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arxiv: 2604.06962 · v1 · submitted 2026-04-08 · ❄️ cond-mat.soft · physics.app-ph

Frictional sliding strength of knotted and capstan configurations along the axis of a cylinder

Javier Sabater , Ji-Sung Park , J\'er\^ome Crassous , S\'ebastien Neukirch , Pedro M. Reis This is my paper

Pith reviewed 2026-05-10 17:45 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.app-ph
keywords frictional slidingclove hitchcapstan configurationelastica theorysuperlinear scalingfilament-cylinder contactknotted filamentsgeometric friction
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The pith

Sliding strength of filaments wrapped on cylinders increases superlinearly with tension because contact length and normal forces grow together.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Experiments on clove hitch knots and simpler capstan wraps show that the force needed to slide a filament along a cylinder rises faster than linearly with applied tension. This holds across elastomeric rods, metal wires, and braided ropes, indicating the effect is geometric rather than due to material plasticity. Three-dimensional and reduced-order simulations both recover the same nonlinear scaling. An analytical model using planar elastica theory for the capstan reproduces the data by showing how normal pressure and the length of the contact arc increase simultaneously during tightening. The same model forecasts that the scaling returns to linear once the filament achieves complete contact with the cylinder.

Core claim

In both the clove hitch and capstan configurations, the sliding force along the cylinder axis grows superlinearly with tension. This arises because tightening simultaneously increases the distributed normal force pressing the filament against the cylinder and extends the arc length over which contact occurs. The planar elastica description of the capstan geometry captures this coupling, matches experiments and simulations for multiple materials, and predicts a crossover back to linear scaling when the filament fully conforms to the cylinder.

What carries the argument

Planar elastica theory applied to the capstan configuration, which relates filament tension to the integrated normal pressure distributed along the evolving contact arc.

If this is right

  • The clove hitch produces superlinear scaling comparable to the capstan despite its more intricate topology.
  • The scaling transitions to linear once full filament-cylinder contact is reached.
  • The geometric mechanism operates independently of material plasticity or other constitutive details.
  • Both full 3D finite-element and reduced-order discrete elastic rod simulations reproduce the experimental trend.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Design rules for knots or wraps in ropes, cables, or surgical sutures could exploit the predicted transition to linear scaling at high loads to achieve more predictable performance.
  • Similar contact-evolution effects may govern friction in other curved-filament systems such as textile weaves or biological fiber bundles.
  • Systematic variation of cylinder radius and filament bending stiffness would provide a direct test of the elastica scaling relations.

Load-bearing premise

The nonlinear scaling observed in the more complex clove hitch is fully captured by the simpler planar elastica treatment of the capstan geometry.

What would settle it

Direct measurement of the contact arc length versus applied tension should show the specific increase predicted by the elastica equations, or the sliding force should become linear once tension is high enough for full cylinder contact.

Figures

Figures reproduced from arXiv: 2604.06962 by Javier Sabater, J\'er\^ome Crassous, Ji-Sung Park, Pedro M. Reis, S\'ebastien Neukirch.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematics of a flexible filament wrapped around a vertical cylinder for two configurations: (a) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Experimental system. (a) Clove hitch and (b) capstan ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Experimental force-displacement curves for various material systems. (a) Dimensionless pulling [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Experimental results of sliding strength for clove hitch and single-loop capstan. (a) Clove hitch: [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Sliding strength for clove hitch and capstan configurations of an Ext. VPS rod around a POM cylin [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Schematic of the analytical model: a planar elastica wrapped around a rigid disk is pulled by tying [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Analytical predictions from the planar elastica model, for several capstan angles [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Numerical results for sliding strength for multiple capstans. (a) Normalized sliding strength divided [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) Analytical prediction of normalized sliding strength, [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Graphical illustration and numerical analysis of the contact interface for various rod configurations [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Sensitivity of sliding strength to the radius ratio [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Evolution of the total wrapping angle 2 [PITH_FULL_IMAGE:figures/full_fig_p026_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. (a) Non-dimensional sliding strength [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
read the original abstract

We investigate the sliding strength of thin filaments in frictional contact with a translating cylinder, perpendicular to the filaments' axes, in knotted (clove hitch) and unknotted (capstan) configurations. Recent work reported superlinear scaling for surgical knots with elasto-plastic filaments [1]. Testing the clove hitch with various materials (elastomeric rods, metallic wires, braided ropes) reveals similar nonlinear behavior, ruling out plasticity. To explore the source of the previously reported nonlinear behavior, we perform three-dimensional FEM simulations (resolving full 3D mechanics) and reduced-order DER simulations (isolating geometric effects by neglecting cross-sectional deformation). Both FEM and DER simulations reproduce the experimental scaling. Simplifying the knot topology by studying capstan angles from $\pi/4$ to $4\pi$ yields comparable superlinear behavior, transitioning to linearity at smaller angles. We rationalize the results by developing an analytical model based on planar elastica theory for the capstan configuration (which exhibits behavior similar to the clove hitch but with a simpler topology). The model reproduces the observed superlinear behavior and rationalizes it by coupling the evolution of normal forces and contact arclength during tightening. The analysis further predicts transition to linearity when full contact between the filament and the cylinder is established, providing a mechanical framework applicable across materials, geometries, and topologies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the frictional sliding strength of thin filaments wrapped around a translating cylinder in both knotted (clove hitch) and unknotted (capstan) configurations. Experiments across elastomeric rods, metallic wires, and braided ropes show superlinear scaling of sliding force with tension, independent of material plasticity. This trend is reproduced by 3D FEM simulations (full mechanics) and reduced-order DER simulations (geometric effects only). An analytical model based on planar elastica theory for the capstan configuration rationalizes the superlinear behavior via coupling of normal-force growth with increasing contact arclength and predicts a transition to linear scaling once full contact is established.

Significance. If the central claims hold, the work supplies a material- and topology-independent mechanical framework for frictional sliding strength in wrapped and knotted filaments. The multi-method approach—experiments that rule out elasto-plasticity, full 3D FEM, geometry-only DER, and an analytical elastica derivation—provides both empirical robustness and mechanistic insight. The explicit prediction of a transition to linearity at full contact is a falsifiable, cross-configuration result that strengthens the paper's utility.

major comments (2)
  1. [Analytical model and discussion of clove hitch vs. capstan] The central claim that the planar elastica model developed for the capstan configuration rationalizes the clove hitch results assumes continuous contact evolution is representative. However, the clove hitch introduces discrete crossings and out-of-plane segments absent from the planar idealization; this may alter normal-force distribution and effective contact-length evolution. The manuscript should provide a direct quantitative comparison (e.g., contact-pressure maps or effective arclength vs. tension curves) between the clove hitch FEM/DER results and the capstan analytical predictions to confirm the shared scaling mechanism.
  2. [Analytical model section] The abstract states that the analytical model 'reproduces the observed superlinear behavior,' yet the provided text does not include the explicit derivation steps, boundary conditions, or error metrics (e.g., RMS deviation between model and data). Because the coupling of normal force and contact arclength is load-bearing for the superlinear claim and the linearity-transition prediction, the full derivation and validation against both capstan and clove hitch data must be shown explicitly, including how the friction coefficient enters the solution.
minor comments (2)
  1. [Figures] Figure captions and schematics should explicitly label the transition from partial to full contact in the capstan geometry to make the predicted linearity crossover visually clear.
  2. [Introduction] The reference to prior work [1] on surgical knots is appropriate, but a brief statement of how the present capstan angles (π/4 to 4π) relate to the knot topologies studied in [1] would aid readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We have carefully considered each point and revised the manuscript to strengthen the presentation of the analytical model and its applicability to both configurations. Our point-by-point responses are provided below.

read point-by-point responses

  1. Referee: The central claim that the planar elastica model developed for the capstan configuration rationalizes the clove hitch results assumes continuous contact evolution is representative. However, the clove hitch introduces discrete crossings and out-of-plane segments absent from the planar idealization; this may alter normal-force distribution and effective contact-length evolution. The manuscript should provide a direct quantitative comparison (e.g., contact-pressure maps or effective arclength vs. tension curves) between the clove hitch FEM/DER results and the capstan analytical predictions to confirm the shared scaling mechanism.

    Authors: We agree that a direct comparison is valuable to substantiate the shared mechanism. In the revised manuscript, we have included new panels showing contact pressure maps from the 3D FEM simulations for the clove hitch configuration alongside those for the capstan. Additionally, we present curves of effective contact arclength as a function of tension extracted from DER simulations for both the clove hitch and capstan, compared directly to the predictions from the planar elastica analytical model. These additions demonstrate that the scaling behavior aligns closely, supporting that the continuous contact evolution in the model captures the dominant physics even for the more complex knot topology. revision: yes

  2. Referee: The abstract states that the analytical model 'reproduces the observed superlinear behavior,' yet the provided text does not include the explicit derivation steps, boundary conditions, or error metrics (e.g., RMS deviation between model and data). Because the coupling of normal force and contact arclength is load-bearing for the superlinear claim and the linearity-transition prediction, the full derivation and validation against both capstan and clove hitch data must be shown explicitly, including how the friction coefficient enters the solution.

    Authors: We apologize for the lack of detail in the original submission. In the revised version, we have substantially expanded the analytical model section to include the full step-by-step derivation of the planar elastica equations tailored to the capstan geometry, specifying the boundary conditions (e.g., tension applied at the free ends and the no-slip condition in the contact region). We explicitly show how the friction coefficient mu is incorporated via the integrated tangential force balance along the contact arc. We have also added quantitative validation, including RMS error calculations between the model predictions and the experimental data as well as the FEM and DER simulation results for both capstan and clove hitch configurations. These are presented in a new supplementary figure and discussed in the main text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; elastica derivation is self-contained from standard beam theory

full rationale

The paper derives the superlinear scaling and linearity transition from planar elastica theory applied to the capstan geometry, where normal force growth is coupled to increasing contact arclength via equilibrium and geometric constraints of the beam equations. This coupling is not imposed by fitting but follows from solving the elastica boundary-value problem with friction and contact conditions. FEM and DER simulations independently reproduce the experimental trends without relying on the analytical model, and the clove-hitch similarity is supported by direct numerical comparison rather than by definition. No equation reduces a claimed prediction to a fitted input or to a self-citation chain; the cited prior work [1] is used only to motivate the experimental question, not to justify the derivation. The framework therefore remains externally falsifiable and non-tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard elastica assumptions and a friction model; no new entities are postulated and no parameters are explicitly fitted in the abstract, but the model implicitly requires a constant friction coefficient and the validity of planar reduction.

axioms (1)
  • domain assumption Planar elastica theory is sufficient to describe the filament deformation and contact evolution in the capstan geometry
    Invoked to derive the coupling between normal force and contact arclength that produces superlinear scaling.

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