Design of Origami-based Actuators*
Minoru Taya, Director
Center for Intelligent Materials and Systems
Nabtesco Endowed Chair Professor
University of Washington
Email: tayam@uw.edu
http://depts.washington.edu/cims/
Collaborators: Profs. Miura, Tachi, University of Tokyo* This work was supported by a AFOSR grant and Nabtesco
contract to University of Washington

November 26, 2013

UW - Center for Intelligent Materials and Systems1

Contents of my talk• 1. Tachi-Miura Bellow under compressiveforce• 2. Bellow actuator based on FSMAcomposite• 3. Bioinspired design of SMA actuator for
beetle wing folding/unfolding• 4. free-falling MAV made of origami

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1. Introduction
Goal: Applying “Origami” to engineering applicationsuch as actuators and developable space structures
Rigid-foldable structures‒ Deformation takes place only along the crease lines

zyx

Tachi-Miura Polyhedron
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Folding
Behaviorloadingof TMP (Proc. Roy. Lond. 2013, A469,20130351)
Compression
Compression TestFH0zyx

Conditions for compression test of TMP bellow
Initial heightH0 [mm]Total displacement[mm]

Displacement rate
[mm/sec]

1501004 2.0

UW - Center for Intelligent Materials and Systems43.
Folding
BehaviorofTMP(2)
ConsideringThicknessof the paper
ResultComparison
betweenexperiment
andprediction(Single layer)
Extended Hamilton Principle (Taya and Mura, 1974)
t1

t1

t0t0

 J    T  U  dt    Ddt
Compression Test of TMPtf tf1 2
 J     v  d dV   2M  dli   F udS  dt     Ddli dtli
S00 li V2BendingWork

Kinetic Energy

Negligible
due to compression speed

Mechanical
WorkEnergy
Dissipation

Apply the prediction forceB   2M dli   F dulis

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3.
Folding
Behavior
ofTMP(2)
Considering
Thicknessof the paper
ResultComparison
betweenexperiment
andprediction(Single layer)

Result of compression test
Mechanical WorkW [J]

Bending Work
B [J]

δJ[J]

δJ/W
[%]

0.338

0.292

0.046

13.6

6

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Where are the energy dissipations ?

• 1. plastic work at the high stressconcentration points; vertices and creaselines• 2. friction work of the top and bottom
surfaces over the fixed boundary

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73.
Folding
Behavior
ofTMP(2)
Considering
Thicknessof the paper
ResultComparison
betweenexperiment
andprediction(Single layer)
TMP without vertices

Result of compression test
Mechanical WorkW [J]

Bending Work
B [J]

δJ
[J]

δJ/W
[%]

0.285

0.254

0.031

10.98

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83.
Folding
BehaviorofTMP(2)
ConsideringThicknessof the paper
ResultEnergyDissipation(Singlelayer)
1) Friction at the top and bottom

Cross-section area [mm2]

4250
4200
4150
4100
4050
40003950
020406080
Displacement u [mm]9UW - Center for Intelligent Materials and Systems

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9Concept A: Hybrid Mechanism of FSMA and FSMA
composites
Stress martensite
phase()Almost parallel

austenite
phase
Temperature(T)

The effect of uniform(constant) magnetic field isvery smallt
σ ij,j f i m  ρ vif i m   0 M jp H j ,iChain-reaction:
Applied magnetic field gradient magnetic force Stress-induced martensite transformation
 low stiffness of FePd large deformation
120

Young’s modulus (GPa)

3D-phase diagram

80martensite
phaseaustenite
phase

40
0-50

Ms 050100150Temperature (°C)

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10Early bellow design• Parametric study on this bellow
using FEA has been done tooptimize the design to reduce thereaction force.

Compressive forceRθtN

Circumferential stressH• However, it was found that thisshape is not suitable to reduce thereaction force because of itscircumferential stress.
• Moreover, this shape is not easy tomanufacture.

dDSwitched to new design
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Segmented type bellow actuator

AA

NiTi curved plate

EM driver

SMA Leg
Rigid part
Bolt & Nut
Section A-A

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Bending fatigue curveεpr = 0.5 %Pulsating 4-point bending
Nominal thickness: 0.7 mm,Frequency: 10 Hz, Temperature: 25 °C, in air• Fatigue life of chemically etched specimen is slightly longer.
• Fatigue limit is around proportional limit strain (εpr).
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Wing folding and unfolding of a beetle(Allomyrina Dichotoma)
During the time on the ground the beetles store
their hind wings under a thick forewing (Elytron)
from damages.
When the beetle is about to fly, it open's the thickfore wing and forcefully opens the hind wing tostraighten the wing.
Unfolding of hindwing(Nomura, 2010)
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Past Study-1 on origami folding(Haas, 1996)

The complex wing of the beetle isa combination of several basicvertex mechanism.
At every vertex where 4 lines
converge 3 mountain folds to 1
valley fold or 3 valley fold to 1
mountain fold is formed.

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Conclusion
Folding Ratio =Surface Area of Unfolded Wing
Surface Area of Folded Wing

Best ratio degrees
Alpha degree

Beta degree

Ratio

14°

85°

3.14

FoldedRatio Comparison
Real BeetleWingbio-inspired
Wing

2.32

3.141

Unfolded

BeetleWing

Bio-inspired
Wing

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Hitching methods
Nature Design: Insect wing
hitching methodBio-inspired hitching
methodFore Wing
Hitching
claw

HeatedOpening
for hook
Wing
Folding(heated)ThoraxHitchingclaw

Room
Temperature(Richard andDavies, 1977)

Hind Wing

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Wingfolded(heatingstopped)

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Bio-inspired Wing Storage
ThoraxWings expandedby the SE in room
temperature

Wings foldedcompletely in theThorax by theSMP, SMA andremain folded by
the hook.

When heatedthe wing will
fold into it's
memorized
shape and
unfold to it's flatstate in room
temperature.
SMA Hookroom
temperature50%
heating80%
heating

Opening for hook
Wing Hitched
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Folding of leaves(Kentucky Blue Grass)

Fig. 2. How a leaf of Kentucky bluegrass Poa pratense (a European weed) can
fold to exhibit large morphing using the concept of expansion and shrinkage ofmotor cells, (a) zoom up of the upper part of the leaf with expanded motorcells, (b)-(e) sequence of expansion, entire leaf showing folded in morphology
by kinking at several hinges.

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19Expansion of Super-configurable MAVUW - Center for Intelligent Materials and Systems20