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A continuous and computationally efficient method for wrapping a “thick” strand over a surface — The planar single-surface case

  • Katharina MüllerEmail author
  • Andrѐs Kecskemѐthy
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

Presented is a new, continuous and computationally efficient approach for wrapping a “thick” strand over a frictionless surface. Such fast wrapping algorithms are needed for example for determining approximate muscle and ligament paths with non-negligible thickness for force estimations in whole-system real-time musculoskeletal computations. Existing approaches either regard the muscle paths as infinitesimally thin, perfectly slack lines, or use discretizations of “thick” strands by a chain of spherical “beads” separated by thin, massless threads. Proposed here is a novel continuous method for tackling this problem by taking the limit of the bead-chain approach for infinitesimally close beads, leading to simple ordinary differential equations which can be solved easily instead of using computationally costly and discontinuous contact iterations as in the existing practise. This paper regards the planar case of an unstretchable strand on a single frictionless surface, illustrating the resulting behaviour in comparison to the discrete bead-chain method for the case of an ellipse as contact curve. It is shown that the continuous approach is much more efficient and precise than the discrete case. The generalization to longitudinally stretchable and cross-section compressible strands as well as general spatial contact surfaces is possible and regarded for future developments.

Keywords

Biomechanics muscle wrapping thick strands continuous Method 

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References

  1. 1.
    S. S. Blemker and S. L. Delp. Three-dimensional representation of complex muscle architectures and geometries. Annals of biomedical engineering, 33(5):661–673, 2005.CrossRefGoogle Scholar
  2. 2.
    I. W. Charlton and G. R. Johnson. Application of spherical and cylindrical wrapping algorithms in a musculoskeletal model of the upper limb. Journal of Biomechanics, 34(9):1209–1216, 2001.CrossRefGoogle Scholar
  3. 3.
    P. Favre, C. Gerber, and J. G. Snedeker. Automated muscle wrapping using finite element contact detection. Journal of Biomechanics, 43(10):1931–1940, 2010.CrossRefGoogle Scholar
  4. 4.
    R. Franci and V. Parenti-Castelli. A new tool to investigate the interactions between elastic fibers and rigid bodies. Proceedings of IFToMM 2007, 2007.Google Scholar
  5. 5.
    F. Gao, M. Damsgaard, J. Rasmussen, and S. T. Christensen. Computational method for muscle-path representation in musculoskeletal models. Biological cybernetics, 87(3):199–210, 2002.CrossRefGoogle Scholar
  6. 6.
    B. A. Garner and M. G. Pandy. The obstacle-set method for representing muscle paths in musculoskeletal models. Computer Methods in Biomechanics and Biomedical Engineering, 3(1):1–30, 2000.CrossRefGoogle Scholar
  7. 7.
    A. V. Hill. The mechanics of active muscle. Proceedings of the Royal Society of London. Series B, Biological sciences, 141(902):104–117, 1953.Google Scholar
  8. 8.
    K. R. S. Holzbaur, W. M. Murray, G. E. Gold, and S. L. Delp. Upper limb muscle volumes in adult subjects. Journal of Biomechanics, 40(4):742–749, 2007.CrossRefGoogle Scholar
  9. 9.
    M. G. Hoy, F. E. Zajac, and M. E. Gordon. A musculoskeletal model of the human lower extremity: The effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle. Journal of Biomechanics, 23(2):157–169, 1990.CrossRefGoogle Scholar
  10. 10.
    W. S. Marras, M. J. Jorgensen, K. P. Granata, and B. Wiand. Female and male trunk geometry: Size and prediction of the spine loading trunk muscles derived from mri. Clinical Biomechanics, 16(1):38–46, 2001.CrossRefGoogle Scholar
  11. 11.
    O. R¨ohrle, J. B. Davidson, and A. J. Pullan. Bridging scales: A three-dimensional electromechanical finite element model of skeletal muscle. SIAM Journal on Scientific Computing, 30(6):2882–2904, 2008.MathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Scholz, M. Sherman, I. Stavness, S. L. Delp, and A. Kecskem´ethy. A fast multi-obstacle muscle wrapping method using natural geodesic variations. Multibody System Dynamics, 2015.Google Scholar
  13. 13.
    L. A. Spyrou and N. Aravas. Muscle-driven finite element simulation of human foot movements. Computer Methods in Biomechanics and Biomedical Engineering, 15(9):925–934, 2012.CrossRefGoogle Scholar
  14. 14.
    Y. H. Tsuang, G. J. Novak, O. D. Schipplein, A. Hafezi, J. H. Trafimow, and G. B. Andersson. Trunk muscle geometry and centroid location when twisting. Journal of Biomechanics, 26(4-5):537–546, 1993.CrossRefGoogle Scholar
  15. 15.
    A. N. Vasavada, R. A. Lasher, T. E. Meyer, and D. C. Lin. Defining and evaluating wrapping surfaces for mri-derived spinal muscle paths. Journal of Biomechanics, 41(7):1450–1457, 2008.CrossRefGoogle Scholar
  16. 16.
    F. E. Zajac. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering, 17(4):359–411, 1989Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Chair of Mechanics and RoboticsUniversity of Duisburg-EssenDuisburgGermany

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