Transformation Dynamics in Origami.
A single origami crease pattern can be folded into many different structures from the flat-unfolded state, effectively transforming in shape and function. This makes origami engineering a promising approach to transforming machines, but predicting and controlling this transformation is difficult because the fundamental dynamics of origami systems at the flat-unfolded state are not well understood. Working with Miura-inspired mechanisms, we identify and validate a model to predict configuration switching in mechanical origami systems. The model incorporates a hidden degree of freedom introduced by material compliance in the Miura mechanism. We characterize this pseudojoint statically and dynamically to identify its lumped stiffness and inertia and use it to create a new dynamic model. This model can be used to predict which configuration an origami mechanism will settle in by balancing the kinetic and potential energy of the system. We apply this model to design a branching origami structure with 17 distinct configurations controlled by a single actuator and demonstrate reliable switching between these configurations with tailored dynamic inputs. Given the fact that origami can replicate almost any shape, we expect that this framework will be applicable to transformation in arbitrary structures and mechanisms.