Twisting Uneven Ropes

TL;DR

This paper investigates the geometry of uneven ropes formed by twisting two circular strands of different diameters, providing numerical solutions to the contact equations to understand how the ratio affects the maximum twist configuration.

Contribution

It introduces a detailed analysis of uneven ropes with different strand diameters and numerically solves the contact equations to determine their maximum twisted geometries.

Findings

Maximum twisted geometry depends on diameter ratio r

Numerical solutions to contact equations for uneven ropes

Provides geometric insights into uneven rope twisting

Abstract

A classical two-stranded rope can be made by twisting two identical strands together under strain. Despite being conceptually simple, the contact-equations for helically twisted identical strands have only been solved within the last 20 years. Our goal here is basic: to understand the twisting of two circular strands, where one is thicker than the other. This is what we call an uneven rope. The geometry of the uneven rope depend on the ratio, $r$, between the diameters of the two strands. In particular, the maximally twisted geometry may be determined as a function of $r$ by solving the contact-equations for the two strands numerically.