Abstract

Tape springs are transversely curved thin strips, of which a carpenter’s tape measure is a familiar example. They are widely used as deployable structures in aerospace applications. One key desirable property is the ability to form elastic folds, where, upon bending, the cross section flattens into a developable surface and large rotations can be applied to the tape spring at a low, constant, moment. This allows tape springs to be packaged by folding up with hinges at various locations, or by coiling the whole spring up on a drum. Predicting the fold radius and moment is of considerable importance for design. Early work by Rimrott predicts a fold radius equal to the transverse radius of the spring, which is approximately true. An improved prediction was recently introduced by Calladine & Seffen. This talk will discuss tape spring folding as a two-phase energy minimisation problem, solved by the Maxwell “equal area” condition, and show how previous solutions are approximations to this condition. The approach is then extended to “tapered” springs where the transverse radius and/or width can vary linearly along the length of the spring, which form spiralling folds that may avoid some practical problems with packaging tape springs for deployment. Finally, arbitrary variations of cross section along the length will be considered.

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