String Contraction via Twisting: Ideal and Nonideal Behavior

Strings are an ancient and extremely common tool for force delivery. They may also be used to deliver torque via twisting, according to tension times the rate of length contraction versus twist angle Θ, and this is important for twisted string actuators in robotics as well as for button-on-a-string toys and hand-powered centrifuges. Idealized behavior for length contraction is predicted to be L² = L₀² – (rΘ)² where L₀ is the initial string length and r is its radius. Here we compare this model with data for single, double and triple stranded strings of parachute cords, rattail cord, nylon, kevlar, monofilament fishing line, and metal wire. We also examine deviation from ideality at small and large twist angles in order to probe the internal structure of our strings. At small angles, we see a systematic decrease in the effective cord radius compared to expectation, as individual strands compress into each other, while at large twist angles we see less contraction than expectation due to the coiling of the strands. In all cases, nonideal effects may be quantified by an effective string radius indicative of internal geometry and string-string interaction, which could play a role in the mechanics of real knots and fabrics.