Intrinsic Bistability Via Thick-Panel Design in High-Degrees-of-Freedom Resch Origami

Abstract Origami with high degrees-of-freedom (DOF), such as the Resch tessellation, offers a vast design space for complex morphing structures but poses significant control challenges. Embedding bistability is a promising strategy to simplify actuation, yet existing methods for creating intrinsic multistability are largely confined to kinematically simple, low-DOF patterns. This article presents a systematic computational framework to design intrinsically bistable thick-panel structures from high-DOF Resch origami. Our decoupled, two-stage approach first employs a stochastic gradient descent-based kinematic simulation to discover a viable, complex folded configuration from the vast design space of a zero-thickness model. Subsequently, it formulates a set of bi-compatibility constraints for both the unfolded and the target folded states, which are then efficiently solved using linear programming to determine the thick-panel geometry. The efficacy of the framework is demonstrated through the design and verification of two Resch-ori units: one with bistability between fully-flat and fully-folded states, and another between the flat and an arbitrarily prescribed spatial state. The bistability is numerically verified by analyzing the kinematic degrees-of-freedom and the minimum energy path between stable states. This work provides a robust and computationally efficient pathway for harnessing the complexity of high-DOF origami to create functional, bistable systems.