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Knitting turns a one dimensional yarn into a highly ramified three-dimensional structure. As a method of additive manufacturing, it holds promise for a new class of lightweight, ultrastrong materials. Here we present a purely geometric model to predict the three-dimensional folding of knitted fabrics made only of the two traditional stitches, knit and purl., Comment: 7 pages, 3 figures, the whole megillah

In this paper, we introduce a method to rapidly create 3D geometries by folding 2D sheets via pull-up nets. Given a 3D structure, we unfold its mesh into a planar 2D sheet using heuristic algorithms and populate these with cutlines and throughholes. We develop a web-based simulation tool that translates users' 3D meshes into manufacturable 2D sheets. After laser-cutting the sheet and feeding thread through these throughholes to form a pull-up net, pulling the thread will fold the sheet into the 3D structure using a single degree of freedom. We introduce the fabrication process and build a variety of prototypes demonstrating the method's ability to rapidly create a breadth of geometries suitable for low-fidelity prototyping that are both load-bearing and aesthetic across a range of scales. Future work will expand the breadth of geometries available and evaluate the ability of our prototypes to sustain structural loads., Comment: In ACM TEI '23: Proceedings of the Seventeenth International Conference on Tangible, Embedded, and Embodied Interaction (ACM TEI '23), February 26-March 1, 2023, Warsaw, Poland. ACM, New York, NY, USA, 10 pages

The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the geometric mechanics of kirigamized sheets as a function of the number, size and orientation of cuts. We show that the geometry of mechanically loaded sheets can be approximated as a composition of simple developable units: flats, cylinders, cones and compressed Elasticae. This geometric construction yields simple scaling laws for the mechanical response of the sheet in both the weak and strongly deformed limit. In the ultimately stretched limit, this further leads to a theorem on the nature and form of geodesics in an arbitrary kirigami pattern, consistent with observations and simulations. By varying the shape and size of the geodesic in a kirigamized sheet, we show that we can control the deployment trajectory of the sheet, and thence its functional properties as a robotic gripper or a soft light window. Overall our study of random kirigami sets the stage for controlling the shape and shielding the stresses in thin sheets using cuts., Comment: 11 pages, 7 figures