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Experimental analysis of the mechanics of a deformable object, and particularly its stability, requires repetitive testing and, depending on the complexity of the object's shape, a testing setup that can manipulate many degrees of freedom at the object's boundary. Motivated by recent advancements in robotic manipulation of deformable objects, this paper addresses these challenges by constructing a method for automated stability testing of a slender elastic rod -- a canonical example of a deformable object -- using a robotic system. We focus on rod configurations with helical centerlines since the stability of a helical rod can be described using only three parameters, but experimentally determining the stability requires manipulation of both the position and orientation at one end of the rod, which is not possible using traditional experimental methods that only actuate a limited number of degrees of freedom. Using a recent geometric characterization of stability for helical rods, we construct and implement a manipulation scheme to explore the space of stable helices, and we use a vision system to detect the onset of instabilities within this space. The experimental results obtained by our automated testing system show good agreement with numerical simulations of elastic rods in helical configurations. The methods described in this paper lay the groundwork for automation to grow within the field of experimental mechanics., Comment: Supplementary video is available at https://youtu.be/O48iDElWy-8

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., Comment: 11 pages, 7 figures