From the Yoshimura origami pattern to foldable structures: Exploration of crease design

Crease design is crucial to the function and application scope of origami projects; however, for the Yoshimura origami pattern, the connection between origami two-dimensional (2D) creases and three-dimensional (3D) forms has not been established, which greatly limits the research and application of origami structures. In this paper, a crease design theory for the Yoshimura origami pattern is proposed to create 3D foldable origami structures. Afterward, the flat origami folding process is described, and the corresponding end trajectory equations are derived from a crease chain folding analysis performed on the element block and the expansion block. Next, the positional and angular constraint equations for single-variable, double-variable, and triple- variable foldable forms with only element blocks are systematically discussed. Finally, a detailed folding simulation analysis is performed based on the positional and angular constraint equations, and the foldable form family diagrams with the corresponding angular value intersection curve constraints are summarized. The theory is verified by finite element programs and experiments. This work provides an effective theory for the design of origami creases and new ideas and methods for the study of the Yoshimura pattern and other origami patterns.