Kinematics and dynamics of non-developable origami

Non-developable origami is a unique type of origami structures that cannot be unfolded into a flat sheet without stretching. In this work, we study the kinematics and dynamics of such origami, theoretically, numerically and experimentally, considering rigid panels and stretchable creases. Unlike developable origami, we find that non-developable origami exhibits distinct folding angle relationships, leading to several separate branches in its kinematic configuration space with snap-through and locking behaviours. By modelling the creases as stretchable torsional springs, we derive a dynamic model to analyse the deployment of non-developable origami structures, from single-vertex origami to origami chains. Our dynamic model unveils the snap-through behaviour between the two kinematics branches of the single-vertex non-developable origami structure, which is further validated by experiments with excellent agreement. We believe that our kinematic and dynamic framework of non-developable origami will greatly expand the current design space of origami structures and guide the design of novel origami actuators.