Kirigami tiled surfaces with multiple configurations

Abstract

This paper presents new kirigami patterns consisting of tiles connected by sub-folds that can approximate multiple specified target surfaces. The curvature of the surfaces approximated by the tiles varies as the patterns are folded, allowing access to a wide range of curvatures. A numerical framework is developed for the synthesis of the fold patterns that approximate a given set of target surfaces. The pattern synthesis process is framed as a tile placement problem, where compatible tile arrangements associated with each target surface are computed by solving a constrained optimization problem. After computing a set of tile arrangements, sub-folds are added to connect adjacent tiles. The resulting patterns are rigid foldable with many kinematic degrees of freedom, allowing them to achieve configurations that approximate the specified target surfaces. Kinematic simulations verify the existence of continuous paths between the target surfaces. A prototype pattern with six target surfaces is fabricated using three-dimensional printed components.