Analyses of Morphological Properties of a Generalized Miura Origami Structure

In this paper, we generalize Miura origami and propose a method for analyzing a generalized Miura origami structure. Morphological properties of the generalized Miura origami element during the deploy motion are analyzed using the proposed method, which mainly utilizes the principle of spherical trigonometry and is verified in the folding limit state. The longitudinal length, horizontal length, and height of the generalized Miura origami element are defined and obtained using the proposed method. Results show the relationship between the range of deployment and the element parameters as well as the changes of the folding plane angles in the deployment process. During the deploy motion, both the longitudinal and horizontal length increased while the height decreased. However, the change speed of horizontal length decreased, whereas those of longitudinal length and height initially increased and then decreased. The increment of the folding element angle difference $Δα$ reduced folding range and put off the severe change time of longitudinal length and height. The length parameters $Ka$⁠, $Kb$⁠, and $Kab$ had slight effects on the results, but their changes did not alter the change trends. These results are useful to the design of fold structure and analysis of errors in standard Miura-ori structures.