An Extended Family of Rigidly Foldable Origami Tubes

Chen, Yan; Lv, Weilin; Li, Junlan; Zhang, You

doi:10.1115/1.4035559

Cited by 43 publications

(23 citation statements)

References 11 publications

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“…Based on the equivalence between linkage and rigid origami [9,23,24], for all the mobile assemblies of the four-spherical-4R-integrated linkages obtained in Section 3 there exist corresponding rigid origami patterns. However, for each equivalent rigid origami, besides the compatibility conditions for the mobile assemblies mentioned above, some extra conditions known as flat-foldability [25,31] should be added.…”

Section: A Novel Origami Pattern Obtained From the Variationsmentioning

confidence: 99%

“…(5) and (15a), we can derive that 12 2 k π α = . Since the pattern can be folded to a plane and deployed to a cuboid, we can also derive that 23…”

Section: Flat-foldability Of Degree-4 Verticesmentioning

confidence: 99%

“…Liu [21] used the assemblies of spherical 4R linkages to analyze the rigid origami patterns and presented several new patterns. Based on the kinematics of spherical 4R linkages, Liu et al [22] presented several types of rigid origami tubes, and recently Chen et al [23] proposed an extended family of them. However, the spherical 4R linkage method applied to analyze rigid origami patterns requests quite complicated closure equations, which limits the design of rigid origami.…”

Section: Introductionmentioning

confidence: 99%

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Mobile assemblies of four-spherical-4R-integrated linkages and the associated four-crease-integrated rigid origami patterns

Chen

Peng

et al. 2019

Mechanism and Machine Theory

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Rigid origami, which can be regarded as assemblies of spherical linkages, inspires a new paradigm of design for mechanical metamaterials and deployable structural systems with large deployable ratio. In this paper, the kinematic properties of assemblies of spherical 4R linkages are studied, and new origami patterns are obtained. Kinematics of a single loop spherical 4R linkage is firstly presented, and by assigning four specified values for the four twist angles, and defining four pairs of specified input and output angles, 16 maps between the input and output angles are obtained together with 256 types of special spherical 4R linkages. By merging four identical spherical 4R linkages into a single loop, three basic mobile assemblies are constructed and the one-degree-of-freedom kinematic compatibility condition is formulated. Through alteration of the four vertex linkages in the three basic assemblies, variations of the basic assemblies are generated. Consequently, by adding further geometric conditions, novel rigid origami patterns are obtained leading to the tessellation of the spherical-4R-linkageintegrated assemblies. Hence, this paper provides a novel approach for generating new rigid origami patterns which can lead to the development of foldable structures and tessellations with potential applications in robotics, smart architectures, and space exploration.

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Section: A Novel Origami Pattern Obtained From the Variationsmentioning

confidence: 99%

“…(5) and (15a), we can derive that 12 2 k π α = . Since the pattern can be folded to a plane and deployed to a cuboid, we can also derive that 23…”

Section: Flat-foldability Of Degree-4 Verticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mobile assemblies of four-spherical-4R-integrated linkages and the associated four-crease-integrated rigid origami patterns

Chen

Peng

et al. 2019

Mechanism and Machine Theory

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“…A single-vertex pattern with all creases intersected at the vertex is kinematically a spherical linkage 21 . Then the multi-vertex crease pattern can be modelled as a network of spherical linkages, and its rigidity can be analysed by kinematic approach 22 – 24 .…”

Section: Introductionmentioning

confidence: 99%

Twist of Tubular Mechanical Metamaterials Based on Waterbomb Origami

Feng

Chen

et al. 2018

Sci Rep

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Origami-inspired mechanical metamaterials have recently drawn increasing attention since their flexible mechanical performance has been greatly enhanced by introducing origami patterns to the thin-shell structures. As a typical origami pattern, the waterbomb tube could be adopted to the design of mechanical metamaterials. However, existing designs predominantly make use of the radial expansion/contraction motion of the structure, thereby limiting its full potential to be explored. Here we report a twist motion of tubular mechanical metamaterials based on waterbomb origami that is previously undiscovered. We demonstrate through a detailed kinematic analysis that the initial twist is a rigid-origami motion if the corresponding row of the tube under twist is fully squeezed with both line and plane symmetry, whereas all the subsequent twist motion requires material deformation. The twist angle per axial strain and its relationship with the geometrical parameters of the tube are revealed. Experimental results show the enhancement in stiffness of the tube with the occurrence of the continuous twist motion. We envisage that this finding could greatly expand the application of the waterbomb tube in the design of origami metamaterials with programmable and tuneable mechanical properties.

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“…Rigidly foldable origami can be modeled using the pseudo-rigid-body model concept [15] where creases are modeled as revolute joints and panels as rigid links. This results in rigidlink spatial mechanisms that can be modeled using the methods traditionally employed to model the kinematics of rigid-link mechanisms [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Rigidly Foldable Quadrilateral Meshes From Angle Arrays

Lang¹,

Howell

2018

Journal of Mechanisms and Robotics

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We present a design technique for generating rigidly foldable quadrilateral meshes (RFQMs), taking as input four arrays of direction angles and fold angles for horizontal and vertical folds. By starting with angles, rather than vertex coordinates, and enforcing the fold-angle multiplier condition at each vertex, it is possible to achieve arbitrarily large and complex panel arrays that flex from unfolded to flatly folded with a single degree-of-freedom (DOF). Furthermore, the design technique is computationally simple, reducing for some cases to a simple linear-programming problem. The resulting mechanisms have applications in architectural facades, furniture design, and more.

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An Extended Family of Rigidly Foldable Origami Tubes

Cited by 43 publications

References 11 publications

Mobile assemblies of four-spherical-4R-integrated linkages and the associated four-crease-integrated rigid origami patterns

Mobile assemblies of four-spherical-4R-integrated linkages and the associated four-crease-integrated rigid origami patterns

Twist of Tubular Mechanical Metamaterials Based on Waterbomb Origami

Rigidly Foldable Quadrilateral Meshes From Angle Arrays

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