Kresling origami mechanics explained: Experiments and theory

From a kinematics perspective, a Kresling origami cell couples axial displacement (contraction/expansion) with twist, leading to non-rigid origami behavior. From an energy landscape perspective, the selection of the Kresling origami geometry, together with its fabrication process and material, lead to energy envelopes allowing single or multiple stable states. In this context, this paper explores the Kresling origami mechanics through mathematical modeling integrated with experimental testing. On the theoretical mechanics front, we present a comprehensive model incorporating the representative geometrical parameters of the Kresling origami cell into the corresponding energy function in order to capture its essential mechanical behavior. On the experimental mechanics front, we create two fixtures that demonstrate the ability to control axial displacement (contraction/expansion) and twist independently, without imposing any constraints on the chiral arrangement of individual cells within the Kresling origami array (composed of multiple cells). Finally, we show the coexistence of multiple mechanical and morphological configurations within the same Kresling array by programming its loading modes, i.e., compression or twist. The fundamental nature of this work makes it applicable to several fields of engineering, including soft robotics and mechanical computing.