Untangling the mechanics of the clove hitch knot*

Knots can impart unique mechanical function to filamentary structures, with examples ranging across length scales, including DNA, polymer-chains, shoelaces climbing ropes, tennis racket, and surgical sutures. Still, the predictive understanding of the mechanics of this class of structures is limited. The fundamental challenge arises from the complex interplay between topology, geometry, elasticity, and friction. Here, we focus on the clove hitch knot, which typically attaches a flexible rod/filament/rope to a rigid post. The clove hitch can sustain a remarkably large tension ratio between the two ends of the rod when compared to the simpler strategy of spooling the rod around the rigid post in a helical configuration. In our study, we combine experiments (mechanical testing and X-ray tomography), finite element and a theory based on the Kirchhoff equations. We find that the twist in the rod increases with the ratio of the tensions applied to the two ends. Furthermore, in contrast to helical spooling, the clove hitch loses a significant amount of its tension at the regions of self-contact, thereby enhancing its mechanical performance.