Twisting Uneven Ropes

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.