Designing Self-Blocking Systems With Non-Flat-Foldable Degree-4 Vertices

Non-flat-foldable origami patterns can be useful for making mechanisms that self-block at a wanted folded state. An origami pattern is “blocked” when at least one of the folds hits 180°. In this paper, we use non-flat-foldable developable degree-4 vertices as building elements for self-blocking one-DOF mechanisms. This paper also presents a method to identify the self-blocking crease from the unfolded pattern and its blocked configuration through spherical trigonometry. Furthermore, we synthesize the blocked state by using the proposed graphical approach. Lastly, we present two case studies: deployable stairs and a foldable chair.