Nonrigidly Foldability Analysis of Kresling Cylindrical Origami

Abstract

Rigid origami is seen as a fundamental model in many self-folding machines. A key issue in designing origami is the rigid/nonrigid foldability. The kinematic and foldability of Kresling origami, which is based on an origami pattern of the vertex with six creases, are studied in this paper. The movement of the single-vertex is first discussed. Based on the quaternion method, the loop-closure equation of the vertex with six creases is obtained. Then, the multitransformable behavior of the single vertex is investigated. Furthermore, the rigid foldability of origami patterns with multivertex is investigated with an improved dual quaternion method, which is based on studying the folding angle and the coordinates of all vertices. It can be found that the Kresling cylinder is not rigidly foldable.

The Kresling origami spring: a review and assessment

“…the resistance offered by panel interaction is negligible. In fact, it was observed experimentally and proven theoretically that the triangular panels do warp during deformation [42,124], and that the deformation of the truss elements exhibits a nonlinear stress-strain behavior especially under larger deformations [125]. Moreover, the creases were observed to buckle under loading, and self avoidance due to panel contact was found to be significant at small deployment heights.…”

Design and analysis of a conical origami tube (COT) composed of quadrilateral unit cells

“…Based on these assumptions, many previous studies have been conducted to demonstrate the accuracy and effectiveness of truss models in capturing the elastic behaviors of flexible foldable mechanisms. Examples include Kresling [50,52], Miura [53], Waterbomb [54][55][56], Yoshimura [57], and Resch [58,59]. Essentially, the truss model is used to capture the featured deformation characteristics, and the potential energy of the COT can be represented by the total strain energy stored in the deformable trusses.…”

An Origami-Based Medical Support System to Mitigate Flexible Shaft Buckling

“…The triangulated cylinder pattern can exhibit bistable behavior because it is not a rigid-foldable pattern [57], meaning it experiences strain and deformation in the creases and panels during actuation. The dimensions of the triangulated cylinder pattern can be tailored to provide a desired degree of stability, and strain energy curves can assist in determining when the pattern becomes bistable.…”