Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the predetermined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist origami pattern using the kinematic equivalence between the rigid origami and the spherical linkages. All schemes of M-V assignment are derived based on the flat-foldable conditions among which rigidly foldable ones are identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard are developed by applying kirigami technique to the rigidly foldable pattern without changing its degree-of-freedom. The proposed method opens up a new way to generate spatial overconstrained linkages from the network of spherical linkages. It can be readily extended to other types of origami patterns

A plane linkage and its tessellation for deployable structure

Deployable structures are widely used in space applications such as solar arrays and antennas. Recently, inspired by origami, more deployable structures have been developed. This paper outlined a novel design scheme for deployable structures by taking a plane linkage as an origami unit with a large deployable ratio. The mountain and valley (M-V) crease assignment and kinematics of the plane linkage were analyzed. Physical interference in the folding progress was discovered geometrically and resolved by the split-vertex technique. Finally, tessellation of the derived pattern was successfully used to create a large-deployable-ratio structure, which was found to exhibit considerable potential in future space applications

Folding of Tubular Waterbomb

Origami has recently emerged as a promising building block of mechanical metamaterials because it offers a purely geometric design approach independent of scale and constituent material. The folding mechanics of origami-inspired metamaterials, i.e., whether the deformation involves only rotation of crease lines (rigid origami) or both crease rotation and facet distortion (nonrigid origami), is critical for fine-tuning their mechanical properties yet very difficult to determine for origami patterns with complex behaviors. Here, we characterize the folding of tubular waterbomb using a combined kinematic and structural analysis. We for the first time uncover that a waterbomb tube can undergo a mixed mode involving both rigid origami motion and nonrigid structural deformation, and the transition between them can lead to a substantial change in the stiffness. Furthermore, we derive theoretically the range of geometric parameters for the transition to occur, which paves the road to program the mechanical properties of the waterbomb pattern. We expect that such analysis and design approach will be applicable to more general origami patterns to create innovative programmable metamaterials, serving for a wide range of applications including aerospace systems, soft robotics, morphing structures, and medical devices

Rigid Folding of Generalized Waterbomb Origami Tubes

The accurate theoretical description of the folding motion of origami structures is the foundation for their design and precise control in engineering applications. However, the folding behavior of most general origami structures is very difficult to analyze because of the lack of theoretical model and analysis methodology for the complex mobile assemblies of spherical linkages. This paper focuses on the widely-used Waterbomb origami tubes. Based on the kinematics and compatibility of spherical linkages, the rigid folding behavior of generalized Waterbomb tubes was systematically analyzed with analytical kinematics equations to describe their rigid contract and twist motion. The effect of various geometrical parameters on the rigid folding behaviour, bifurcation property as well as physical blockages of the Waterbomb origami tube was studied. This work lays a theoretical foundation for the design and control of programmable metamaterials, deformable structures, and robots based on Waterbomb origami tubes, while such kinematic model can be readily applied to other origami patterns

Helical structures with switchable and hierarchical chirality

Chirality is present as a trend of research in biological and chemical communities for it has a significant effect on physiological properties and pharmacological effects. Further, manipulating specific morphological chirality recently has emerged as a promising approach to design metamaterials with tailored mechanical, optical, or electromagnetic properties. However, the realization of many properties found in nature, such as switchable and hierarchical chirality, which allows electromagnetic control of the polarization of light and enhancement of mechanical properties, in man-made structures has remained a challenge. Here, we present helical structures with switchable and hierarchical chirality inspired by origami techniques. We propose eggbox-based chiral units for constructing homogeneous and heterogeneous chiral structures and demonstrate a theoretical approach for tuning the chirality of these structures by modulating their geometrical parameters and for achieving chirality switching through mechanism bifurcation. Finally, by introducing a helical tessellation between the chiral units, we design hierarchical structures with chirality transferring from construction elements to the morphological level and discover a helix with two zero-height configurations during the unwinding process. We anticipate that our design and analysis approach could facilitate the development of man-made metamaterials with chiral features, which may serve in engineering applications, including switchable electromagnetic metamaterials, morphing structures, and bionic robots

Residual Stress-Driven Non-Euclidean Morphing in Origami Structures

Non-Euclidean surfaces are ubiquitous in numerous engineering fields, such as automotive, aerospace, and biomedical engineering domains. Morphing origami has numerous potential engineering applications, including soft robots, mechanical metamaterials, antennas, aerospace structures, and biomedical devices, owing to its intrinsic morphing features from two-dimensional (2D) planes to three-dimensional (3D) surfaces. However, the current one-dimensional (1D) hinge deformation-driven transformation of foldable origami with rigid or slightly deformable panels cannot achieve a 3D complex and large curvilinear morphing. Moreover, most active origami structures use thin hinges with soft materials on their creases, thus resulting in a lower load capability. This study proposes a novel origami morphing method that demonstrates large free-form surface morphing, e.g., Euclidean to non-Euclidean surface morphing with shape-locking. We embedded tensorial anisotropic stress in origami panels during the extrusion-based 3D printing of shape memory polymers. The extrusion-based 3D printing of isotropic shape memory polymers can produce tensorial anisotropic stress in origami panels during fabrication, which can realize large non-Euclidean surface morphing with multiple deformation modes. The connecting topology of the origami unit cells influences the global morphing behavior owing to the interaction of the deformation of adjacent panels. Non-Euclidean morphing integrated with four-dimensional (4D) printing can provide multimodal shape locking at material and structural levels. The non-Euclidean surface morphing caused by tensorial residual stress in the panel during 3D printing expands the design space of origami and kirigami structures

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

Using non-rigid-foldable origami patterns to design mechanical metamaterials could 14 potentially offer more versatile behaviors than the rigid-foldable ones, but their applications are 15 limited by the lack of analytical framework for predicting their behavior. Here, we propose a 16 theoretical model to characterize a non-rigid-foldable square-twist origami pattern by its rigid origami 17 counterpart. Based on the experimentally observed deformation mode the square-twist, a virtual 18 crease was added in the central square to turn the non-rigid-foldable pattern to a rigid-foldable one. 19 Two possible deformation paths of the non-rigid-foldable pattern were calculated through kinematic 20 analysis of its rigid origami counterpart, and the associated energy and force were derived 21 analytically. Using the theoretical model, we for the first time discovered that the non-rigid-foldable 22 structure bifurcated to follow a low-energy deformation path, which was validated through 23 experiments. Furthermore, the mechanical properties of the structure could be programmed by the 24 geometrical parameters of the pattern and material stiffness of the creases and facets. This work thus 25 paves the way for development of non-rigid-foldable origami-based metamaterials serving for 26 mechanical, thermal, and other engineering applications

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

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 4 R linkages. We also convert a non-rigid pattern into a rigid one by introduc- ing 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 pro- vides us an effective way to create more rigidly foldable origami patterns from non-rigid ones

Altered resting-state functional connectivity of insula in children with primary nocturnal enuresis

ObjectivePrimary nocturnal enuresis (PNE) is a common developmental condition in school-aged children. The objective is to better understand the pathophysiology of PNE by using insula-centered resting-state functional connectivity (rsFC).MethodsWe recruited 66 right-handed participants in our analysis, 33 with PNE and 33 healthy control (HC) children without enuresis matched for gender and age. Functional and structural MRI data were obtained from all the children. Seed-based rsFC was used to examine differences in insular functional connectivity between the PNE and HC groups. Correlation analyses were carried out to explore the relationship between abnormal insula-centered functional connectivity and clinical characteristics in the PNE group.ResultsCompared with HC children, the children with PNE demonstrated decreased left and right insular rsFC with the right medial superior frontal gyrus (SFG). In addition, the bilateral dorsal anterior insula (dAI) seeds also indicated the reduced rsFC with right medial SFG. Furthermore, the right posterior insula (PI) seed showed the weaker rsFC with the right medial SFG, while the left PI seed displayed the weaker rsFC with the right SFG. No statistically significant correlations were detected between aberrant insular rsFC and clinical variables (e.g., micturition desire awakening, bed-wetting frequency, and bladder volume) in results without global signal regression (GSR) in the PNE group. However, before and after setting age as a covariate, significant and positive correlations between bladder volume and the rsFC of the left dAI with right medial SFG and the rsFC of the right PI with right medial SFG were found in results with GSR in the PNE group.ConclusionTo the best of our knowledge, this study explored the rsFC patterns of the insula in children with PNE for the first time. These results uncovered the abnormal rsFC of the insula with the medial prefrontal cortex without and with GSR in the PNE group, suggesting that dysconnectivity of the salience network (SN)-default mode network (DMN) may involve in the underlying pathophysiology of children with PNE. However, the inconsistent associations between bladder volume and dysconnectivity of the SN-DMN in results without and with GSR need further studies