Equilibria and Instabilities of a Slinky

 (A) A Slinky on a  at surface in two stable states, and (B) an accompanying schematic showing bar i (on left) and bar i + 1 (on right) for the discrete model, along with displacements and axial, rotational, and shear springs.

(A) A Slinky on a at surface in two stable states, and (B) an accompanying schematic showing bar i (on left) and bar i + 1 (on right) for the discrete model, along with displacements and axial, rotational, and shear springs.

Douglas P. Holmes, Andy D. Borum, Billy F. Moore III, Raymond H. Plaut, David A. Dillard

The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically nonlinear deformations from minimal applied forces.

By considering it as a system of coils that act to resist axial, shearing, and rotational deformations, we develop a discretized model to predict the equilibrium configurations of a Slinky via the minimization of its potential energy.

 

Careful consideration of the contact between coils enables this procedure to accurately describe the shape and stability of the Slinky under different modes of deformation.

In addition, we provide simple geometric and material relations that describe a scaling of the general behavior of flexible, helical springs.

Read more at http://arxiv.org/pdf/1403.6809v1.pdf