Origami Structure: Kinematics and Applications

Transcription

1 Origami Structure: Kinematics and Applications Professor Yan Chen School of Mechanical Engineering Tianjin University, China

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3 Spatial Mechanisms Deployable Structures Origami Structures Fundamental Engineering Motion Structures Theory Application Aerospace Structures Light-weight Structures Robotics 3

4 Contents Origami: Art, Mathematics, Engineering Kinematics of rigid origami Engineering applications of origami structures Future development 4

5 Origami 5

6 Origami: Art 6

7 Origami: Mathematics 7

8 Origami: Engineering You, Z. (2014). Folding structures out of flat materials. Science, 345(6197), Felton, S., Tolley, M., Demaine, E., Rus, D., & Wood, R. (2014). A method for building self-folding machines. Science, 345(6197),

9 Contents Origami: Art, Mathematics, Engineering Kinematics of rigid origami Engineering applications of origami structures Future development 9

10 Rigid Origami Rigid Origami = Mechanism Motion Rigid origami pattern: α + β + γ + δ = 2π 10

11 Rigid Origami Patterns The deformable polygons in discrete differential geometry 11

12 Rigid Origami: Planar structures 12

13 Rigid Origami: Tubular structures 13

14 Square-twist pattern θ = θ, θ = θ. Conditions for square-twist pattern: α12 + α34 = π, π α23 = α41 =. 2 four-fold rotational symmetry. 14

15 Square-twist pattern Corresponding mechanism network of square twist pattern Compatibility condition: 15

16 Square -twist Pattern 0 θ π, π θ 0. M Maekawa-Justin theorem: M V =± 2 Big-Little-Big Angle theorem V Different arrangement of Mountain-Valley fold lines Type 1 Type 2 Type 3 Type 4 16

17 Square -twist Pattern Type 1 Type 2 Type 3 Type 4 17

18 Square -twist Pattern: Type 1 18

19 Square -twist Pattern: Type 3 19

20 Square-twist Tessellation Crease Pattern 20

21 Type 1 Type 2 Type 3 Type 4 21

22 Contents Origami: Art, Mathematics, Engineering Kinematics of rigid origami Engineering applications of origami structures Future development 22

23 Metamaterial with negative Poisson s ratio 23

24 Medical devices based on origami structures Kuribayashi, K., Tsuchiya, K., You, Z., Tomus, D., Umemoto, M., Ito, T., & Sasaki, M. (2006). Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil. Materials Science and Engineering: A, 419(1),

25 Medical devices based on origami structures NOTES: Natural Orifice Translumenal Endoscopic Surgery 25

26 Origami structures for absorbing energy and carrying load Conventional square tube Origami crash box Force (kn) Displacement (mm) 26

27 Origami structures for absorbing energy and carrying load 27

28 Large-scale deployable structures 28

29 Contents Origami: Art, Mathematics, Engineering Kinematics of rigid origami Engineering applications of origami structures Future development 29

30 Future development Rigid origami: Tessellation is a powerful tool in synthesis; Kinematics of the linkages is the fundamental; To find more new rigid origami patterns, especially with large deployable ratio. Engineering applications: Compliant structures are the bridge; To widen the application areas; To enhance the advantages of origami structures. Collaboration in the interdisciplinary research! 30

31 Acknowledgement Professor Zhong You in University of Oxford, UK Professor Shuxin Wang in Tianjin University, China Professor Guoxing Lu in Nanyang Technological University, Singapore Professor. Kaori Kuribayashi-shigetomi in Hokkaido University, Japan Dr. Jianmin Li in Tianjin University, China Dr. Jiayao Ma in University of Oxford, UK Mr. Kunfeng Wang in NTU Singapore Mr. Peng Rui and Mr. Guokai Zhang in TJU China 31

32 Acknowledgement 32

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