M.P.T., Ambrosio, J.A.C.: Sensitivity of the results produced by the inverse dynamic analisys of a human stride to perturbed input data. Gait Posture 19, 35–49 (2004)

    Article  Google Scholar 

  10. Vaughan, C.L.: Smoothing and differentiation of displacement-time data: an application of splines and digital filtering. Int. J. Bio-Med. Comput. 13, 375–386 (1982)

    Article  Google Scholar 

  11. Giakas, G., Baltzopoulos, V.: Optimal digital filtering requires a different cut-off frequency strategy for the determination of the higher derivatives. J. Biomech. 30, 851–855 (1997)

    Article  Google Scholar 

  12. Giakas, G., Stergioulas, L.K., Vourdas, A.: Time-frequency analysis and filtering of kinematic signals with impacts using the Wigner function: accurate estimation of the second derivative. J. Biomech. 33, 567–574 (2000)

    Article  Google Scholar 

  13. Alonso, F.J., Del Castillo, J.M., Pintado, P.: Application of singular spectrum analysis to the smoothing of raw kinematic signals. J. Biomech. 38, 1085–1092 (2005)

    Article  Google Scholar 

  14. Alonso, F.J., Pintado, P., Del Castillo, J.M.: Filtering of kinematic signals using the Hodrick-Prescott filter. J. Appl. Biomech. 21, 271–285 (2005)

    Google Scholar 

  15. Adham, R.I., Shihab, S.A.: Discrete wavelet transform: a tool in smoothing kinematic data. J. Biomech. 32, 317–321 (1999)

    Article  Google Scholar 

  16. Newmark, N.M.: A method of computation for structural dynamics. J. Eng. Mech. Div. 85, 67–94 (1959)

    Google Scholar 

  17. Modak, S., Sotelino, E.D.: The generalized method for structural dynamics applications. Adv. Eng. Softw. 33, 565–575 (2002)

    Article  MATH  Google Scholar 

  18. Garcia de Jalon, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer, Berlin (1994)

    Google Scholar 

  19. Alonso, F.J., Del Castillo, J.M., Pintado, P.: Motion data processing and wobbling mass modelling in the inverse dynamics of skeletal models. Mech. Mach. Theory 42, 1143–1169 (2007)

    Article  Google Scholar 

  20. Bayo, E., Ledesma, R.: Augmented Lagrangian and mass-orthogonal projection methods for constrained multibody dynamics. Nonlinear Dyn. 9, 113–130 (1996)

    Article  MathSciNet  Google Scholar 

  21. Alonso, F.J., Cuadrado, J., Del Castillo, J.M., Pintado, P.: Projection methods for the kinematic data consistency of biomechanical systems. In: Multibody Dynamics 2007, Eccomas Thematic Conference, Milano, Italy (2007)

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Alonso, F.J., Cuadrado, J., Lugrís, U. et al. A compact smoothing-differentiation and projection approach for the kinematic data consistency of biomechanical systems. Multibody Syst Dyn 24, 67–80 (2010). https://doi.org/10.1007/s11044-010-9191-1

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  • DOI: https://doi.org/10.1007/s11044-010-9191-1

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