Rigid foldability and mountain-valley crease assignments of square-twist origami pattern

Abstract

Rigid foldability allows an origami pattern to fold about crease lines without twisting or stretching component panels. It enables folding of rigid materials, facilitating the design of foldable structures. Recent study shows that rigid foldability is affected by the mountain-valley crease (M-V) assignment of an origami pattern. In this paper, we investigate the rigid foldability of the square-twist origami pattern with diverse M-V assignments by a kinematic method based on the motion transmission path. Four types of square-twist origami patterns are analyzed, among which two are found rigidly foldable, while the other two are not. The explicit kinematic equations of the rigid cases are derived based on the kinematic equivalence between the rigid origami pattern and the closed-loop network of spherical 4R linkages. We also convert a non-rigid pattern into a rigid one by introducing an extra crease. The kinematic analysis of the modified pattern reveals an interesting bifurcation behaviour. This work not only helps to deepen our understanding on the rigid foldability of origami patterns and its relationship with the M-V assignments, but also provides us an effective way to create more rigidly foldable origami patterns from non-rigid ones.

Theoretical characterization of a non-rigid-foldable square-twist origami for property programmability

“…4A, the dihedral angles of all the 13 creases, as well as the diagonal tension displacement, can be determined by only one input dihedral angle, which is set as φ4, from the kinematic model recently developed by the authors [52] (detailed mathematical equations in Supplementary Section 1). The kinematic research in ref [52] shows that arbitrary φ4 corresponds to one φi (i=1, 2, 3, 7, 8, 9, 10) and two different values of φj (j=5, 6, 11, 12, 13), which implies that there are two kinematic paths between the fully folded and deployed configurations of type 2M pattern. The kinematic relationship of φ6 and φ4 is drawn in Fig.…”

“…1A and B) and two rigid-foldable ones (type 3 and 4 in Fig. 1C and D) [48,51], whose rigidity is analyzed by the kinematic method based on the motion transmission path [52]. The type 1 pattern was found to have a hidden degree of freedom and bi-stability [46], which was recently employed to design origami-equivalent compliant mechanism [53], frequency reconfigurable origami antenna [54], and mechanical energy storage [55].…”

“…A mathematical model was developed to study the kinematics of the pattern with a special twist angle of 45°, from which multiple folding paths were observed [57]. In a recent study, the authors explicitly derived the kinematic equations for the generalized type 2M pattern with an arbitrary twist angle [52]. Nevertheless, little work has been published on the mechanical properties of the type 2 square-twist.…”

Tensile behavior of square-twist origami inspired mechanical metamaterials with soft joints and chirality applications

“…Current study of type 1 foldable pattern is mainly focused on the unidirectional formation between the stable states and lacks a comprehensive study on the bi-directional changes between the stable states. This can be understood by the fact that transition from high-energy states to low-energy states has been extensively studied [60][61][62][63], while the lack of a full study of the whole process from low-energy states to high-energy states and back to low-energy states would ignore different important features of the transition between energy states. Here, we have also designed the CMMs based on STOMMs and combinatorial design principles, which retain the inherent behavior of STOMMs while generating new behavior.…”

Multi‐Stability of the Extensible Origami Structures

“…[19][20][21][22] Origami is an ancient art of folding flat sheets of paper to form complex two-dimensional (2D) or 3D structures without cutting or bonding. Though traditional origami articles mainly DOI: 10.1002/advs.202303454 originate from art, nowadays various design approaches, including periodic [23] and non-periodic [24] tessellation, assignment of mountain-valley crease, [25] think-panel transformation, [26] biomimicry, [27] have been proposed to develop novel origami structures with remarkable mechanical properties for applications in engineering fields from aerospace, [28,29] robotics, [30,31] metamaterials. [32,33] Alongside, series of analytical and numerical tools, including kinematics, [34] computational geometry, [35,36] and crystallography, [37] have also been utilized for the design and analysis of origami structures.…”