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)


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.


Biomechanics muscle wrapping thick strands continuous Method 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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