저 시-비 리- 경 지 2.0 한민

는 아래 조건 르는 경 에 한하여 게

l 저 물 복제, 포, 전송, 전시, 공연 송할 수 습니다.

다 과 같 조건 라야 합니다:

l 하는, 저 물 나 포 경 , 저 물에 적 된 허락조건 명확하게 나타내어야 합니다.

l 저 터 허가를 면 러한 조건들 적 되지 않습니다.

저 에 른 리는 내 에 하여 향 지 않습니다.

것 허락규약(Legal Code) 해하 쉽게 약한 것 니다.

Disclaimer

저 시. 하는 원저 를 시하여야 합니다.

비 리. 하는 저 물 리 목적 할 수 없습니다.

경 지. 하는 저 물 개 , 형 또는 가공할 수 없습니다.

공학석사학위논문

분산형 자가 접힘 종이접기 모듈을 통한

프로그래밍 가능한 시트

Morphing Voxel:

Development of the Physical Programmable Matter

Composed of Distributed Self-Folding Origami Modules

2017년 2월

서울대학교 대학원

기계항공공학부

김 사 름

i

Abstract

Morphing Voxel: Development of

the Physical Programmable Matter

Composed of Distributed Self-

Folding Origami Modules

Sa-Reum Kim

Department of Mechanical and Aerospace Engineering

The Graduate School

Seoul National University

Developing programmable matter in material world is a challenging issue. This

thesis presents a new programmable shape-changing system that is lightweight,

and compact composed of distributed morphing voxel. Mobility of the system

is generated by a multitude of identical units, so that the integrated system can

make and change into specific shapes. Morphing Voxel can generate the

dimensional variation between 3-D cubic block and 2-D flat sheet like physical

3-D pixel by designing simple origami pattern and embedding low-profile

actuator. Single voxel has 30 mm side length, weighs 2.2 g, and takes average

3 to 4 seconds for single transformation. By separating the system with

actuation unit–Morphing Voxel–and infrastructure–base layer–, the system

ii

have more freedom to the system in rearrangement, replacement, and repairing

of the unit.

The thesis presents a design and fabrication method of the morphing voxel for

compact shape-changing system as a way of building programmable matter in

physical world. Also, the thesis contains demonstration of the concept with 4×4

matrix form arrangement, and made 5×3 tangible letter shifting display. In

future, this system can be used as a shape-change platform for multi-functional

devices e. g. haptic interface, 3-D morphing map, and tangible display.

Keywords: Programmable Matter, Origami, Self-Folding, Modular System,

Smart Actuator

Student Number: 2015-20714

iii

Contents

Abstract .............................................................................. i

Contents ........................................................................... iii

List of Figures ....................................................................... iv

Chapter 1 Introduction ......................................................... 1

1.1 Motivation .............................................................................. 1

1.2 Research Objectives and Contributions ................................. 3

1.3 Research Overview ................................................................ 4

Chapter 2 Morphing Voxel Design ...................................... 5

2.1 Origami Pattern Design .......................................................... 5

2.2 Actuator and Structural Modeling ......................................... 5

Chapter 3 Fabrication ......................................................... 13

Chapter 4 Experiment and Result ..................................... 13

4.1 Single Morphing Voxel Transformation Performance ........ 13

4.2 Programmable Shape-changing sheet with matrix formation

arrangement .................................................................................. 16

Chapter 5 Conclusion .......................................................... 19

Bibliography ......................................................................... 20

iv

List of Figures

Figure 1.1 Programmable matter scheme of distributed origami morphing

voxel. (a) System composed of morphing voxel and the base layer,

(b) Shape-changing scheme by the integration of arranged

identical units... ........................................................................... 3

Figure 2.1 Side view of the morphing voxel with simple four-bar based

origami pattern. Origami structure is a composite consists of

flexure hinge for folding line and facet for panel.... ................... 6

Figure 2.2 Principle of torsional SMA wire actuator. .................................. 6

Figure 2.3 Design parameters of the morphing voxel. ................................. 8

Figure 2.4 Relationship of θ2 and θ3 compared to θ1 when 𝑙lf is

increasing. ................................................................................... 8

Figure 2.5 Relative angular velocity plot of joint based on θ1and θ2 as the

morphing voxel transforms from cubic block to flast sheet. .... 11

Figure 2.6 Relative angular velocity plot of joint based on θ1and θ2 as the

morphing voxel transforms from flat sheet to cubic block ....... 11

Figure 2.7 Transformation mechanism of the single morphing voxel. ...... 12

Figure 3.1 Fabrication process of the single origami pop-up cell (a) flexure

with etched circuit (b) facet lamination in one side (c) actuator

embedding (d) facet lamination on the other side (e) soldering the

electrodes (f) assembly (g) single origami pop-up cell ............. 14

v

Figure 4.1 Performance of the single origami morphing voxel. (a)

Assembled cell (b) 2-D planar view of the Origami pop-up cell

and its assembly (c) Close-up view of the actuator and the bottom

facet electrodes, and single cell performance (c) side view (d) top

view. ......................................................................................... 15

Figure 4.2 Voxel grouping and by-pass control circuit (a) 4 different cell

grouping (b) By-pass circuit with activated SMA group 1 and 2

(c) By-pass circuit with activated SMA group 2 and 3. ............ 17

Figure 4.3 Shape-changing performance of the 4×4 programmable sheet (a)

Front view (b) Diagonal view. .................................................. 17

Figure 4.4 Tangible letter shifting display with 5×3 matrix formation of

morphing voxels, (a) Letter ’B’, (b) Letter ’R’, (c) Letter ’L’. . 18

1

Chapter 1 Introduction

1.1 Motivation

Developing programmable matter in material world is a challenging issue.

Among various property of matter, shape represents visual information

delivered through sight, and affects the mechanical property of the structure so

that one of a primary consideration for the desired functionality. Shape-

changing material can be used as a hardware platform for multi-funtional device

by changing the form of the material, and also can be a new way of delivering

digital information [1] e.g. re-configurable robotic systems [2] , dynamic

architecture [3] , form display [4] , and smart packaging [5] .

Recently, as the emergence of the programmable matter concept, which aims

to program the property of material for building versatile material which have

a command of adapting its property for certain task, developing programmable

shape-changing system is a next goal of the shape-changing hardware design.

e. g. Claytronics [6], tangible interfaces [7], and 4-D printing [8].

Developing shape-changing hardware in physical 3-D world does not follow

the technology of digital world—general shape planning [9], acquisition [10],

re-shaping algorithm [11], and graphical animation of their appearance—due

to the mechanical constraints in material world. To realize shape-changing

hardware, researchers have tried various methods which can be categorized into

three approaches–modular system, discrete actuation unit system, and foldable

system.

Firstly, modular approach is the mostly exploited methods that employs

small modules as building blocks. For example, especially robotics researchers

2

developed a modular robot systems [2], a swarm robot systems [12] which can

reconfigure its shape into various combination of different terrain. The modular

approach is intuitive and universal method to make arbitrary shapes, but a

special protocol between each modules is required to define the final shape of

structure as the number of independent unit increases. These complicated

communication methodology algorithms acts as a bottleneck of modular

approaches, therefore, the number of units are limited or time for reshape takes

for lone time for more complex shape.

Secondly, discrete actuation unit system puts lots of dynamic units by

distributed manner. e.g. tangible interfaces with linear motor driven block panel

[l7] , with shape memory alloy(SMA) driven block [13], or linkage structured

re-configurable theater [3]. They are relatively free of communication problem

between units due to the fixed position, but dynamic units require bulky

infrastructures.

Lastly, foldable system which is based on the origami theory concept. It has

been suggested for building various complex three-dimensional (3-D) shapes

or deployable structures by folding two-dimensional (2-D) material. This

approach has made shape-changing systems more compact and easy to build

due to the underlying modularity14 and universality15 of the origami structure.

Also, self-folding technologies enables folding for diverse shape autonomously.

e. g. 4-D printing [8], self-assembly robot [16], reversely self-folding origami

sheet [14], [17]. However, the complexity of geometrical relationships between

folding units require complex pattern generation and folding sequence to build

diverse 3D shapes. Therefore, it is hard to realize shape-changing material that

has multiple configuration.

3

1.2 Research Objectives and Contributions

This thesis suggests a new approach of building shape-changing system

based on the discrete actuation unit system, but exploits both the modular and

the folding approach. illustrated as Figure 1.1.

The mobility of the system is generated by a multitude of discrete actuation

unit–morphing voxels. Morphing voxel rapidly generates dimensional variation

between 3-D cubic block and 2-D flat sheet by self-folding, shown in Figure

1.1 (a) with the color shifting of the top facet like three-dimensional pixel

(voxel). By designing origami pattern and embedding low-profile actuator, the

morphing unit can transform rapidly and reversely with low-profile and

lightweight hardware. We arranged 2-D matrices of these modules and

designated the shape combinations of distributed modules, so that the integrated

system can make and change into specific shapes.

Fig. 1.1. Programmable matter scheme of distributed origami morphing voxel.

(a) System composed of morphing voxel and the base layer, (b) Shape-changing

scheme by the integration of arranged identical units.

4

1.3 Research Overview

The thesis is arranged as follows. From the design of single morphing voxel

to multi-module system integration. System hardware is consists of two part,

morphing voxel as an actuation unit and the base layer as an infrastructure.

Morphing voxel is a transformable body embedded with the actuators and the

electrodes for the supply of the control signal and power comes from the base

layer. The base layer consist of fixation layer includes module contact point and

circuit layer for the power and signal input to the cell for designating target

configuration. Also, morphing voxel and the base layer can be attached or

detached through simple magnet contact. By separating the actuation unit and

infrastructure, we give more freedom to the system in rearrangement,

replacement, and repairing of the unit.

We made the morphing voxel with 30 mm side length, which weigh 2.2 g,

and took average 3 to 4 seconds for single transformation. For a proof-of-

concept study, we demonstrated the systems with 4×4 matrix form arrangement.

By designating the shape of each module for the goal shape, we made 5

different shape-changing performance among 216 different shape combination

with 16 number of modules. Also, we showed the possible application of the

system as a tangible letter changing display by rearranging of the module into

5×3 matrix form. We believe this system can be a new way of shape-changing

system which can be used as an intuitive and compact multi-functional devices.

e. g. haptic devices, morphing 3-D map, or dynamic architectures.

5

Chapter 2. Origami Morphing Voxel Design

2.1. Origami Pattern Design

The characteristics of an active origami structure primarily depend on its

folding pattern. In particular, key characteristics of an active origami structure

(ROM), degrees of freedom (DOFs), and required force and actuator type. To

make dimensional variation between 3-D cubic block and 2-D flat sheet with

small size for high density arrangement, simple origami pattern – four-sided

structure with parallel fold-lines was exploited. Origami structure composed of

rigid links connected by flexure joints for making both target shapes with

compound folding.

2.2. Actuator and Structural Modeling

For the actuation, a novel low-profile torsional SMA wire actuator (TSW

actuator) [17] was used. This TSW actuator is a simple wore type actuator

which directly use the torsional restoring energy of the shape memory alloy

wire. It simple making self-folding hinge of the unit, and generates mobility of

the origami morphing voxel. The principle of this actuator is shown in Figure

2.2. The torsion SMA wire actuator uses twisting of a straight SMA wire to

rotate. In pre-straining process, by twisting the SMA wire with certain angle,

the wire has pre-strain in martensite state. After the pre-straining, actuator is

embedded to the fold line with each end fixed. Joule Heat caused by current

input to the SMA wire generates restoring twisting force on the embedded hinge,

and finally generated self-folding origami hinge with simple actuation method.

6

Fig. 2.1. Side view of the morphing voxel with simple four-bar based origami

pattern. Origami structure is a composite consists of flexure hinge for folding

line and facet for panel.

Fig. 2.2. Principle of torsional SMA wire actuator.

7

Determining the placement, direction, and the design parameters of the

actuator is important for the efficient transformation. In this thesis, modeling

deals with the kinematics of the morphing unit, and analysis of the optimal

position and direction of the actuator is included. Also, by applying virtual work

theory, specification of the actuator parameters are followed.

Selection of position and direction of the TSW is evaluated from specifying

the design parameters and of the structure as in Figure 2.3 to make simple

kinematic structure modeling. The structure is composed of rigid linkage and

flexure joint. Flexure joint is the key component of the active origami structure

which undergoes repetitive motion. Flexure joint change the relative position

of connected linkages as the relative angle is changed unlike the conventional

rotational joint of the mechanism. This flexure joints have high degrees of

freedom, so calculating the specific position of the linkage based on the kinetic

conditions requires a lot of computational cost.

To understand the behavior of the structure more intuitively, we assumed that

flexure joint always follows a circular arc which minimize the stored elastic

energy in specific relative angle, and built a simple kinematic model based on

the assumption. From this assumption, the effect of the flexure joint can be

described as length variation of the linkage. We call it a virtual linkage. In other

words, the structure with a flexure joint behaves like conventional four-bar

linkage structure except the length of the linkage is changing. Following

equations show length of the virtual linkage depending of the relative angle.

Using the virtual linkage, it is possible to formulate a kinematics of the flexure

four-bar linkage as equation (3).

8

Fig. 2.3. Design parameters of the morphing voxel.

𝑙vr1 = 𝑙r1 +𝑙sf

(𝜋2

− 𝜃1) tan 𝜃1

+𝑙sf

(𝜋2

− 𝜃2) tan 𝜃2

(1)

𝑙vr2 = 𝑙r2 +𝑙sf

(𝜋2

− 𝜃2) tan 𝜃2

+𝑙lf

(𝜋2

− 𝜃3) tan 𝜃3

(2)

Ψ(Θ) = [𝑙𝑣𝑟1(𝜃1, 𝜃2) sin 𝜃1 − 𝑙𝑣𝑟2(𝜃2, 𝜃3) sin 𝜃3

𝜃1 + 2𝜃2 + 𝜃3 − 𝜋 ] = 0 (3)

Fig. 2.4. Relationship of θ2 and θ3 compared to θ1when 𝑙lf is increasing.

60 80 100 120 140 160

0

20

40

60

80

100

(

degre

e)

1 (degree)

2 (100 %)

2 (150 %)

2 (200 %)

2 (250 %)

3 (100 %)

3 (150 %)

3 (200 %)

3 (250 %)

9

Figure 2.4 shows the behavior of θ2 , θ3 compared to θ1 when 𝑙lf is

increasing. Percentage in the graph means relative length between 𝑙lf and 𝑙sf.

Shape shifting of the module contains a singular point. Four-bar linkage

mechanism has single degrees of freedom, but not all joints uniquely determine

the whole configuration if the movement contains singularity. θ1 always can

determine the whole configuration because θ1 can determine one specific value

of other angle, so we call it a dominant angle. When 𝑙lf is same with 𝑙sf, θ2

cannot determine the whole configuration, but when 𝑙lf is increasing, θ2 can

determine the other angle, so we call it a conditional-dominant angle. θ3 cannot

uniquely determine the other angle always, so we call it a sub angle. TSW

provides one-way actuation, therefore, each module has two actuator for shape

transformation – one for the cubic block and the other for flat sheet shape. From

the result, we choose θ1 and θ2 as actuation joints.

Because the TSW can be actuated in single direction, not only the actuator

torque but also direction of actuation could be important design issue. This issue

requires information about torque of each joint, but complexity of the dynamics

of the structure preclude from the achieving this data without the complex

numerical simulation. Similar with previous part, to understand the behavior of

the structure more intuitively, we applied the simple assumption – antagonistic

stiffness of the TSW is the most dominant factor of the mechanism. We only

consider the stiffness of the TSW, and ignore the stiffness of the flexure joint

and the weight of the structure. Based on the assumption, the structure can be

treated as a gear train with two gear – input gear (activated TSW) and output

gear (deactivated TSW). The required torque can be achieved from the relative

rotation speed of each angle based on principle of virtual work for gear train.

10

For the movement of the mechanism, the work of activated angle should be

larger than deactivated angle as equation (4).

δWork = ∑ 𝑇𝑖𝛿𝜃𝑖

𝑖

= ∑ (𝑇𝑖

𝜕𝜃𝑖

𝜕𝑡) 𝛿𝑡

𝑖

= (𝑇𝐴𝑐𝑡�̇�𝐴𝑐𝑡 − 𝑇𝐷𝑒𝑎𝑐𝑡�̇�𝐷𝑒𝑎𝑐𝑡)𝛿𝑡 > 0 (4)

𝑇𝐴𝑐𝑡

𝑇𝐷𝑒𝑎𝑐𝑡

>�̇�𝐷𝑒𝑎𝑐𝑡

�̇�𝐴𝑐𝑡

(5)

where T means torque of the joint.

By calculating Jacobian matrix of equation (5), the relative speed can be

derived as follows.

𝜃2̇

𝜃1̇

=1

2(

𝜕𝑙𝑣𝑟1

𝜕𝜃1sin 𝜃1 + 𝑙𝑣𝑟1 cos 𝜃1 +

𝜕𝑙𝑣𝑟2

𝜕𝜃3sin 𝜃3 + 𝑙𝑣𝑟2 cos 𝜃3

𝜕𝑙𝑣𝑟2

𝜕𝜃3sin 𝜃3 + 𝑙𝑣𝑟2 cos 𝜃3 +

𝜕𝑙𝑣𝑟1

𝜕𝜃2sin 𝜃1 −

𝜕𝑙𝑣𝑟2

𝜕𝜃2sin 𝜃3

) (6)

Fig. 2.5. and Fig. 2.6. shows graphical plot of relative angular velocity of

joint based on θ1 and θ2. On the assumption that high ratio means high torque,

θ1 requires high torque at cubic block shape and small torque at flat sheet shape.

θ2 shows opposite behavior. Because TSW’s torque is highest at initial point

and decreased gradually due to the restoring force decreases as pre-strain angle

is smaller during self-folding, the direction of θ1 should be set in folding

direction and the direction of θ2 should be set in unfolding direction.

Additionally, variation of 𝑙lf does not have great effect on θ1, but dramatically

decrease the required torque on θ2. After the determination of the actuation

direction of the TSW actuator, the design parameter of the TSW actuator can

be derived.

11

Fig. 2.5. Relative angular velocity plot of joint based on θ1 and θ𝟐 as the

morphing voxel transforms from cubic block to flat sheet.

Fig. 2.6. Relative angular velocity plot of joint based on θ1 and θ𝟐 as the

morphing voxel transforms from flat sheet to cubic block.

12

Fig. 2.7. Transformation mechanism of the single morphing voxel.

The design parameters of the TSW can be determined from following

equations. Because the initial ratio of the angular speed is highest at both case,

the TSW should satisfy the following condition.

𝑇𝐴𝑐𝑡

𝑇𝐷𝑒𝑎𝑐𝑡

=𝑇Austenite

𝑇Martensite

>�̇�𝐷𝑒𝑎𝑐𝑡

�̇�𝐴𝑐𝑡

|initial

(7)

From the structure design parameter we choose, the initial ratio of the angular

speeds were calculated as #a in case of θ1 and #b in case of θ2 . So the

conditions are summarized as follows.

(𝑇𝜃1,Aus − #𝑎 𝑇𝜃2,Mar

𝑇𝜃2,Aus − #𝑏 𝑇𝜃1,Mar) > 0 (8)

To satisfy the condition, the diameter and the length of the TSW is determined

as 12mm, and 8mil and 10mil, each.

13

Chapter 3 Fabrication

Single morphing voxel consists of a laminated composite structure. The

facets consists of paper (basis weight, 112g/m 2 attached by an adhesive layer

(140 µm named flaxweave which has grid pattern and used for hot foil stamping

and embossing, it can make the laminate module can avoid irregularities in

thickness between layer despite the embedded actuators. We used double-sided

tape as an adhesive layer which has adhesion force = 3500 gf/in. The body is

made from composites consisting laser-patterned paper as a facet material and

copper-laminated Kapton film (Dupont Co.) as a flexure joint. They are

assembled with adhesive layer which is a double-sided adhesive tape (5316K,

Coretec Co.). We used the VLS 3.5, Universal Laser System for laser

machining. By etching process of the copper-laminated Kapton film, we made

designed circuit on the flexure (Fig. 3.1. (a)). We attached the laser-patterned

facet material on the one side of the flexure (Fig. 3.1. (b)), and embedded the

actuator after flip it (Fig. 3.1. (c)). The actuator is clamped with wire clamp

(DSHT-1), and pre-strained before embedded. By attaching the facets on other

side of the flexure with fixation of the actuator at the slit of the facet (Fig. 3.1.

(d)). We soldered piece of the steel plate (0.7mm thickness) to the exposed

copper circuit for making electrodes which can contact with the magnet of the

base layer. After that, the laminates are rolled up and attached along the

assembly line (f), and we can get the final single morphing voxel (g) after

attaching the angle constraint ribbon (25μm Kapton film).

14

Fig. 3.1. Fabrication process of the single origami pop-up cell (a) flexure with

etched circuit (b) facet lamination in one side (c) actuator embedding (d) facet

lamination on the other side (e) soldering the electrodes (f) assembly (g) single

origami pop-up cell

15

Chapter 4 Experiment and Result

4.1. Single Morphing Voxel Shape Transformation

Fig. 4.1. shows the fabricated single morphing voxel, including the actuator

position in planar view, and assembled feature. Each one weighs 2.2 g, and has

25mm side length. We put 0.8 A uniform current through power supply to the

actuator, and switch the control sequence through electrodes.

Fig. 4.1. Performance of the single origami morphing voxel. (a) Assembled cell

(b) 2-D planar view of the Origami pop-up cell and its assembly (c) Close-up

view of the actuator and the bottom facet electrodes, and single cell

performance (c) side view (d) top view.

16

As shown in Fig. 4.1. (c) and (d), a single morphing voxel can transform its

shape between 2-D flat sheet and 3-D cubic block after attached to the base

layer.

4.2. Programmable Shape-changing sheet with matrix

formation arrangement

Based on the performance test of the single morphing voxel, programmable

sheet is made by expansion of the single morphing voxel in matrix arrangement.

Programmable sheet can be changed into different shape can be controlled by

pre-determined sequence. The control issue of the large number of shape

memory alloy (SMA) actuator is independent actuation. We aim to control the

SMA actuator by constant current control because it is largely used method for

SMA heating. However, it is hard to build independent and digitally controlled,

constant current control circuit. We tried to build circuit with MOSFET, but the

resistance deviation between the SMA actuators is quite large. Therefore, we

build bypass circuit scheme which can make always series circuit for constant

current through power supply, even though the activated SMA actuator group

which have different number of SMA actuators should be changed by

designated sequence. The basis scheme of this circuit stats from the difference

of resistance between the electric wire with negligible resistance and the SMA

with relatively large resistance.

17

Fig. 4.2. Voxel grouping and by-pass control circuit (a) 4 different cell grouping

(b) By-pass circuit with activated SMA group 1 and 2 (c) By-pass circuit with

activated SMA group 2 and 3.

Fig. 4.3. Shape-changing performance of the 4×4 programmable sheet (a) Front

view (b) Diagonal view.

18

By rearrangement of the cells into 5×3 matrix form, we made letter-shifting

display which can shift its shape between 3 different letter(Fig5)–English

Letter ’B’, ’R’, and ’L’. We divided the cells with 5 different groups and control

the sequence with manual switching. This can be used as a tangible letter

display system.

Fig. 4.4. Tangible letter shifting display with 5×3 matrix formation of morphing

voxels, (a) Letter ’B’, (b) Letter ’R’, (c) Letter ’L’.

19

Chapter 5 Conclusion

This thesis suggests a new way to build shape-changing system that is

lightweight and have compact low-profile structure. By designing the

distributed module with self-folding dimensional variable unit, Origami pop-

up cell, we can build shape-changing hardware without complex control

method. Owing to variability in the manual fabrication process and actuator

unevenness, performance was not uniform among the cells. It is came from the

alignment process in laminating, and manual actuator manufacturing process.

Precise alignment method in laminating process and the automation in actuator

embedding process can solve this problem. In cell control, digital control circuit

which can divide all control nodes for each module is not yet been completed

due to the current distribution problem. Also, control scheme of the SMA

actuator is quite low-level without feedback loop, so that it could be more

consideration for reliable performance. We plan to exploit thermal couple and

current regulator in the control circuit for reliable and stability. We plan to

expand this system into multi-layer system to build diverse 3-D shape. By

making the cell more robust, and stacking with layer, we can expand the system

in height dimension so that we can build 3-D morphing architectures, maps,

and furnitures etc. Also, it is possible to expand the system in much larger area

by reducing the size of the cell with increased density in arrangement. By

investigating about various origami pattern, we can diversify the activation unit.

Also, we can make dynamically shape-changing hardware with the

combination of various kinds of activation unit. We believe this system can be

a hardware platform for multi-functional device merged with current existing

technologies such as new haptic device using sensor and vision technologies.

20

Bibliography

[1] H. Ishii, "Tangible bits: beyond pixels.” Proceedings of the 2nd

international conference on Tangible and embedded, vol. 20, no. 4,

pp. xv-xxv, 2008.

[2] M. Yim, W.-M. Shen, B. Salemi, D. Rus, M. Moll, H. Lipson, E.

Klavins, and G. S. Chirikjian, “Modular self-reconfigurable robot

systems: Challenges and opportunities for the future,” IEEE Robot.

Automat. Mag.,vol. 14, no. 1, pp. 43–52, Mar. 2007.

[3] J. P. Jobin, and C. Gosselin, “Discretely deformable surface based on

mechanical interpolation: Application to the design of a dynamically

reconfogurable theater stage.” Journal of Mechanisms and Robotics,

vol. 1, no. 011005, 2009.

[4] M. Nakatani, H. Kajimoto, K. Vlack, D. Sekiguchi, N. Kawakami,

and S. Tachi, “Control method for a 3D form display with coil-type

shape memory alloy.” Robotics and Automation, Proceedings of the

2005 IEEE International Conference on, pp. 1332-1337, 2005.

[5] V. M. Gandhi, and B. D. Thompson. Smart materials and structures.

Springer Science & Business Media, 1992.

[6] S. C. Goldstein, and T. C. Mowry, “Claytronics: An instance of

programmable matter”, 2004.

[7] D. Leithinger, S. Follmer, A. Olwal, and H. Ishii, “Physical

telepresence: shape capture and display for embodied, computer-

mediated remote collaboration.” In Proceedings of the 27th annual

ACM symposium on User interface software and technology, pp. 461-

470, 2014.

21

[8] S. Tibbits, “4D printing: multi‐material shape change.” Architectural

Design, vol 84, nov.1, pp. 116-121, 2014.

[9] R. Kimmel, and J.A. Sethian, “Optimal algorithm for shape from

shading and path planning.” Journal of Mathematical Imaging and

Vision, vol. 14, no. 3, pp. 237-244, 2001.

[10] L. Zhang, B. Curless, and S. Seitz, “Rapid shape acquisition using

color structured light and multi-pass dynamic programming.”

In Proceedings of First Ingernational Symposium on 3D Data

Processing Visualization and Transmission, pp. 24-36, 2002.

[11] A. W. Lee, D. Dobkin, W. Sweldens, and P. Schröder,

“Multiresolution mesh morphing.” In Proceedings of the 26th annual

conference on Computer graphics and interactive techniques, pp.

343-350, 1999.

[12] J. Werfel, K. Petersen, and R. Nagpal, “Designing collective behavior

in a termite-inspired robot construction team.” Science, vol. 343, no.

6172, pp. 754-758, 2014.

[13] I. Poupyrev, T. Nashida, S. Maruyama, J. Rekimoto, and Y. Yamaji,

“Lumen: interactive visual and shape display for calm computing.”

In ACM SIGGRAPH 2004 Emerging technologies, p.17, 2004.

[14] E. Hawkes, B. An, N. M. Benbernou, H. Tanaka, S. Kim, E. D.

Demaine, D. Rus, and R. J. Wood, “Programmable matter by folding,”

Proceedings of the National Academy of Sciences, vol. 107, no. 28, p.

12441, 2010.

[15] E. D. Demaine, M. L. Demaine, and J. S. B. Mitchell, “Folding flat

silhouettes and wrapping polyhedral packages: New results in

22

computational origami,” Computational Geometry, vol. 16, no. 1, pp.

3–21, 2000.

[16] S. Felton, M. Tolley, E. Demaine, D. Rus, and R. Wood, R. “ A

method for building self-folding machines.” Science, vol. 345, no.

6197, pp. 644-646, 2014.

[17] J. Koh, S. Kim, and K. Cho. "Self-folding origami using torsion shape

memory alloy wire actuators." ASME 2014 International Design

Engineering Technical Conferences and Computers and Information

in Engineering Conference. American Society of Mechanical

Engineers, 2014.

[18] R.J. Wood, S. Avadhhanula, S. Sahai, R. Steltz, and R.S. Fearing,

“Microrobot design using fiber reinforced composites.” Journal of

Mechanical Design, vol. 130, no. 5, 2008.

[19] D.Y. Lee, J.S. Kim, J.J. Park, S.R. Kim, and K.J. Cho, “Fabrication of

origami wheel using pattern embedded fabric and its application to a

deformable mobile robot.”, In 2014 IEEE International Conference

on Robotics and Automation (ICRA), pp. 2565-2565, 2014.

23

국문 초록

분산형 자가 접힘 종이접기 모듈을

통한 프로그래밍 가능한 시트

물질 세계에서 프로그램 가능한 물질을 구현하는 것은 난제이

다. 본 논문은 분산형 자가 접힘 종이접기 모듈로 구성된 가볍고

컴팩트한 새로운 프로그램 가능한 형상 변경 시스템을 제안한다.

시스템의 형상 변화 자유도는 여러 개의 동일한 단위 모듈의 배열

로부터 생성되어, 전체 시스템이 특정 모양을 만들고 변경할 수

있게 한다. 자가 접힘 종이접기 모듈은 간단한 종이 접기 패턴의

구조로 이루어지고, 그 자가 접힙 조인트에 납작한 구동기를 내장

하여 물리적 3차원 픽셀과 같은 3차원 정육면체 형상과, 2차원 시

트 모양 사이의 형상 변화가 가능하다. 단일 모듈은 한 변의 길이

가 30mm이고 무게가 2.2g이며 단일 변형의 경우 평균 3 ~ 4 초

가 소요됩니다. 또한, 전체 시스템을 형상 변형 모듈로 구성된 변

형 모듈과, 기반 레이어로 분리하여, 모듈 위치를 자유롭게 변화

시킬 수 있게 하였다. 이는 모듈의 재배치, 교체 및 수리에 있어

24

장점을 지닌다.

이 논문은 물질 세계에서 프로그램 가능한 물질을 구축하는 방

법으로서 간단하고 가벼운 형상 변화 시스템 하드웨어를 위한 모

핑 복셀의 설계 및 제조 방법을 제시한다. 그 결과로서, 4 × 4 매

트릭스 형태로 시스템의 구현 가능성을 보이고, 5 × 3 매트릭스

배열의 문자 변화 디스플레이를 만들었다. 이는 다기능 디바이스

의 형상 변화 플랫폼으로서, 다양한 소프트웨어 기술과의 융합을

통해 햅틱 인터페이스, 3차원 변형 지도 및 형상 디스플레이 등에

이용될 수 있다.

주요어: 프로그래밍 가능한 물질, 종이접기, 자가 접힘, 모듈러

시스템, 지능형 구동기