Tailoring anisotropy in kirigami metamaterial skins with pop-up folding hinges

Kirigami metamaterial sheets and tubes, owing to their capacity to undergo large elastic deformations while developing three-dimensional surface textures, have enormous potential as skins for soft robots. Here, we propose to use kirigami skins with folding hinges in this same context. These recently-introduced kirigami feature counter-rotating panels connected by pop-up folding hinges. So far, researchers have only explored auxetic and highly-symmetric versions of such patterns. Yet, some of these attributes have to be relaxed in order to explore their full potential as robotic skins. Thus, we parameterize these patterns and relax symmetry constraints, with the goal of using this same platform to obtain a wide range of shape-morphing behaviors. We use a combination of: matrix analysis tools and analytical kinematic formulas to thoroughly explore the vast design space that ensues; experiments for validation purposes; and numerical simulations to explore the mechanics of selected planar and tubular patterns. We demonstrate that it is possible to tailor parameters to obtain skins that globally expand or contract due to axial elongation, and that present asymmetric pop-ups that can yield anisotropic friction -- the most desired attribute for one-way locomotion of soft robots.