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Frictional mechanics of knots

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Abstract

For some important knots, closed-form solutions are presented for the holding forces which are needed to keep a knot in equilibrium for given pulling forces. If the holding forces become zero for finite pulling forces, the knot is self-locking and is called stable. This is only possible when, first, the friction coefficient exceeds a critical value and, second, when there is additional pressure on some knot segments sandwiched by surrounding knot segments. The number of these segments depends on the topology of the knot and is characteristic for it. The other important parameter is the total curvature of the knot. In this way, the complete frictional contact inside the knot is taken into account. The presented model can explain the available experiments.

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Acknowledgements

The author thanks Ira Leuthäusser for helpful discussions and critical reading of the manuscript.

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  1. Kufstein/Schwoich, Austria

    Ulrich Leuthäusser

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  1. Ulrich Leuthäusser
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Correspondence to Ulrich Leuthäusser.

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Leuthäusser, U. Frictional mechanics of knots. Arch Appl Mech 94, 1041–1053 (2024). https://doi.org/10.1007/s00419-024-02566-w

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