Tailoring asymmetry for anisotropic friction 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 derive kinematic formulas to explore the vast symmetry-enabled design space. We then use numerical simulations and experiments to validate the kinematic predictions and to explore the morphing mechanics of tubular skins. Finally, via experiments, we provide preliminary evidence of the anisotropic friction enabled by patterns with asymmetric pop-ups. We therefore demonstrate that it is possible to tailor parameters in kirigami with folding hinges to obtain skins that globally expand or contract due to axial elongation, and that present asymmetric pop-ups that yield anisotropic friction - the most desired attribute for one-way locomotion of soft robots.