Multistable origami and its snapping behaviors between the folded states have attracted scientists' and engineers' attention as the building block for the design of mechanical devices and metamaterials. We propose a novel method for designing origami-based multistable structures, by which we mean (1) to obtain the prescribed overall motion and (2) to control the stiffness of snapping provided by the elastic strain. We solve this design problem by first representing the desired motion with linkage structures with quadrilateral holes, called the frames, and then filling the frames with origami modules, called quadrilateral boundary modules. By introducing an intentional incompatibility between the motions of the frames and the modules, we design the snapping behavior that follows the linkage motion. We provide the representation model to evaluate the incompatibility and propose an optimization-based framework for the design. We also validate our design applied to a Sarrus-linkage through bar-and-hinge analysis and experiments using physical prototypes.

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