Professor Yan Chen School of Mechanical Engineering

Tianjin University, China http://motionstructures.tju.edu.cn

yan_chen@tju.edu.cn

Origami Structure: Kinematics and Applications

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 2

1895

2015

Motion Structures

Origami Structures

Light-weight Structures

Robotics

Aerospace Structures

Deployable Structures

Spatial Mechanisms

Theory

Application

Fundamental

Engineering

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 3

Contents

• Origami: Art, Mathematics, Engineering

• Kinematics of rigid origami

• Engineering applications of origami

structures

• Future development

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 4

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 5

Origami

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 6

Origami: Art

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 7

Origami: Mathematics

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 8

Felton, S., Tolley, M., Demaine, E., Rus, D., & Wood, R. (2014). A method for building self-folding machines. Science, 345(6197), 644-646.

Origami: Engineering

You, Z. (2014). Folding structures out of flat materials. Science, 345(6197), 623-624.

Contents

• Origami: Art, Mathematics, Engineering

• Kinematics of rigid origami

• Engineering applications of origami

structures

• Future development

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 9

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 10

Rigid Origami = Mechanism Motion

Rigid origami pattern: πδγβα 2=+++

Rigid Origami

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 11

Rigid Origami Patterns

The deformable polygons in discrete differential geometry

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 12

Rigid Origami: Planar structures

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 13

Rigid Origami: Tubular structures

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 14

12 34

23 41

,

.2

+ =

= =

α α ππα α

Conditions for square-twist pattern: 1 4 4 1, .′ ′= − =θ θ θ θ

four-fold rotational symmetry.

Square-twist pattern

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 15

Compatibility condition:

Corresponding mechanism network of square twist pattern

Square-twist pattern

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 16

Square -twist Pattern

Different arrangement of Mountain-Valley fold lines

Type 1 Type 2 Type 3 Type 4

Big-Little-Big Angle theorem Maekawa-Justin theorem: 2M V− = ±

0 , 0.M V≤ ≤ − ≤ ≤θ π π θ

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 17

Square -twist Pattern

Type 1 Type 2 Type 3 Type 4

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 18

Square -twist Pattern: Type 1

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 19

Square -twist Pattern: Type 3

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 20

Square-twist Tessellation Crease Pattern

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 21

Type 1 Type 2

Type 3 Type 4

Contents

• Origami: Art, Mathematics, Engineering

• Kinematics of rigid origami

• Engineering applications of origami

structures

• Future development

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 22

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 23

Metamaterial with negative Poisson’s ratio

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 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), 131-137.

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 25

Medical devices based on origami structures

NOTES: Natural Orifice Translumenal Endoscopic Surgery

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

Displacement (mm)

Forc

e (k

N)

Conventional square tube Origami crash box

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 26

Origami structures for absorbing energy and carrying load

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 27

Origami structures for absorbing energy and carrying load

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 28

Large-scale deployable structures

Contents

• Origami: Art, Mathematics, Engineering

• Kinematics of rigid origami

• Engineering applications of origami

structures

• Future development

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 29

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 30

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!

Future development

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 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

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 32

Acknowledgement

http://motionstructures.tju.edu.cn/ yan_chen@tju.edu.cn 33