Design of compliant mechanisms for origami metamaterials

As an art of paper folding, origami has been widely explored by artists for centuries. Only in recent decades has it gained attention from mathematicians and engineers for its complex geometry and rich mechanical properties. The surge of origami-inspired metamaterials has opened a new window for designing materials and structures. Typically, to build origami structures, a sheet of material is folded according to the creaselines that are marked with compliant mechanisms. However, despite their importance in origami fabrication, such compliant mechanisms have been relatively unexplored in the setting of origami metamaterials. In this study, we explore the relationship between the design parameters of compliant mechanisms and origami mechanical properties. In particular, we employ single hinge crease and Kresling origami, representative examples of rigid and non-rigid origami units, fabricated using a double-stitch perforation compliant mechanism design. We conduct axial compression tests using different crease parameters and fit the result into the bar-hinge origami model consisting of axial and torsional springs. We extract the relationship between the spring coefficients and crease parameters using Gaussian process regression. Our result shows that the change in the crease parameter contributes significantly to each spring element in a very different manner, which suggests the fine tunability of the compliant mechanisms depending on the mode of deformation. In particular, the spring stiffness varies with the crease parameter differently for rigid and non-rigid origami, even when the same crease parameter is tuned. Furthermore, we report that the qualitative static response of the Kresling origami can be tuned between monostable and bistable, or linear and nonlinear, by only changing the crease parameter while keeping the same fold pattern geometry. We believe that our compiled result proffers a library and guidelines for choosing compliant mechanisms for the creases of origami mechanical metamaterials.