Tension-Stabilized Coiling of Isotropic Tape Springs

A tape spring can be held tightly coiled on a circular cylinder by means of a tension force applied at the tip. This paper determines the smallest value of the required tension force by means of analytical methods, experiments and detailed numerical simulations. The minimum force depends on the coiling ratio, defined as the ratio between the transverse radius of the tape spring and the radius of the cylinder. It varies with an inverse quadratic relation for coiling ratios smaller than 1 (bending-dominated regime) and with a linear relation for coiling ratios greater than 3.424 (tension-dominated regime). For coiling ratios between 1 and 3.424 there is an intermediate behavior, and the required tension force is non-unique and rather small.