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Research Papers

Deployable Prismatic Structures With Rigid Origami Patterns

[+] Author and Article Information
Sicong Liu

School of Mechanical and
Aerospace Engineering,
Nanyang Technological University,
50 Nanyang Avenue,
Singapore 639798, Singapore

Weilin Lv

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China;
School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China

Yan Chen

Key Laboratory of Mechanism Theory and
Equipment Design of Ministry of Education,
Tianjin University,
Tianjin 300072, China;
School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
e-mail: yan_chen@tju.edu.cn

Guoxing Lu

Faculty of Science,
Engineering and Technology,
Swinburne University of Technology,
Hawthorn, VIC 3122, Australia

1Corresponding author.

Manuscript received June 5, 2015; final manuscript received October 22, 2015; published online March 7, 2016. Assoc. Editor: Larry L. Howell.

J. Mechanisms Robotics 8(3), 031002 (Mar 07, 2016) (11 pages) Paper No: JMR-15-1129; doi: 10.1115/1.4031953 History: Received June 05, 2015; Revised October 22, 2015

Rigid origami inspires new design technology in deployable structures with large deployable ratio due to the property of flat foldability. In this paper, we present a general kinematic model of rigid origami pattern and obtain a family of deployable prismatic structures. Basically, a four-crease vertex rigid origami pattern can be presented as a spherical 4R linkage, and the multivertex patterns are the assemblies of spherical linkages. Thus, this prismatic origami structure is modeled as a closed loop of spherical 4R linkages, which includes all the possible prismatic deployable structures consisting of quadrilateral facets and four-crease vertices. By solving the compatibility of the kinematic model, a new group of 2n-sided deployable prismatic structures with plane symmetric intersections is derived with multilayer, straight and curvy variations. The general design method for the 2n-sided multilayer deployable prismatic structures is proposed. All the deployable structures constructed with this method have single degree-of-freedom (DOF), can be deployed and folded without stretching or twisting the facets, and have the compactly flat-folded configuration, which makes it to have great potential in engineering applications.

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Figures

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Fig. 1

Setup of the coordinate system and linkage geometric parameters in the links (i − 1)i and i(i + 1) connected by joint i

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Fig. 2

Definition of a single spherical 4R linkage

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Fig. 3

Assembly of two spherical 4R linkages j and j + 1

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Fig. 4

Closed assembly of N spherical 4R linkages

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Fig. 5

Transformations TUP(j+1)j and TLPj(j+1) in UP and LP

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Fig. 6

The projection of the intersection to the plane perpendicular to ridgelines

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Fig. 7

The plane symmetric relationship between linkages in the closed assembly

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Fig. 8

A 2n-sided prism with plane symmetric intersections: (a) quadrilateral, (b) hexagon, and (c) octagon

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Fig. 9

A four-sided prism with kite intersection

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Fig. 10

The kite intersection prism deploys from the (a) first 2D state to (b) a 3D structure; after reaching (c) the maximum height, it folds from (d) the 3D structure to (e) the second 2D state

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Fig. 11

The rotational symmetric relationship between linkages in the closed assembly

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Fig. 12

A 2n-sided prism with rotational symmetric intersections: (a) quadrilateral, (b) hexagon, and (c) octagon

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Fig. 13

A four-sided prism with a parallelogram intersection

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Fig. 14

The parallelogram intersection prism deploys from (a) the first 2D state to (b) a 3D structure until reaches (c) the maximum volume; then, it continues folding from (d) the 3D structure to (e) the second 2D state

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Fig. 16

A 2n-sided straight, multilayer prismatic structure with plane symmetric intersections

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Fig. 17

A 2n-sided straight, multilayer prismatic structure with rotational symmetric intersections

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Fig. 18

Construction of curvy prismatic structures with (a) plane symmetric intersection and (b) rotational symmetric intersection

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Fig. 19

Three examples of curvy prismatic structures: (a) all the dihedral angles have the same sign; (b) the dihedral angles change from being negative to positive; and (c) the dihedral angles are arbitrary

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Fig. 20

The origami tents, based on the deployable prismatic structures, were deployed in the stadium of the Tianjin University for temporary accommodations during the university activity

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