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Research Papers

An Extended Family of Rigidly Foldable Origami Tubes

[+] Author and Article Information
Yan Chen, Weilin Lv, Junlan Li

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

Zhong You

School of Mechanical Engineering,
Tianjin University,
Tianjin 300072, China
Department of Engineering Science,
University of Oxford,
Parks Road,
Oxford OX1 3PJ, UK
e-mail: zhong.you@eng.ox.ac.uk

1Corresponding author.

Manuscript received October 17, 2016; final manuscript received December 13, 2016; published online March 9, 2017. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 9(2), 021002 (Mar 09, 2017) (7 pages) Paper No: JMR-16-1320; doi: 10.1115/1.4035559 History: Received October 17, 2016; Revised December 13, 2016

Rigidly foldable origami tubes with open ends have been reported in the past. Here, using a mechanism construction process, we show that these tubes can be used as building blocks to form new tubes that are rigidly foldable with a single degree-of-freedom (SDOF). A combination process is introduced, together with a possibility of inserting new facets into an existing tube. The approach can be applied to both single and multilayered tubes with a straight or curved profile. Our work provides designers great flexibility in the design of tubular structures that require large shape change. The results can be readily utilized to build new structures for engineering applications ranging from deployable structures, meta-materials to origami robots.

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References

Figures

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Fig. 1

Construction of a tube by summation: (a) Tube 1, (b) Tube 2, (c) Tube 2 is attached to Tube 1, and (d) common portion of the joined tube is removed forming a new rigidly foldable tube

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Fig. 2

(a) Schematic diagrams of the summation method with shorter sides joined together, and the expansion sequence of a tube model from its flat folding state I and (b) schematic diagrams of the summation method with longer sides joined together, and the expansion sequence of a tube model from its flat folding state I to its second flat folding state V

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Fig. 3

Construction of a tube by subtraction: (a) Tube 1, (b) Tube 2, (c) Tube 2 is nested inside of Tube 1, (d) common portion of the joined tube is removed forming a new rigidly foldable tube, (e) Tube 2 is nested inside a corner of Tube 1 and (f) common portion of the joined tube is removed forming a new rigidly foldable tube

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Fig. 4

(a) Schematic diagrams of the subtraction method with Tube 2 nested inside the shorter side of Tube 1, and the expansion sequence of a tube model from its flat folding state I and (b) schematic diagrams of the subtraction method with Tube 2 nested inside the longer side of Tube 1, and the expansion sequence of a tube model from its flat folding state I to its second flat folding state V

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Fig. 5

(a) Schematic diagrams of the subtraction method in which Tube 2 with a kite cross section nested inside a corner of Tube 1 with a parallelogram cross section, and the expansion sequence of a tube model from its flat folding state I and (b) schematic diagrams of the subtraction method where Tube 2 with a parallelogram cross section is nested inside Tube 1 of a kite cross section, and the expansion sequence of a tube model from its flat folding state I to its second flat folding state V

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Fig. 6

(a) Schematic diagrams showing the combination of three tubes, and the folding sequence of a model tube and (b) schematic diagrams showing a different way of combining three tubes, and the folding sequence of a model tube

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Fig. 7

A spherical 4R linkage with the D-H notations, which is used to model a four-crease rigid origami

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Fig. 8

Formation of a shifted tube: (a) the original tube, (b) the transition part, and (c) the shifted tube after insertion of the transition pair

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Fig. 9

(a) Folding sequence of a shifted Tube. IV is the side view of the tube at configuration II, showing it has a nonplanar cross section and (b) folding sequence of another shifted tube. It is flat foldable, and has a planar cross section as demonstrated by IV: The side view of the tube at configuration II.

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Fig. 10

Folding sequence of a shifted tube with two transition pairs, T1 and T2 added

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Fig. 11

(a) Folding sequence of a shifted tube with transition pair T1 added. IV is the side view of configuration II and (b) folding sequence of the other shifted tube with transition pair T1 added at a place different from that in (a). IV is the side view of configuration II.

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Fig. 12

Folding sequences of multilayered straight tubes formed by (a) combination and (b) by shifting, respectively

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Fig. 13

A curved tube constructed by summation. (a) Two tubes (top) and their front view (bottom), (b) the combination of the tubes before and after the removal of the common side, and (c) a multilayered curved tube that deploys from flat folding state I.

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Fig. 14

(a) A portion of a curved multilayered tube, (b) a transition part is added, and (c) folding sequence of a model tube with an added transition pair

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