Mobility Analysis of Thin-Panel Origamis Based on a Coplanar 2-Twist Screw System

Abstract

This paper presents an intuitive approach for mobility analysis of thin-panel origamis based on a coplanar 2-twist screw system, which consists of a pair of parallel/concurrent line vectors. In this study, we first proved that in any thin-panel origami, the allowable instantaneous mobility for any two facets connected to a third one can be described by a coplanar 2-twist screw system because this mobility is generated by two coplanar creases in the third facet. Second, the mobility of the basic origami units with a single facet loop was analyzed by using this coplanar 2-twist screw system. Third, the mobility analysis approach was extended to analyze the mobility of other planar/circular arraying origami patterns with multiple facet loops; typical origami patterns such as leaf-fold, Miura-ori were subjected to this analysis process. Furthermore, we proved that the proposed approach can be applied to the mobility analysis of complicated origamis; this approach proved to be considerably more intuitive than the traditional approach for mobility analysis.