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4D printing of self-folding structures using polystyrene film

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4D printing of self-folding structures using polystyrene film

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4D PRINTING OF SELF-FOLDING STRUCTURES USING
POLYSTYRENE FILM
By
Dongping Deng

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)

May 2017

Copyright 2017 Dongping Deng

i
Acknowledgements
During the past five and a half years at USC, I have gone through easy and tough moments in the
process of completing this PhD research, in those moments I was lucky enough to receive company, help
and guidance from remarkable individuals around, whom I would like to thank sincerely.
First of all, I would like to express my deep gratitude to my advisor, Dr. Yong Chen for his advising
and mentorship during these years on both this research as well as my career. I would like to thank him for
his patience, care and help at the moments when the research progress was hindered, when I was in a
confusion of selecting my future career path. His serious attitude towards scientific research as well as
everything else inspires me a lot in being a person who cares and digs into details.
I am also grateful for Dr. Behrokh Khoshnevis for his valuable suggestions and comments on my
research. His innovative view towards problems and great passion in making a difference for the human
race by putting research work into real life applications teach me to target on the real challenges and real
life application of my research work.
I would like to thank Dr. Wei Wu for serving as my committee member both in my PhD Qualifying
Exam as well as Thesis Defense. Dr. Wu's research on the really "small" things helps me think problems in
different scales and dimensions. Also his easygoing personality made me feel really comfortable every
time I met him and discussed with him.
I also owe special thanks to my other committee members for their help and support. I want to thank
Dr. Qiang Huang for his suggestion on using analytic approaches such as design of experiment to study
processes. I would like to thank Dr. Yan Jin for his help in clarifying the research scope of this thesis
during the Qualifying Exam.

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Next I'd like to recognize Dr. Yang Yang, Dr. Tsz Ho Kwok and Dr. Xuan Song for the cooperation
and contributions that each of them made to the completion of this work. Dr. Yang gave me a lot of advices
and help in writing and editing scientific research papers. His insights and knowledge of what a good paper
should look like helped me a lot in improving the quality of this research. Dr. Kwok helped to develop a
simulation framework for predicting the shape deformation of the self-folding structures, which enriched
the content of this research. Dr. Xuan Song cooperated with me in the developing of framework to generate
constraint patterns for the self-folding structures.
I am really lucky to have an opportunity to work at TE Connectivity as an intern in Summer 2015
under the mentoring of Dr. Ting Gao, Dr. Megan Hoarfrost Beers and Dr. Quentin Polosky. Dr. Gao shared
a lot of her life experience in career development in industry and gave me a lot of valuable advices. Dr.
Beers and Dr. Polosky worked side by side with me, they taught me a lot of new skills and how to play a
good role in a tech company. They all provided me with help and resources for the cool projects I did
during my stay at TE, which made the experience meaningful and really wonderful.
Furthermore, I want to thank my lab mates at the Advanced Manufacturing Lab: Dr. Chi Zhou, Dr.
Yayue Pan, Dr. Yongqiang Li, Dr. Kai Xu, Dr. Jing Zhang, Dr. Xiao Yuan, Dr. Xuan Song, Pu Huang, Dr.
Matthew Petros, Dr. Payman Torabi, Behnam Zahiri, Aref Vali, Dr. Amir Mann, Hadis Nouri, Ali
Kazemian, Xiang Gao, Huachao Mao, Xiangjia Li, Jie Jin, Zhengcai Zhao, Yang Xu for all the help, care
and company they provided during the past few years. I enjoyed working with them.
My gratitude also extends to the undergraduate and graduate students who volunteered to work with
me on different projects: Faraz Jalil, Narut Yodvanich, Archit Jain, Arthur Araujo, Junhong Lin. They are
really motivated and hard working.
Lastly and most importantly, I want to sincerely thank my wife Dr. Hui Gui, who took good care of
me during my stay at USC, my parents, my parents-in-law, my sister and all the other family members in
China for their constant and unconditional love. I could not have completed this research without their
support. I am forever indebted to them.

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Table of Contents
Acknowledgements .................................................................................................................................. i
List of Tables ........................................................................................................................................... v
List of Figures ........................................................................................................................................ vi
Abstract ................................................................................................................................................. 12
Chapter 1 Introduction .................................................................................................................... 15
1.1 Research Background and Motivation .................................................................................... 15
1.1.1 Origami and Origami-based Engineering ..................................................................... 15
1.1.2 Self-folding Structures ................................................................................................. 16
1.1.3 Polystyrene Film .......................................................................................................... 19
1.1.4 4D Printing ................................................................................................................... 21
1.1.5 3D Printing Processes for self-folding structures ......................................................... 22
1.1.6 Smooth Curved 3D Shell Structures ............................................................................ 28
1.1.7 Sequential Folding ........................................................................................................ 30
1.2 Research Questions and Hypotheses ....................................................................................... 32
1.3 Contributions ........................................................................................................................... 36
1.4 Outline of this work ................................................................................................................. 37
Chapter 2 Literature Review: Self-folding Designs and Mechanisms With Polystyrene Film ...... 40

ii
2.1 Self-folding Structure Categories ............................................................................................ 40
2.2 Self-folding Structures with Polystyrene Film ........................................................................ 45
2.2.1 Self-folding of polystyrene film by local light absorption ........................................... 46
2.2.2 Self-folding of polystyrene film by laser light ............................................................. 47
2.2.3 Self-folding of polystyrene film by joule heating ........................................................ 47
2.2.4 Self-folding of polystyrene film by uniform heating ................................................... 49
2.2.5 Self-folding of polystyrene film by microwave ........................................................... 51
2.3 Smooth curved shape folding .................................................................................................. 53
2.4 Sequential folding designs and mechanisms ........................................................................... 55
2.5 Summary ................................................................................................................................. 56
Chapter 3 Origami-based Self-folding Structure Design and Fabrication Using Projection based
Stereolithography.............................................................................................................58
3.1 Folding Mechanism Analysis .................................................................................................. 58
3. 2 Self-folding Origami Structure Design and Fabrication ........................................................ 60
3.3 Hinge Design and Self-folding Angle Analysis ...................................................................... 62
3.3.1 Shrinkage of polystyrene film ...................................................................................... 62
3.3.2 Design parameters of the origami structure.................................................................. 64
3.3.3 Hinge folding analysis .................................................................................................. 65
3.3.4 Modeling using the assumption of elastic deformation ................................................ 67
3.3.5 Modeling using the assumption of plastic deformation ............................................... 69
3.4 Fabrication Process of an Origami Sheet ................................................................................ 71

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3.5 Self-folding Experiments ........................................................................................................ 75
3.5.1 Calibration experiments ............................................................................................... 75
3.5.2 Verification Experiments ............................................................................................. 78
3.5.3 Discussion on folding angle control ............................................................................. 80
3.6 Applications ............................................................................................................................ 81
3.6.1 Self-folded Origami structures ..................................................................................... 81
3.6.2 Self-folded 3D Circuit Design ...................................................................................... 84
3.6.3 Mesh based triangulated shape fabrication ................................................................... 90
3.7 Summary ................................................................................................................................. 93
Chapter 4 Design and Fabrication of Smooth Curved Surface Using Controlled Self-Folding....95
4.1 Overview ................................................................................................................................. 95
4.2 Mapping 3D Thin Shell Structures .......................................................................................... 98
4.2.1 Process Overview ......................................................................................................... 98
4.2.2 Folding Types and Parameters ..................................................................................... 98
4.3 Folding Control Using Constraint Patterns ........................................................................... 101
4.3.1 Shrinkage Study of Polystyrene Film ......................................................................... 102
4.3.2 Deformation Principle and a Simulation .................................................................... 104
4.3.3 Folding Type and Axis Control Using Constraint Patterns ........................................ 106
4.3.4 Folding Curvature and Orientation Control Using Constraint Patterns ..................... 109
4.4 Constraint Pattern Design and Fabrication ............................................................................ 114
4.5 Computational framework of the constraint pattern design .................................................. 118

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4.5.1 Unfolding of a 3D Mesh ............................................................................................. 118
4.5.2 Mesh Parameterization &Constraint Pattern Generation ........................................... 120
4. 6 Summary .............................................................................................................................. 123
Chapter 5 Sequential Folding Structures By Silver Ink Printed Polystyrene Film ... ................. 125
5.1 Folding behavior of the polystyrene film activated by current. ............................................ 125
5.2 Printing parameters optimization .......................................................................................... 130
5.3 Sequential folding using single circuit loop .......................................................................... 135
5.3.1 Angle lock design ....................................................................................................... 136
5.3.2 Constraint layer design ............................................................................................... 138
5.4 Sequential folding using decoupled multiple circuit ............................................................. 139
5.4.1 Decoupled circuit design through circuit "jump" ....................................................... 141
5.4.2 Updated angle lock design. ........................................................................................ 143
5.5 A twp-phase 3D antenna case design .................................................................................... 146
5.6 Summary ............................................................................................................................... 146
Chapter 6 Conclusions and recommendations ............................................................................ 148
6.1 Answering the Research Questions and Testing Hypothesis ................................................ 148
6.2 Contributions and Intellectual Merit ..................................................................................... 150
6.3 Recommendations for Future Work ...................................................................................... 150
Reference ............................................................................................................................................. 152

v
List of Tables
Table 3.1 Folding test data based on designs with different ( , Ld ) values ........................................ 76
Table 3.2 Parameters of the small angle test cases .............................................................................. 79
Table 3.3 Parameters of the large angle test case ................................................................................. 79
Table 3.4 Folding test result ................................................................................................................. 88
Table 4.1 Illustration of folding codes for labeling folding units ...................................................... 100
Table 4.2 Results of the folding curvature and bar width from Fig.4.13 and Fig.4.14 ...................... 113

vi
List of Figures
Figure 1.1 Origami and Origami-based Engineering. .......................................................................... 16
Figure 1.2 An illustration of four different self-folding structures ...................................................... 18
Figure 1.3 Shrinky Dinks film ............................................................................................................. 19
Figure 1.4 Thin film sheet manufacturing process. .............................................................................. 20
Figure 1.5 4D Printing by MIT Self-Assembly Lab ............................................................................ 21
Figure 1.6 Illustration of StereoLithography ....................................................................................... 23
Figure 1.7 Illustration of MIP-SL Process ........................................................................................... 23
Figure 1.8 Illustration of SLS process ................................................................................................. 24
Figure 1.9 Illustration of DIW and FDM process. ............................................................................... 25
Figure 1.10 Illustration of the Inkjet Binder Jetting process and Material Jetting ............................... 26
Figure 1.11 Illustration of LOM process ............................................................................................. 27
Figure 1.12 Applications of smooth curved 3D shell structures .......................................................... 28
Figure 1.13 A sequential folded plane model ...................................................................................... 30
Figure 1.14 A sequential folded boat model ........................................................................................ 31
Figure 1.15 A self locked structure by sequential folding ................................................................... 31
Figure 1.16 A self blocking design using sequential folding ............................................................... 32
Figure 1.17 Related chapters to research questions and hypotheses .................................................... 36
Figure 1.18 Overview of the dissertation ............................................................................................. 39

vii
Figure 2.1 Folding of a patterned gold films ....................................................................................... 41
Figure 2.2 Thin film self-folding micro grippers ................................................................................. 41
Figure 2.3 Self-folding of elastic sheet by capillary force induced by droplet .................................... 42
Figure 2.4 Three main types of self-folding structures ........................................................................ 43
Figure 2.5 Sequences of the shape recovery of sample CB10 by passing an electrical current 44
Figure 2.6 SEM photographs of the micro cubes ................................................................................. 44
Figure 2.7 Fabrication process of the bilayer structure ........................................................................ 44
Figure 2.8 Thermoresponsive self-folding SU-8 photoresist-polycaprolactone thin films .................. 45
Figure 2.9 Principle of the self folding by local light absorption ........................................................ 46
Figure 2.10 Self folded samples of the ink printed polystyrene film ................................................... 46
Figure 2.11 Self-folding through absorption of laser beam. ................................................................ 47
Figure 2.12 Self-folding of a inchworm robot ..................................................................................... 48
Figure 2.13 Composite design of the self-folding structure ................................................................. 48
Figure 2.14 Self-folded robot ............................................................................................................... 49
Figure 2.15 Self folded pyramid, locks and crane ............................................................................... 49
Figure 2.16 Design of the self-folding structure .................................................................................. 50
Figure 2.17 Self-folded geometries by uniform heating ...................................................................... 50
Figure 2.18 Self folding origami robot ................................................................................................ 51
Figure 2.19 Design of the self-folding structure .................................................................................. 51
Figure 2.20 Folding process induced by microwave ........................................................................... 52
Figure 2.21 Structures folded along different orientations inside the oven ......................................... 52

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Figure 2.22 Self-folding of a light weight flower case ........................................................................ 53
Figure 2.23 Various curved shapes through folding of thin composite ............................................... 54
Figure 2.24 Micro structures fabricated through releasing of stress .................................................... 54
Figure 2.25 Sequential folding of a mailbox model ............................................................................. 55
Figure 2.26 Sequential folding of a cube ............................................................................................. 56
Figure 3.1 The bending principle of a bilayer structure and the constraining effect of cured resin ..... 59
Figure 3.2 Two self-folding structure designs ..................................................................................... 60
Figure 3.3 Two fabrication processes for the sandwiched structure design and related test examples 61
Figure 3.4 Shrinkage behavior of the tested polystyrene films ............................................................ 63
Figure 3.5 Design parameters of a hinge and its neighboring body portion in the origami sheet ........ 65
Figure 3.6 Bending analysis of a self-folding hinge ............................................................................ 65
Figure 3.7 The bottom-up projection based MIP-SL setup as well as a modified chamber design ..... 72
Figure 3.8 The physical structure of a chamber ................................................................................... 73
Figure 3.9 Origami sheets with unidirectional and bidirectional folding ............................................ 73
Figure 3.10 The fabrication process of a bidirectional folding design with extra feature layers ......... 74
Figure 3.11 Built samples in the folding experiment ........................................................................... 75
Figure 3.12 Data fitting using both elastic and plastic model based on the folding angle ................... 77
Figure 3.13 Two verifying test cases for small angles (α<80
o
) ............................................................ 78
Figure 3.14 A verifying test case for large angles ( α≥80
o
) ............................................................... 79
Figure 3.15 Angle lock design for self-folding control ........................................................................ 80
Figure 3.16 A string test case using letters of “USC” .......................................................................... 82

ix
Figure 3.17 A test case of an origami structure with eight “legs” - four in each side .......................... 83
Figure 3.18 Two self-folding origami structures (a crane and a cube) with letters (‘‘USC’’) ............. 84
Figure 3.19 A self-folded 3D spiral antenna design ............................................................................ 85
Figure 3.20 Unfolding of a 3D circuit design ...................................................................................... 86
Figure 3.21 Foldable structure design .................................................................................................. 86
Figure 3.22 CNC based ink printer ...................................................................................................... 87
Figure 3.23 Folding Test ...................................................................................................................... 88
Figure 3.24 A LED Cube case ............................................................................................................. 89
Figure 3.25 Sequential lighting of a LED Cube ................................................................................... 90
Figure 3.26 One ring patch model ....................................................................................................... 91
Figure 3.27 Two ring patch model ....................................................................................................... 91
Figure 3.28 A face mesh model with optimized interior cut design .................................................... 92
Figure 3.29 A waved form model ........................................................................................................ 93
Figure 3.30 A flower blade model.. ..................................................................................................... 93
Figure 4.1 An illustration of the principle for self-folding shapes with smooth curved surfaces. ....... 96
Figure 4.2 A test case of a self-folding flower.. ................................................................................... 97
Figure 4.3 Main steps of the process .................................................................................................... 98
Figure 4.4 Folding unit and the four folding parameters. ..................................................................... 99
Figure 4.5 Illustration of mapping a curved surface. ......................................................................... 101
Figure 4.6 Shrinking behavior of the polystyrene film. ..................................................................... 103
Figure 4.7 Folding axis analysis. ....................................................................................................... 104

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Figure 4.8 Deformation principle used in simulation and the developed simulation......................... 105
Figure 4.9 An illustration of the constrain patterns............................................................................ 108
Figure 4.10 Comparison analysis of the folded model vs. simulated model ..................................... 108
Figure 4.11 Folding performance of one axis folding using different distributions of materials. ..... 109
Figure 4.12 Two examples of constraint patterns for two base types. ............................................... 110
Figure 4.13 Curvature control with parallel bar pattern. .................................................................... 111
Figure 4.14 Curvature control with cross shape pattern. ................................................................... 112
Figure 4.15 Curvature control curves. ............................................................................................... 113
Figure 4.16 The constraint pattern design process. ............................................................................ 115
Figure 4.17 A fabrication system based on MIP-SL. ......................................................................... 116
Figure 4.18 A test case of a bowl. ...................................................................................................... 117
Figure 4.19 A test case of “USC” letters. .......................................................................................... 118
Figure 4.20 A unfolding "CS" letter test case .................................................................................... 120
Figure 4.21 Square mesh of the "CS" letter case ............................................................................... 121
Figure 4.22 A custom-defined curvature calculation diagram ........................................................... 122
Figure 4.23 Generated constraint patterns for "CS" case ................................................................... 123
Figure 5.1 Principle of the self-folding structure. .............................................................................. 127
Figure 5.2 Folding behavior of the self-folding structure.. ................................................................ 130
Figure 5.3 Printing platform. .............................................................................................................. 131
Figure 5.4 Printed traces. (a) Nozzle size study. (b) Printing speed study. ........................................ 132
Figure 5.5 Extruder model. ................................................................................................................ 133

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Figure 5.6 Printed trace width vs. Nozzle height. .............................................................................. 135
Figure 5.7 Sequential folding in a single circuit loop. ....................................................................... 136
Figure 5.8 Self-folding structure with angle lock design.. ................................................................. 137
Figure 5.9 Self-folding structure with Constraint layer. .................................................................... 139
Figure 5.10 A sequentially folded self lock structure ........................................................................ 140
Figure 5.11 Self-folding origami structures. ...................................................................................... 141
Figure 5.12 Circuit design layouts for multiple hinge structures. ...................................................... 143
Figure 5.13 Angle lock design and its variation for angle control. .................................................... 144
Figure 5.14 Calibration of the folded angle controlled by angle lock ................................................ 145
Figure 5.15 A two phases antenna design. ......................................................................................... 146

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Abstract
Self-folding structures have been extensively studied over the past few decades due to their potential
application in areas such as biomedical devices, reconfigurable robots, packaging, micro grippers, etc,
especially with the emerging concept of 4D printing since 2013. Different self-folding mechanisms as
well as processes have been developed for different self-folding designs, most of them require complex
material preparation procedures; also most of the self-folding designs are based on origami type structures
with folded small facets and it is until most recently, the idea of sequential folding has been used in
implementing new design capabilities. This study aims to design and fabricate self-folding structures
through 4D printing process, that is to prepare 2D self-folding structures using 3D printing processes and
then use stimuli to trigger the folding of the structures, turning them into 3D structures.
The main challenges in the 4D printing of self-folding structures are how to make the fabrication of
self-folding structures simple and fast, how to design the 2D structures that can fold into desired 3D
configurations with different surfaces including flat surfaces as well as smooth curved surfaces and how
to realize sequential folding in a simple as well as controlled manner. Typically the self-folding structures
require a lot of steps in material preparation because they are made of various kinds of materials, each
with different behaviors during the folding, such steps can take a very long time. Also, most of the self-
folding designs realized so far are of shapes composed of many facets; No method has been developed for
achieving shapes with smooth curved surfaces because it's difficult to control the folding of the globally
curved shapes. It requires accurate control of the local folding in order to achieve the target shapes. The
sequential folding gives more freedom as well as potential in the self-folding structural designs, so far
sequential folding is realized mainly by varying different hinge designs so that the hinges will fold in
certain order, there is no simple and general method developed for the sequential folding purpose.

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To overcome aforementioned challenges, we developed two processes to design and fabricate self-
folding structures in a fast and simple manner using 3D printing processes combined with self-folding
mechanism, namely, the 4D printing processes. The first process we developed uses a MIP-SL(Mask
Image Projection based StereoLithography) process to fabricate self-folding structures by coating
photocurable resin SI500 on pre-stressed polystyrene film, different coating patterns provide different
physical constraints so the structures can fold along hinge portions; this process provides an easy and fast
way to fabricate self-folding structures. We then developed a design method based on this process to
fabricate 3D structures with smooth curved surfaces. 3D models are mapped into 2D designs based on
surface parameters such as folding type, folding orientation, folding axis and folding curvature. Constraint
patterns to control the surface parameters were developed and tested such that curved 3D structures can
be fabricated. The second process uses a Direct Ink Writing (DIW) method to print conductive silver ink
on top of the pre-stressed polystyrene film such that when the ink traces generate heat by conducting
current, the film will fold. Sequential folding designs were realized through local heat generation, a
simple and extendable decoupled circuit design was also developed for the sequential folding purpose.
Our study has great potential in reconfigurable structure designs such as robotics, wearable devices
as well as 3D circuit designs. The 4D printing processes we developed can fabricate self-folding
structures really fast with existing materials such as polystyrene film, photocurable resins & conductive
ink. Our processes can fabricate a self-folding structure in several seconds, the folding procedure takes
around 30secs as well, so we can make a folded structure rapidly. With the capability of fabricating
complex 3D structures with curved smooth surface, wearable devices could be fabricated to fit the shapes
of human body, applications such as cushion pads could be fabricated using the folded structures as molds.
With the capability of sequential folding in our process, 3D designs with shape transformation capability
can be fabricated so that the structures can go through various phases to realize different functionality. 3D
antenna design is demonstrated in our study as well to test the feasibility of this study.

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Chapter 1 Introduction
1.1 Research Background and Motivation
1.1.1 Origami and Origami-based Engineering
Origami is a traditional paper art, where a two dimensional (2D) paper is folded along certain pre-
defined hinges in specific sequence to form different three dimensional (3D) shapes, such as the origami
crane design shown in Fig. 1.1(a). Origami designs are compact, light-weighted and highly deployable,
thus have continuously attracted attention from both scientists as well as artists. Most of the early origami
research were focused on mathematical representation of the folding theory as well as the crease design
pattern optimization, mainly used very thin materials such as paper(O'Rourke, J, 2011). In the recent few
years, a new concept of origami based engineering has been widely spread among researchers, the
terminology describes the adoption of origami designs to real engineering applications in different scales
such as micro level, meso level as well as macro level as shown in Fig.1.1(b) - (d). Fig.1.1(b) shows a
deployable solar panel based on origami design, it's simple and more reliable as one compliant part with
hinges connecting all the sub panels. The structure is folded during transportation, which saves a lot of
space, while deployed later at the time of service. Fig.1.1(c) is a research conducted in 2014 using
origami design to grip single cell for medical analysis. The size of the gripper is around 10 micron. The
structure can fold and capture blood cells in the body liquid, this study enables the analysis of the effect of
medicine to a single cell, which provides a new approach in medicine study. Fig.1.1(d) presents an
origami inspired mobile robot design that uses magic ball origami pattern(Lang, R. J, 2011) which can
shrink and expand under tension to realize the transformation of its wheels such that the robot can pass
through narrow gaps for searching and exploring missions.

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Figure 1.1 Origami and Origami-based Engineering. (a) Origami crane (b) Origami inspired
deployable solar panels (Larry Howell, 2013) (c) Micro gripper(Gracias, 2014) (d) Reconfigurable robots
(Cho, K, 2014)
Those examples mentioned above are just a very small portion of the potential applications of the
origami designs. Some products have already benefit from origami designs such as the foldable paper
bags from convenience store as well as products such as umbrellas. The actuation of origami designs is
important due to the variety of requirements each application has, for example, when the scale of the
structure is too small for actuators to get installed; also, in certain cases, automated folding is required
because external control might not be accurate enough and would be too complex due to the needs of
adding motors, actuators as well as sensors, thus we need some structures called Self-folding Structures,
namely, the structures that can fold by themselves with accurate shape control.
1.1.2 Self-folding Structures
Self-folding structures are structures that can fold by themselves under certain stimuli environments
such as heat, moisture, water as well as certain solvents (refer to [6 - 10]). Different self-folding
mechanisms have been developed, prior to 2012, there were three major types of self-folding mechanisms
as shown in Fig. 1.2 (a) - (c). The first category uses shape memory material such as shape memory alloy

17

or polymers to realize self-folding (refer to [11 - 13]), in this mechanism, shape memory material need to
get "trained" in order to remember the original shape, then the structure is deformed under external force,
afterwards, by applying certain stimuli such as heat, the structure will go back to its original shape. The
training of the shape memory materials takes hours, for example, to train a shape memory nickel-titanium
wire to bend into 90 degree, the wire has to be fixed in a mold that bends it into 90 degree and holds it
there in 400 degree C for four hours. Afterwards, the material needs to be embedded into the self-folding
structure, a lot of manual steps are required to prepare the structure. The second category uses a structure
design named "bilayer structure" to realize self-folding (refer to [14-16]), in the bilayer structure, two
types of materials are glued together physically to form two layers, one of the materials called active
material will expand or shrink under certain stimuli, the other type of the materials is relatively stable
under the stimuli environment such that it works as physical constraint to the active material such that the
bilayer will curve up and bend. The two types of materials have to be carefully selected and glued
together, the designs reported in research prior to 2012 using this mechanism took a lot of time to prepare
the bilayer structure, the overall processes can take several hours since multiple steps could be involved
such as material deposition and etching. The third category uses a foldable hinge design where the
foldable structure is decomposed into two portions, the body portion and the hinge portion, the body
portion is made of regular material while the hinge portion is made of active material that can fold
afterwards (refer to [17-18]), this hinge design is classic based on origami designs, the active hinge
portion can be triggered with different mechanisms based on different materials used. One example would
be using a solvent sensitive material that can get melt and the surface tension will bring the neighboring
body portions together, in this way the structure can realize automatic folding in very small scale such as
several micron, which is really difficult for us to manipulate and control the folding using other methods.
The material preparation is time consuming due to complex steps required as well. To boost the
application of self-folding structures and designs, the material preparation speed, namely the fabrication
process speed should be improved.

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Figure 1.2 An illustration of four different self-folding structures
In 2012, a novel idea was proposed by Liu Y. etal (2012) that used a pre-strained polystyrene film,
also known as Shrinky Dinks film, for self-folding purpose. In the method, several lines of black ink were
printed onto the polystyrene film working as the hinge of the structure as shown in Fig.1.2 (d), infrared
bulb light source was used to trigger the folding of the structure, portions with black ink could absorb
more heat than the other portions without black ink such that different temperature distribution was
realized on both sides of the polystyrene film, causing the different shrinking ratio between the two sides
of the film, thus generating a folding behavior. This method was really inspiring in the following ways:
first of all, it used existing materials such as polystyrene film and black ink to realize simple and fast self-
folding structure preparation; secondly, the folding mechanism relied in the shrinking difference of two
sides of one film by varying the performance of these two sides with external constraints or layers, such
as the black ink used here; and the third, the way of using infrared light and black ink material to realize
local heat generation could inspire other heating mechanisms such that local heat absorption or generation
could be realized. More research were conducted along these lines using shrinkable film after that, which
will be elaborated in Chapter 2.
(a) Shape Memory Material
(b) A bilayer Structure
(c) A foldable hinge Structure
(d) A Shrinky-Dinks film
based Structure
Passive Material Active Material
Passive Material Active Material
Shrinky-Dinks film
Ink

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1.1.3 Polystyrene Film
Aforementioned Shrinky Dinks film as shown in Fig.1.3 is one type of pre-stressed polystyrene film,
the film has a large shrinking ratio (~ 55% shrinking compared with original size). The film is
manufacturing through several steps, heating, rolling and cooling as shown in Fig.1.4(a), the material first
comes as small polystyrene pellets, then they get melt in the extruder and pushed forward towards a die to
form a layer of thin sheet, several set of rollers are then used to further press the film sheet to make it
thinner and also make the film more uniform in thickness, afterwards, the film is cooled in room
temperature, post processing might be added to the film to provide certain surface quality, for example, in
order for the film to be printable, a layer of thin film will be coated on to the polystyrene film such that
the surface is a little bit rough and more suitable for printing.

Figure 1.3 Shrinky Dinks film
By nature, polymer trains inside polystyrene are bunched up and in random order, it's the most stable
form of the polymer. During the manufacturing process of the polystyrene film, especially the rolling and

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pressing, polymer trains are forced to straighten out and get into a more orderly configuration[20]. when
the temperature rises above its glass transition temperature, the polymer trains will bounce back into its
original disordered state which results in a large shrinking of the film. Since the rolling and cooling of the
film provides residual stress on the polystyrene film that tends to contract within the structure, the
material will shrink after the stress is released above its glass transition temperature. This residual stress
also stores certain amount of potential energy inside the film, which could be estimated during the
releasing of the stress.

Figure 1.4 Thin film sheet manufacturing process. (a) Thin film sheet extrusion system(Source:
http://www.extrapackaging.com/polyurethane/whatispolyurethane.php) (b) Roller set( Source:
http://www.nanotech-now.com/news.cgi?story_id=42453)
In general, the polystyrene film provides a very good material candidate in the design and fabrication
of self-folding structures. The original method of printing black ink on both sides of the film to achieve
different shrinking ratios between two sides of the shrinking film can realize self-folding of the structure
in a fast and easy manner. However, there are certain limitations of the method as well. First of all, the
transforming condition needs to be strictly controlled in order to actuate the desired folding movements.
For example, the infrared bulb needs to be homogeneous and the related film temperatures on both sides
need to be well controlled. Secondly, the method can only work with transparent films in order for the
printed black inks on the back side to absorb the exposed infrared light through the film. Hence a large
number of non-transparent films will not be able to work based on the method. Finally, the bending angle

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control based on the presented method is unknown and has not been further discussed, detailed model of
the folding angle control and methods for more accurate and robust folding angle control with larger
design allowance is needed.
1.1.4 4D Printing
In the year 2013, a new terminology of "4D Printing" was proposed by Skylar Tibbits from MIT
Self-Assembly Lab (Skylar Tibbits, 2013) in a TED Talk, a bunch of research activities surrounding that
concept have been conducted ever since. 4D Printing describes the technology that uses 3D printing
methods to fabricate structures that can self-assemble or self-folding afterwards due to the use of phase
changing material properties over time as well as smart feature designs that can self-assemble, which
introduces the fourth dimension, that is time into 3D printing technology.

Figure 1.5 4D Printing by MIT Self-Assembly Lab (Image Source: https://all3dp.com/4d-printing/)
Fig. 1.5 shows a 4D printing process proposed by MIT Self-Assembly Lab cooperated with Stratasys
Inc (Tibbits, 2014), the process used a multiple material 3D PolyJet printer named Connex to print the
self-foldable designs with two types of materials, one of them was rigid polymer, the other was a
hydrophilic polymer that expands 150 % when it encountered water. By carefully designing the structure

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with both materials in the hinge portion, a programmed folding could be achieved. The printed structure
could fold inside water tank gradually after several hours depended on the size of the structure. This
technology was inspiring in the following ways: first of all, by taking advantage of material deformation
properties under certain stimuli, various materials could be combined in 3D printing method to achieve
self-folding structure designs, thus achieving 4D printing. However, it's not easy and trivial to develop
and select new materials for 4D printing purpose. Secondly, 3D printing methods could be used to
fabricate self-folding structures, especially complex structural designs such as the hinge portion of the
origami based self-folding designs that has complex hinge patterns made of various materials such as the
hinge designs shown in the Fig. 1.5.
1.1.5 3D Printing Processes for self-folding structures
Since 3D Printing processes have great potential in fabricating self-folding structures, an overview of
major 3D Printing methods is conducted and the details are listed as follows, since "3D Printing" has
become a more general term, not specifically limited to the original 3D Printing process, the processes list
below are all considered as 3D Printing methods.
1) StereoLithography (SLA)
StereoLithography (SLA) is a process that uses laser to cure photopolymer resins layer by layer as
shown in Fig.1.6. With computer control of motion, laser scans through the sliced area of the model and
the cured materials can form a 3D shape. SLA process provides a method to cure photopolymer resins,
the materials are mainly polymer based materials, the process is fast and the fabrication resolution is high
so that it can be used to fabricate complex small features, thus it is suitable for fabricating self-folding
structures if the materials identified can be cured by laser.

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Figure 1.6 Illustration of StereoLithography (SLA) Process (Image Source:
https://3dprintingindustry.com/3d-printing-basics-free-beginners-guide/processes/)
2) Mask Image Projection based StereoLithography (MIP-SL)
Mask Image Projection based StereoLithography process is a projection based StereoLithography
process as shown in Fig. 1.7, the process is also known as Digital Light Processing(DLP) process in some
other notations. Compared with the original SLA process, MIP-SL uses a more conventional light source,
such as an arc lamp, with a liquid crystal display device or digital micromirror device (DMD) to control
the output image.

Figure 1.7 Illustration of MIP-SL Process (Zhou, 2013)

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The MIP-SL process is faster than SLA process in a way that it cures an entire layer of the part at
single shot. The process is also good for curing photo sensitive resin materials, it is also considered in our
research to fabricate self-folding structures with identified materials.
3) Selective Laser Sintering (SLS) / Selective Laser Melting(SLM) / Electron Beam Melting (EBM)
Selective Laser Sintering (SLS) and Selective Laser Melting(SLM) are powder based 3D printing
technologies, the processes use laser as a heating source to bind the powder particles together in a powder
bed layer by layer, powders are refilled in each layer using rolls as shown in Fig.1.8. Based on the
temperature used regarding the powder material, either sintering or melting could happen in the process.
SLS and SLM processes work mainly with polymer materials since their melting temperatures are low.
Electron Beam Melting (EBM) is a quite similar process except that it uses electron beam as the heating
source such that it is suitable for metal powders with high melting points.

Figure 1.8 Illustration of SLS process (Rombouts, 2005)
The potential of using SLS/SLM/EBM to fabricate self-folding structures remains to be investigated,
since most of the self-foldable structures are made of at least two types of materials as discussed in
section 1.1.2. So identifying or developing two types of materials that are both suitable for these

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processes and can be bound together is critical in the applying of these processes to make self-foldable
parts. If we are using existing active materials such as the polystyrene film, we should be careful with the
high amount of heat generated by the laser or electron beam such that it will not damage the active
material since it has a melting temperature around 200 degree C.
4) Direct Ink Writing (DIW) / Fused Deposition Modeling (FDM)
Both Direct Ink Writing (DIW) and Fused Deposition Modeling (FDM) processes are extrusion
based 3D Printing technology as illustrated in Fig. 1.9. Materials are extruded out through a nozzle and
deposited onto a Z-stage to form one layer, continuing the deposition steps for multiple layers can form a
3D shape. Both DIW and FDM processes have a wider material pool than the other processes, for DIW
process, as long as the material can stick with each other without collapse and also can be extruded, it's
good enough to use this process to fabricate 3D parts, for FDM process, as long as the material can get
melt inside the heated nozzle and can be continuously extruded out, it can be used.

Figure 1.9 Illustration of DIW and FDM process. (a) DIW process (Larson, 2016) (b) FDM Process
(Image source: http://3devo.eu/guide-fdm-printable-plastics-3d-printing-filament/)
For fabrication of self-folding structures, both DIW and FDM processes have great potential for the
following reasons: first of all, both processes have a wider material selection than the other processes so
that it's easier to identify multiple materials that could be used to fabricate self-folding structures;

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secondly, both processes have the capability of fabricating structures with multiple materials. As most of
the self-foldable structures are composed of different materials due to the functional requirement of
folding, it is possible to use these two processes to prepare the self-folding structures with various
materials.
5) Inkjet Binder Jetting and Inkjet Material Jetting
Both Binder Jetting and Material Jetting use inkjet printing technology. As shown in Fig 1.10(a),
Inkjet Binder Jetting process prints out binder materials to the powder bed so that powders are bound
together to form one layer. Repeating the powder refilling and printing process, 3D objects can be
fabricated, post processing might be needed to strengthen the mechanical property of the part. Unlike
Binker Jetting, Material Jetting technology as illustrated in Fig.1.10(b) prints out materials that
accumulate to become the layers of the object, most of the materials used are photocurable polymers, such
that after the material is jet out, a flash of the UV light is used to cured the printed out material. The
printing speed of the process depends on the size of the printing nozzle, typically it takes hours to
fabricate a part with the similar size of a human hand.

Figure 1.10 Illustration of the Inkjet Binder Jetting process and Material Jetting (a) Inkjet Binder
Jetting (b) Inkjet Material Jetting (Image source: http://3dprinting.com/what-is-3d-printing/)
Regarding the fabrication of self-folding structures, Inkjet Material Jetting is more suitable than
Inkjet Binder Jetting since it has the capability of fabricating objects with multiple materials, which is
critical in fabrication self-folding structures.

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6) Laminated Object Manufacturing (LOM)
The Laminated Object Manufacturing (LOM) process deals with materials such as paper, plastic and
thin metal film as shown in Fig.1.11. The process uses laser to cut the contour of the desired layer and
applies binders between each layer to bind them together. A material supply roll will continue to fill in a
new layer of paper and this process can go on layer by layer.

Figure 1.11 Illustration of LOM process(Image Source: http://aaq.auburn.edu/node/1359)
The LOM process is suitable for laminating thin film layers so it's also a good alternative in
fabricating self-folding structures. For example, in preparing the bilayer structure design, two layers could
be bound together using the LOM process.

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1.1.6 Smooth Curved 3D Shell Structures
Self-folding structures fabricated are typically of origami designs, which are composed of hinge
portions and body portions, the structures are folded into 3D shapes along defined hinges, each body
portion is small flat facet. The folded structures have sharp corners at hinge portions, which are of pretty
high curvatures. However, among both structures in nature as well as daily product designs, smooth
curved 3D shell structures are seen very often as shown in Fig. 1.12.

Figure 1.12 Applications of smooth curved 3D shell structures
Smooth curved 3D shell structures or freeform 3D shell structures are very popular in engineering
design fields such as automobile designs, bio-medical devices as well as customized ergonomic designs.
The benefits of using curved 3D shell structures include several aspects: first of all, light-weighted; due to
the nature of shell structures, compared with solid parts, hollows and cavities are created in the shell
structures such that the weight of the parts is greatly reduced, this property is really beneficial in
automobile designs since it can lower the load of the vehicle. Secondly, it saves a lot of material by using
shell structures since only a thin layer of material is used in the structure. Furthermore, freeform 3D shell
structures provide the capability to conform their shapes with specific alignments, this property is critical

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for user oriented customized designs as well as ergonomic designs such as hearing aids, neck protectors
as well as heel protector that have conformable shape requirements to align with human body. Wearable
devices are also a hot potential application for the freeform 3D shell structures due to similar reasons.
Although freeform 3D shell structures have so many benefits, their fabricating methods are limited.
The traditional way to fabricate 3D shell structures is either through delicate tooling such as die and
punch or by injection molding, sometimes machining is used as well. These methods all have limitations
in rapid prototyping customized designs. Die and punch method as well as injection molding require
complex mold design process and are expensive for small amount of parts. Machining through CNC
machine is also an expensive way, and it takes a lot of time for fabricating complex geometries. Two new
techniques for 3D shell structure fabrication are incremental sheet forming and 3D printing, however,
they have their own limitations as well. Incremental sheet forming works only for metal sheets, though it's
a cheaper way to build shell structures, it takes a lot of time to gradually deform the sheet into a target
geometry. 3D printing has the capability of fabricating complex shapes through accumulating of materials
layer by layer. It's a promising method for customized geometric designs. However, most of the available
processes such as SLA (Stereolithography), FDM(Fused Deposition Modeling) require support structures
in fabricating 3D shell structures, the removal of these support structures is a heavy duty work and
requires careful operation in order not to break the 3D shell structures; also, for these processes, the shell
structures will deform after the removal of supporting structures due to the releasing of constraints.
Powder bed 3D printing can fabricate 3D shell structures without using support structures, however, the
strength of the part and fabrication resolution is limited. Another shortcoming in using 3D printing to
fabricate 3D shell structures is that the material accumulating efficiency is low because only a little bit of
material is added in each layer.
Self-folding has great potential in fabricating smooth curved 3D shell structures since there are
curved features that can be realized through folding, such as in the case of bilayer structural design, the

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folding will generate smooth curvature; however so far it's a barely investigated area, which motivates us
to further study this problem.
1.1.7 Sequential Folding
Sequential folding of self-folding structures provides additional freedom in structural designs such as
various phase transformation of structures, self interlocking of the structure and self locked angle control.
Various phase transformation of the structure means that the structure can undergo series of folding steps
sequentially to form into different configurations such that the functionality of the structure can be
changed. Shown in Fig.1.13 is one such reconfigurable structure, the structure is programmed to fold into
a plane, it can also change its shape through folding along different hinges into a boat model as shown in
Fig.1.14.

Figure 1.13 A sequential folded plane model (Hawkes, 2010)
Sequential folding also allows structures to realize self-lock as well as self-block. Fig. 1.15 shows a
design using sequential folding to realize self-lock, the structure has five hinges, by carefully
programming the folding sequence, hinge No.4 and No.5 can be used to lock the structure by itself. This

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type of locking design has to use sequential folding because proper folding sequence has to be planned
ahead to make the locking successful, otherwise, it might fail.

Figure 1.14 A sequential folded boat model (Hawkes, 2010)

Figure 1.15 A self locked structure by sequential folding (Mao, 2015)

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Figure 1.16 A self blocking design using sequential folding (Lee, 2015)
Fig. 1.16 shows a sequential folding design that can self block to achieve accurate folding angle. As
shown in Fig. 1.16 (a), the structure without sequential folding design might fail due to the uncontrollable
folding behavior of each hinge; the design shown in Fig. 1.16 (b) fixes this by using sequential folding, it
first folds up the block features called "Collar face", then uses the collar face to block the folding of the
neighboring body portions, thus achieving controllable folding angle.
The details of the sequential folding mechanisms mentioned above will be discussed in Chapter 2,
the sequential folding method developed can implement certain types of designs, however, a more general
sequential folding method is needed for achieving fast self-folding structure designs. For example, the
sequential folding shown in Fig. 1.16 uses the similar principle of local light absorption to achieve self-
folding, the blocking of infrared light by the structure itself is one big issue that needs to be further
addressed.
1.2 Research Questions and Hypotheses
As discussed in previous sections, this research project was initiated from origami based designs to
self-folding structures, three basic needs are identified, which are the easiness and high speed of self-
folding structure fabrication, the self-folding of smooth curved 3D shell structures as well as an easy and
general way to realize sequential folding. Based on these, the principle goal of this dissertation is to

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develop rapid processes for design and fabrication of self-folding structures that can self fold into smooth
curved 3D shell structures with the capability of sequential folding using 4D printing. The primary
research questions are listed as follows:
RQ1. How to use 3D printing methods to fast fabricate self-folding structures?
RQ2. How to design and fabricate smooth curved 3D shell structures using self-folding method?
RQ3. How to achieve sequential folding in an easy and fast manner?
Three hypotheses are made in response to the three questions above, they are:
Hypothesis 1 Projection based stereolithography can be used to fast fabricate self-folding structures with
polystyrene film.
Hypothesis 2 Constraint pattern controlled self-folding with bilayer design can be used to design and
fabricate smooth curved 3D shell structures.
Hypothesis 3 Direct ink writing can be used to achieve sequential folding with silver ink printed
polystyrene film.
For Hypothesis 1, as discussed before in section 1.1.5, several 3D printing methods have the
potential to fabricate self-folding structures, to increase the fabricating speed of the structure, we
proposed to use existing materials such as polystyrene film as active material, then use 3D printing
methods to add passive materials on top of it to fabricate self-folding structures. Projection based
stereolithography can fabricate the layers very fast with photopolymer resins. It also provides high
resolution for complex feature requirements, so it could be a very good candidate process.
For Hypothesis 2, to realize the self-folding of smooth curved 3D shell structures, a design
methodology needs to be developed to achieve the global deformation of the desired shape. Bilayer

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structure could be used to form the basic curved shape and deform a local unit. By combining the
deformation of each unit, a global deformation could be achieved.
For Hypothesis 3, to achieve sequential folding of the structure, both global stimuli and local stimuli
can be used, for the global stimuli, such as heating inside the oven, the requirements for the variety of
folding hinges is high, so we proposed a method of using a local stimuli, which uses circuit designs to
trigger the folding of each hinge locally by printing silver ink traces on top of the polystyrene film.
Each research question as well as the corresponding hypothesis can be further subdivided into
smaller and more detailed ones as shown as follows:
RQ1.1 What structural design should be used in the self-folding structure?
RQ1.2. How to control the folding angle of the self-folding structure?

Hypothesis 1.1 A sandwiched structural design based on bilayer structure could be used in the self-
folding structure.
Hypothesis 1.2 Theoretic model as well as physical design features could be used to guide the design of
the folding angle .
The proposed self-folding structure fabricated by projection based stereolithography uses a
sandwiched structure, where the top layer and bottom layer are photopolymer resin layers, middle layer is
the active layer, we proposed to use existing materials such as polystyrene film as active layer. By coating
the hinge portion and body portion differently, self-folding behavior of the structure could be achieved.
Theoretic models for the folding behavior could be developed to analyze the relationship between design
parameters and the folding angle; some physical design features such as angle lock could be used to
constrain the maximum folding angle.

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RQ2.1 How to map a smooth curved 3D surface into 2D design?
RQ2.2 How to control the folding parameters on each folding unit to achieve the global shape?

Hypothesis 2.1 A surface discretization method can be used to map curved 3D surface into 2D design
with folding parameters.
Hypothesis 2.2 Constraint patterns can be identified and designed to control the corresponding folding
parameter that can realize the deformation control of each folding unit.
To verify the hypothesis, we proposed a method to map 3D surface mesh to a 2D design based on the
folding parameters of each local surface patch unit obtained by mesh discretization, by reversing the
desired shape, we can get the folding requirements of each surface patch unit. Different constraint
patterns could be studied to realize the control of the folding parameters such that the constriant pattern
can be used in the fabrication of 2D self-folding structures.
RQ3.1 How to control the folding angle?
RQ3.2 How to achieve sequential folding through local heating?

Hypothesis 3.1 Factors that affecting the folding angle can be analyzed and calibrated to control the
folding angle with the help of angle lock.
Hypothesis 3.2 Decoupled circuit design can be used to heat up the self-folding structure locally to
achieve sequential folding.
We conducted theoretical analysis regarding the relationship between thermal condition and the
folding angle. Experimental tests were also done to verify the hypothesis. Circuit designs in the self-

36

folding structure are designed and tested to achieve locally heating in single hinge, thus achieving
sequential folding of the overall structure.
The chapters relating to each research question and hypothesis are shown in Fig. 1.17.

Figure 1.17 Related chapters to research questions and hypotheses
1.3 Contributions
In this research, we aim to develop self-folding methods based on 4D printing technology that can
achieve fast and easy fabrication of self-folding structures. To be more specific, the major goal and
contributions of this work include:
1) Develop a process using MIP-SL to fabricate self-folding structures with polystyrene film.

37

2) Design a sandwiched structure based on bilayer design and hinge based design for self-folding
design purpose.
3) Study the relationship between design parameters and the folding angle.
4) Design physical lock features to achieve a better and more robust folding angle control.
5) Develop a method to map 3D smooth curved surface design to 2D printable layout based on
defined folding parameters.
6) Identify constraint patterns that can achieve the folding parameter requirements to realize global
shape approximation.
7) Develop tools to simulate the deformation of the self-folding structure and compare the simulated
data with the folded parts.
8) Develop process using direct ink writing to print silver ink on polystyrene film to realize
sequential folding purpose.
9) Conduct thermal analysis to identify factors that affect the folding angle.
10) Develop angle lock designs to assist accurate folding performance of the structure.
11) Explore the applications that can use the processes developed such as 3D antenna designs.
1.4 Outline of this work
Fig. 1.18 gives an overview of the chapters in this dissertation.
Chapter 1 gives an introduction of the research background and motivations, research problems as
well as the corresponding hypotheses are discussed.

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Chapter 2 reviews the state-of-the-art self-folding mechanisms, specifically focused on the
mechanisms using existing materials for material preparation such as polystyrene film developed in most
recent few years.
Chapter 3 presents the development of the fabrication process of self-folding structures using
projection based stereolithography, theoretical modeling, angle lock designs, experimental verification
and application cases are discussed as well.
Chapter 4 discusses the design and fabrication of smooth curved surfaces using self-folding method,
both the mapping method of turning 3D curved surface designs into 2D layout as well as the constraint
pattern design are elaborated.
Chapter 5 introduces a process using Direct Ink Writing (DIW) to fabricate self-folding structures
using polystyrene film that can fold sequentially. The details of the factors that affect the folding angle as
well as the methodology for circuit design are given.
Chapter 6 gives a summary of the dissertation and provides some recommendations for future work.

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Figure 1.18 Overview of the dissertation

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Chapter 2 Literature Review: Self-folding Designs and Mechanisms
With Polystyrene Film
Different designs are mechanisms have been developed for self-folding structures in various scales
as well as various applications. A lot of research have been reported in recent decades regarding the
process, design as well as applications regarding the self-folding structures. The use of polystyrene film in
self-folding structure was first proposed in a research paper in 2012, since then a lot of other groups have
been using this material as well in their research. In this Chapter, we will review the main methods that
have been used in designing and fabricating self-folding structures, with specific focus on the structures
using polystyrene film; Methods regarding curved shape folding as well as sequential folding designs are
also reviewed.
2.1 Self-folding Structure Categories
Self-folding structures were first studied in micro and nano level trying to fabricate 3D micro
structures that can be used for biomedical applications as well as micro- and nano-electronic devices.
Smela et al (Smela, 1995) and Jager etal (Jager, 2000) did some pioneering work with folding and
unfolding of patterned gold films using bilayer designs as shown in Fig.2.1. Others also developed
methods to fabricate 3D micro structures using self-folding. For example, Gracias et al developed
approaches to use metallic particles and films to self-fold microelectronic devices that could be used in
controlled encapsulation of cells as well as drugs (Gracias, 2000, 2009) as shown in Fig.2.2. Although
metallic self-folding structures have a lot potential for optics and photovoltaic power applications, their
limited biocompatibility and non-biodegradability constrained their usage in biomedical purposes. Thus
more and more research on polymers, especially self-folding polymer films were conducted since

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polymers are more suitable in physiological environment also there are a variety of biocompatible and
biodegradable polymers that can be candidate materials that could be used.

Figure 2.1 Folding of a patterned gold films (Smela, 1995)

Figure 2.2 Thin film self-folding micro grippers (Gracias, 2009)
The self-folding mechanisms are quite similar in certain aspect of view, most of the self-folding
structures are implemented through bending due to material expansion or shrinking. Bending could be
achieved in two ways, either by using homogeneous materials in gradients of field or by using
inhomogeneous materials under uniform stimuli field. In the first case, it has a very high requirement for

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the gradients of field, for example in the work shown in Fig.2.3, the researchers used capillary force
introduced by a droplet to fold an elastic film, the capillary force that triggered the folding would not last
when the water fully evaporated. Since gradients of field are really difficult to maintain, it's more
complex to use homogenous materials than using inhomogeneous materials in achieving self-folding
designs. The inhomogeneous designs used in the self-folding structures were pre-programmed through
different structural design as well as constraint patterns.

Figure 2.3 Self-folding of elastic sheet by capillary force induced by droplet (Py, 2007)
Self-folding structures seen in literature before 2012, were mainly micro level structures because of
the research areas were mainly in biomedical science, MEMS as well as Nano technology and most of the
structures were designed using inhomogeneous materials. Based on structural design, three main
categories of the self-folding structures can be identified as shown in Fig.2.4. The first category uses
shape memory materials, the structure will fold when the temperature rises above its phase transition

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temperature, typically the glass transition temperature. To realize self folding of a desired shape, the
shape memory polymer has to be trained first into that shape, then external forces are applied to deform it,
the shape of the material recovers after heated. Fig.2.5 shows an example of the first type, where current
is used to heat the structure to recover its original shape gradually. The second category uses bilayer
structural designs, where two layers of materials are laminated, one of them is active polymer, which will
expand or shrink under stimuli environment, the other one is passive polymer that is more stable under
stimuli environment and will remain its original shape. The passive polymer provides constraints to the
active material such that the structure will curve up and bend when the active material expands or shrinks.
Fig.2.6 shows an example of this type, the preparation steps are shown in Fig.2.7. The third type uses a
foldable hinge design, where the hinge portion is made of active material that can deform and brings the
body rigid portion together and realize folding. For example, as shown in Fig.2.8, the active material in
between at the hinge portion will dissolve and the rigid portion will be assembled together through
surface tension. The preparation of the structure is shown in Fig.2.8(a), steps involved are spin coating,
photolithography as well as deposition.

Figure 2.4 Three main types of self-folding structures (Ionov, 2011)

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Figure 2.5 Sequences of the shape recovery of sample CB10 by passing an electrical current (Leng, 2009)

Figure 2.6 SEM photographs of the micro cubes (Suzuki, 2007). (a) Two out-of plane microcubes
assembled simultaneously on a chip. (b) Close-up view of a microcube

Figure 2.7 Fabrication process of the bilayer structure (Suzuki, 2007)

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Figure 2.8 Thermoresponsive self-folding SU-8 photoresist-polycaprolactone thin films (Gracias,
2011)
2.2 Self-folding Structures with Polystyrene Film
All these types mentioned above require very complex material preparation due to specific
application requirements, in micro level research, most of the materials used are prepared by themselves
thus the process takes a long time. In 2012, Liu et al proposed a new idea to use pre-stressed polystyrene
film, also known as Shrinky Dinks film to fabricate self-folding structures by printing black ink on the
surface of the film, making the material preparation way faster than the previous approaches. Since then,
tons of research activities have been conducted around this type of material and various of folding
mechanisms have been developed using the polystyrene film.

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2.2.1 Self-folding of polystyrene film by local light absorption
Fig.2.9 shows the principle of the self-folding by local light absorption proposed in 2012. In this
mechanism, black ink is printed on the surface of the polystyrene film, when the structure is exposed to
infrared light, the energy absorption of the portion with black ink is far more than the other areas, thus
resulting in the shrinking difference between both sides of the film at the hinge portion and generating the
bending behavior. Folded samples are shown in Fig.2.10.

Figure 2.9 Principle of the self folding by local light absorption (Liu, 2012)

Figure 2.10 Self folded samples of the ink printed polystyrene film (Liu ,2012)

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2.2.2 Self-folding of polystyrene film by laser light
This self-folding mechanism was extended to trigger by laser light by the same group in 2014 (Liu,
2014). Fig.2.11 shows the folding effect of a single hinge.

Figure 2.11 Self-folding through absorption of laser beam. (Liu, 2014) (a) Schematic of the polymer
sheet exposed to laser light. (b) Photographs of the folding of a pre-strained polymer sheet coated with
black ink
2.2.3 Self-folding of polystyrene film by joule heating
Mechanisms to self fold polystyrene film based on jour heating were developed in 2013 in a group at
Harvard. Fig.2.12 shows an inch worm robot case by the group, the structure has four layers as shown in
Fig.2.13. The structure uses polystyrene as active layer and a copper trace layer underneath as the trigger
of the folding. By conducting current to the structure, the 2D sheet will fold. This structural design can
realize sequential folding.
Similar designs can been found in their following research. For example, in 2014, they published a
paper in Science regarding a self-folded robot as shown in Fig.2.14. The structure had five layers, they

48

added paper layers to be the rigid part of the structure and used the Pre-Stretched Polystyrene (PSPS) as
active layers to trigger the folding. They also made structures like pyramid, self-lock structure as well as
origami crane as shown in Fig.2.15.

Figure 2.12 Self-folding of a inchworm robot (Felton, 2013)

Figure 2.13 Composite design of the self-folding structure (Felton, 2013) (a) Polystyrene Layer (b)
copper-polyimide layer for jour heating purpose (c) PEEK layer (d) Polystyrene Layer (e) Design layout.

49

Figure 2.14 Self-folded robot (Felton, 2014)

Figure 2.15 Self folded pyramid, locks and crane (Felton, 2014)
2.2.4 Self-folding of polystyrene film by uniform heating
Uniform heating mechanisms for self-folding of polystyrene film were also developed around 2013
by a MIT group cooperating with the Harvard group. The structure became simpler as shown in Fig. 2.16,
it had only three layers laminated together, two hard paper layers sandwiched with the polystyrene layer.
The folding pattern was designed through laser cutting of the two paper layers, the opening at the top
layer allow the structure to contract by the shrink polystyrene film while the bottom layer stays connected
as a constraint. Fig.2.17 shows several self-folded geometries by this method.

50

Figure 2.16 Design of the self-folding structure (Tolley, 2014)

Figure 2.17 Self-folded geometries by uniform heating (Tolley, 2014)
They did some following research in fabricating miniature self-folding structures using the exact
same structural design. For example, shown in Fig.2.18 is a tiny robot that can move controlled by
magnetic field.

51

Figure 2.18 Self folding origami robot (Miyashita, 2015)
Our group also developed a method to self fold polystyrene film through uniform heating in 2013
(Deng, 2015), we used bilayer design in the structure as shown in Fig.2.19. Instead of using hard paper as
rigid parts, we coated photopolymers on both sides of the polystyrene film through stereolithography. By
leaving a gap at the hinge portion, the structure can fold when heated since the shrinking ratio of the
polystyrene film at the hinge portion is different between its two sides. This structural design is really
simple and the preparation steps are easy as well. Details of our process will be elaborated in Chapter 3.

Figure 2.19 Design of the self-folding structure
2.2.5 Self-folding of polystyrene film by microwave
In 2015, a paper came out regarding a new mechanism to trigger the folding of the polystyrene film
that used graphene ink to harvest microwave energy on the hinge portion as shown in Fig.2.20. The
mechanism was relatively new, however, it required a uniform energy distribution inside the microwave

52

oven, which was difficult to achieve. Fig.2.21 shows the folding result on a sample along different
orientations. The energy distribution inside the microwave oven is not uniform though.

Figure 2.20 Folding process induced by microwave (Davis, 2015)

Figure 2.21 Structures folded along different orientations inside the oven (Davis, 2015)
In this Section 2.2, methods to fold the polystyrene film are reviewed, basically, there are two types
of methods, the first one is using different stimuli to generate different shrinking ratios of the polystyrene
film, such as the one using infrared light, laser as well as microwave. The second one is using structural
designs to realize folding through the shrinking of the film, for example the laminated layer design as
shown in Section 2.2.3 and Section 2.2.4. for the first type of method, the material preparation is really
simple, just by printing some material on top of the film, for the second type, it's relatively complex since

53

multiple layers of materials are needed, steps such as laser cutting, film laminating are needed. The
structures are more bulky compared with the first type.
2.3 Smooth curved shape folding
Few papers were seen directly trying to solve the self-folding of smooth curved shapes, however,
there are still some papers that have mentioned a bit regarding this topic. For example, one paper
published in 2016 used a 3D printing method to fabricate light weight structures that were with curved
shapes through releasing of thermal stress between the two materials as shown in Fig.2.22. This method
prints a very thin layer (~100 micron) of PLA using a regular FDM 3D printer on top of the hard paper,
since the PLA will shrink after cooling down, the structure will curve up and fold. By designing different
patterns, various curved geometries could be achieved as shown in Fig.2.23.

Figure 2.22 Self-folding of a light weight flower case (Zhang, 2016)
This method, although can fabricate curved shapes, was not intended for self-folding purpose,
actually, the releasing of internal stress to form curved geometries could be seen in early research works
as well, such as the one shown in Fig.2.24. It's a micro structures fabricated through releasing of the top
layer from substrates.

54

Figure 2.23 Various curved shapes through folding of thin composite (Zhang, 2016)

Figure 2.24 Micro structures fabricated through releasing of stress (Moiseeva, 2007)
Bilayer designs are really promising in fabrication of smooth curved structures due to the property
that the bilayer will form a natural curvature. Smart designs as well as optimization method could be used
to further investigate the folding of smooth curved structures. We developed one method to fabricate
structures with smooth curved surfaces in 2014, Details of our method will be elaborated in Chapter 4.

55

2.4 Sequential folding designs and mechanisms
Sequential folding has become more and more popular over the past few years because it adds more
design freedom and functionality to the structures that can be achieved. In general there are two types of
sequential folding mechanisms, the first one uses uniform hinge designs with local control of each hinge,
such as the ones shown in Section 2.2.3, folding by joule heating. The circuits can be separated to control
each hinge, thus realizing sequential folding of the structure. The second one uses non uniform hinges
with a uniform stimuli environment. Following are two examples. The first one uses various composite
shape memory polymer hinges by multiple material 3D printers that have different starting time to fold
with various temperature as shown in Fig.2.25.

Figure 2.25 Sequential folding of a mailbox model (Mao, 2015)

56

The second one shown in Fig.2.26 uses the local light absorption mechanism, while instead of using
uniform black ink on the hinge, it uses ink patterns with different grey scales so that the temperatures on
different hinges were different, so was the initiation times of folding for each hinge.

Figure 2.26 Sequential folding of a cube (Lee, 2015)
Since the preparation of different hinges that respond to stimuli in sequential order is complex and
difficult, most of the sequential designs are still using uniform hinges but with local control of each hinge.
This is typically done through joule heating by embedded circuits. We developed a method to realize
sequential folding using uniform hinges as well as non uniform hinges. Which will be discussed in detail
in Chapter 5.
2.5 Summary
In this Chapter, we first went through different categories of self-folding structures, they are shape
memory based structures, bilayer structures, hinge based structures. Folding mechanisms and examples
are given for each of them, the material preparation is also introduced. For these three types of self-
folding structures, the materials used require a complex preparation procedure. Which is a major
motivation for developing faster processes for self-folding structures.

57

We then reviewed the self-folding structures using polystyrene films, the research idea first initiates
in 2012, several other mechanisms came out after that using the similar materials, five types of folding
mechanisms reviewed are folding by local light absorption, folding by laser beam absorption, folding by
joule heating, folding by uniform heating and folding by microwave. Mechanisms of each type are
discussed. Among them, the folding by uniform heating shows great potential in fabricating controllable
self-folding structures.
Self-folding methods of structures with smooth curved surfaces were also reviewed. So far, only few
papers have mentioned the curved structure fabrication through internal stress releasing using bilayer
structures. Which gives a hint that bilayer structure is promising for fabricating smooth curved structures.
Sequential folding methods including local hinge folding through joule heating as well as non
uniform hinge designs were also reviewed. The preparation of various hinges are difficult and complex,
so far, sequential folding by local joule heating is still the main method.

58

Chapter 3 Origami-based Self-folding Structure Design and
Fabrication Using Projection based Stereolithography
Following the previous chapters, we now recognize that self-folding structures have unique
capability and can be beneficial for a wide variety of applications including biomedical and electronics
products. However, how to inexpensively fabricate and accurately control self-folding structures is still an
ongoing research topic. In this chapter a novel fabrication approach based on a three-dimensional (3D)
printing process is presented for fabricating self-folding structures that can be actuated in a heating
environment. The thermo-actuating structures that are designed and fabricated by our method are two-
dimensional (2D) origami sheets that have multiple printed layers. The middle layer of the origami sheet
is a pre-strained polystyrene film with large shrinkage ratios when heated. Both its top and bottom
surfaces are covered with cured resin that is printed in designed shapes. A foldable hinge is achieved by
constraining the shrinkage of the film on one side while allowing the shrinkage of the film on another side
when the origami sheet is exposed to a heating environment. Heuristic models of hinge’s folding angles
are developed based on the related folding mechanism. A 2D origami sheet design and fabrication method
is presented for a given 3D structure. Various experimental tests are performed to verify the self-folding
performance of the designed and fabricated origami sheets. Techniques on improving folding angle
control are also discussed with possible applications.
3.1 Folding Mechanism Analysis
The folding of a bilayer structure is realized either through the inhomogeneous expansion or
contraction of materials with different volumetric shrinkage ratios in different directions. For a direction

59

that needs to be folded, a different shrinking behavior is required along that direction. For example, for a
structure that is required to be folded in the Z axis, the desired folding will be generated only if the
shrinking ratio increases along the Z axis (refer to Fig.3.1 (b)). If the material has the same shrinkage
ratio along the Z axis, the structure will uniformly shrink with no folding effect (refer to Fig.3.1(a)).

Figure 3.1 The bending principle of a bilayer structure and the constraining effect of cured resin
In our method, a bilayer structure is used to realize the desired self-folding of hinges in a 2D origami
sheet. In the structure, the pre-strained polystyrene film (e.g. the Shrinky-Dinks film) is used as the active
material to provide the energy that is required for folding. Another kind of material (photocurable resin) is
printed on the polystyrene film to work as the passive material to control the folding behavior. Note that,
in order to realize the bending of the structure, the passive material needs to constrain the active material
such that the shrinkage ratio of the polystyrene film will change along the Z axis. Such bottom
constraining effect is illustrated in Fig.3.1 (c), in which the top portion of the polystyrene film is exposed
to a pre-heated oven with a temperature that is higher than the glass transition temperature of the film.
Consequently, the top portion will shrink; however, the printed passive material can stop the bottom
portion of the film from shrinking, which leads to the bending of the structure. To ensure the bottom
constraining effect, photocurable resin needs to be well cured such that it can strongly attach to the film;
otherwise, the cured resin may detach from the film when the film begins to shrink under a raised
temperature.
(a) Shrinking ratio remains the same along the Z direction
(b) Shrinking ratio increases along the Z direction
Z
X
Z
X
(c) Bottom constraining effect
0.5mm

60

In addition to constraining volumetric shrinkage, the printed passive material also blocks heat
transfer from the heating environment to the bottom portion of the polystyrene film. Hence the top and
bottom portions of the film may have varying temperatures due to different heat transfer rates. We believe
both effects contribute to the self-folding of bilayer structures while the bottom constraining effect plays a
major role. This is because the bilayer structure will still fold even in situations where the samples are put
in an oven with gradually increased temperatures (i.e. there is little temperature difference throughout the
whole structure during the heating process).
3. 2 Self-folding Origami Structure Design and Fabrication
Based on the previously discussed bilayer structure design, two types of hinge designs (refer to Fig.
3.2) are explored for a self-folding origami structure. Fig.3.2(a) shows a partial film design, in which only
the hinge portions incorporate the bilayer structure while all the other portions are made by 3D printing
processes. Fig.3.2(b) shows a sandwiched film design by incorporating the bilayer structure in the whole
origami structure. In the sandwiched design, the polystyrene film will be used as the middle layer not only
in the hinge portions but also in all other areas. To achieve desired folding, the top and bottom resin
layers in such a design are cured in designed shapes and thicknesses on the polystyrene film in order to
define the related hinges in the self-folding structure.

Figure 3.2 Two self-folding structure designs
Although the two origami structure designs are based on the same self-folding mechanism, they will
have quite different fabrication complexity. In the partial film design model, every hinge has a piece of
polystyrene film to be embedded in. During the fabrication process, the film portion related to a hinge

61

needs to be cut and inserted at each hinge position precisely. Note the hinges of an origami sheet can be
small and the number of hinges in an origami sheet can be large. Such a film inserting process is rather
difficult and tedious if doing manually. In comparison, in the sandwiched design, a much larger film
related to the whole origami structure is used. Each hinge is defined by projection mask images that will
cure liquid resin into desired shapes. Hence the hinge portion can have a high resolution (< 0.1mm). The
building process can be automated and fast regardless of the number of hinges. Considering the
fabrication requirements, the sandwiched structure design is better suited for the self-folding origami
structures and further studied.
Fig.3.3 shows two fabrication approaches for the sandwiched structure design. The first one is a
cure-before-cut approach (refer to Fig.3.3(a)). The approach is based on using a large piece of
polystyrene film that is placed on the building platform. After curing liquid resin on both sides of the
film, the extra portion of the film is cut either manually or using a CNC cutter. However, two problems
have been found for this approach. (i) The cutting of extra portions of the film is difficult with cured resin
on both sides. In addition, a cutting tool may damage the neighboring cured resin during the cutting
process. (ii) After cutting the extra portion, the film has edges that are directly exposed to the heating
environment. Such edges will shrink, which could separate the top and bottom layers of the film along
the edges (refer to a test example in Fig.3.3(b)). Hence an additional step is required to seal all the
boundary edges.

Figure 3.3 Two fabrication processes for the sandwiched structure design and related test examples
(a) a cure-before-cut approach
(c) a cut-before-cure approach
(d) A cut-before-cure built box model
(b) A cure-before-cut built box model
Film Resin material
Film Resin material

62

Another fabrication approach is based on a cut-before-cure approach (refer to Fig.3.3(c)). The
approach requires drawing the outline of an origami structure (with certain offset distance). Accordingly
the polystyrene film is cut into the drawn shape either manually or using a CNC cutter. The cut film is
then placed in the building platform for the liquid resin to be cured on the film. An appropriate offsetting
distance can be used in drawing the outline such that the edges of the film will be covered by the cured
resin. Hence, except the designed hinge areas, the film will have all the areas covered by cured resin.
This will effectively reduce the heat transfer from the heating environment to the film in the non-hinge
areas. Thus the origami structure will not have the detaching issue as shown in the cure-before-cut
approach during the folding process. Fig.3.3(d) show a test example based on the cut-before-cure
approach. The red line on the test part is the drawn outline for cutting the polystyrene film.
In this study, the cut-before-cure approach is used in experimental study. Two portions, hinges and
bodies, of a sandwiched structure need to be considered in order to design a self-folding structure. The
design of the body portions of an origami structure is relatively straightforward. The body portions should
have sufficient strength such that they will not bend during the folding process. In addition, the body
portions should be light as well since raising them up during the folding process will require energy. In
comparison, the design of the hinge portions of an origami structure is more challenging. Analytical
models and a related design method are required in designing each hinge such that the hinge can be self-
folded to a desired angle when the origami sheet is exposed to a heating environment. The hinge design is
discussed in more details in the next section.
3.3 Hinge Design and Self-folding Angle Analysis
3.3.1 Shrinkage of polystyrene film
The pre-strained polystyrene film shrinks in the XY plane and expands in the Z axis when heated. The
shrinkage behavior varies with the set temperatures. We investigate two types of polystyrene films, one

63

transparent and another white (as shown in Fig.3.4(a) and 3.4(b) respectively). The shrinkage ratios of the
two films are found to be similar.

Figure 3.4 Shrinkage behavior of the tested polystyrene films
Fig.3.4(c) shows the shrinkage of the transparent film in the XY plane under different temperatures.
The original dimension is 100× 100mm. Multiple identical samples are made for the tests (one sample is
shown Fig.3.4(a)). Each sampling point in the plot is generated by positioning the samples in an oven
with a preset temperature (e.g. 98
o
C or 130
o
C) for a certain time period. The samples are then taken out
and the shrunk lengths in the X axis are measured.
Based on the length measurement results, the film starts to shrink at ~98
O
C. The film shrinkage in
the XY plane then starts to grow rapidly, and becomes stable around 120
o
C. Note the polystyrene film
will become soft around 130
o
C, which sets the maximum temperature that the film can be used in a
heated environment. The maximum shrunk length is about 43% of the original length. It takes 5 to 10
seconds for the film to be totally transformed. The film’s shrinkage ratio in the XY plane is fixed when the
samples are heated under a temperature between 98
o
C to 120
o
C for a certain time. Assume  denotes the
(a) Transparent polystyrene film
(b) White polystyrene film
(c) Shrinking plot: length vs. temperature
(Degrees Celsius)
(before heating)
(after heating)
(after heating)
(before heating)

64

shrinkage ratio in the XY plane, which is measured as the shrunk length over the original length.  is a
function of heating time t and environment temperature T. That is,  = f (T, t).
Denote  as the transferred mass ratio of the film, which is the mass of the material that deforms
over the total mass of the material. The transformed mass ratio will be used for calculating the energy
released by the film in the deformation process. It is also related to heating time t and environment
temperature T. that is,  = g (T, t).
Assume the implicit relationship between  and  can be represented as:  = F( ). To better control
the bending behavior of a designed origami structure, the heating time t is set to be long enough in our
study. That is, it is assumed the film is totally transformed by exposing it for a long enough time. So the
functions above would be:  = f (T);  = g (T); and  = F( ).
3.3.2 Design parameters of the origami structure
Fig.3.5 shows a detailed design of a hinge used in the sandwiched structure design. The design
parameters of a self-folding origami sheet include:
1) The dimensions of the body portion include Length
1
S and
2
S , width a , thickness c , top layer
thickness
1
d , and bottom layer thickness
2
d ;
2) The dimensions of the hinge portion include Length L , width b , thickness of the film h , and
thickness of the constraint resin layer d ;
3) The mass of the two neighboring body portions is denoted as
1
M and
2
M ; in addition, the
mass of the polystyrene film in the hinge portion is denoted as
1
m , and the mass of the
constraint resin in the hinge portion is denoted as
2
m .

65

Figure 3.5 Design parameters of a hinge and its neighboring body portion in the origami sheet
To determine an appropriate value of each design parameter, the folding process is analyzed for
establishing related deformation models. Note that the thermal analysis is not performed since time
parameter t is set to be sufficiently long in the experiments.
3.3.3 Hinge folding analysis
As discussed in Section 3.3.1, when the origami structure is put in a heated environment with a
raised temperature (e.g. 120
o
C), the polystyrene film will go through the shrinking process and release the
transformation energy that will deform the coated constraint resin layer on the film. The energy will also
overcome the gravitational potential energy of neighboring body portions if they are raised up in the Z
axis. For example, as shown in Fig.3.6,
2
M will be raised up in the folding process if
1 1 2 2
M S M S  .

Figure 3.6 Bending analysis of a self-folding hinge
s
1
s
2
a
c d
1
d
2
h
d
b
L
M
1 M
2
m
1
m
2

66

An assumption made in our analysis is that the bending between the film and the constraint resin
layer is sufficiently strong such that the interface will have the same length during the folding process.
For the purpose, liquid resin should be cured for a sufficient exposure time to ensure strong bonding
between the cured resin and the film.
Due to the small size of the hinge (~1mm), it is assumed that the hinge portion will be bent into an
arc shape. Accordingly, the geometric relationship of the deformed hinge is given as:
RL   ,
1
() R d L  
(3.1)
The maximum strain of the constraint layer is:
1
max
LL d
LL




(3.2)
Thus the maximum stress in the constraint resin layer is:
max max
T
T
Ed
E
L

 
(3.3)
where E
T
is the Flexural Modulus of the cured resin under temperature T.
Hence, one of the design criteria to make sure the deformed constraint layer will not break is:
max sin
T
re
Ed
L

 
(3.4)
Usually such a design criterion can easily be satisfied by selecting design parameters L and d .
As mentioned before, the energy conservation function during the bending movement is:
dg
Q E E      (3.5)

67

Where Q  is the energy released from the polystyrene film;
d
E  is the energy used in generating the
deformation of the constraint resin layer; and
g
E  is the energy used to overcome the gravitational
potential energy of the load (e.g. raising up
2
M in Fig.3.6).
(i) For a fixed temperature T, the mass shrinking ratio  is fixed. Denote q as the unit releasing
energy of the polystyrene film (q is in a range of 2~3J/g). Denote  as the density of the film, then:
1
() Q m q Lhb q      
(3.6)
(ii) Since
2
SL  , a simple model for the increased gravitational energy for
1
m and
2
m is:
22
sin
2
g
M gS
E



(3.7)
In the experiments, E
g
can be reduced if the origami sheet can be positioned to avoid the raise-up of
large body portions in the gravity direction. More importantly, the magnitude of E
g
, when compared to
the other two terms in the equation, is usually multiple orders of magnitudes smaller.
(iii) Depending on the bending angles, there are two types of models for calculating E
d
. The first
one is to treat the deformation as a large elastic deflection of a “wide” beam, which is appropriate for
modeling small elastic deformation of the constraint resin layer. The second one is to treat the
deformation of the constraint resin layer as the plastic deformation. For different constraint materials and
folding angles, either elastic or plastic deformation can be used. Both types of models are considered in
our study. They are discussed in details as follows.
3.3.4 Modeling using the assumption of elastic deformation
Since the magnitude bL  in a hinge, the elastic deformation is modeled as large deflections of a
“wide” beam. That is,

68

1
2
d
EM   ,
2
(1 )
T
EI
M
R 



(3.8)
where M is the moment that is required to bend the structure; E
T
is the Flexural Modulus of the resin
material under temperature T; v is the Poisson ratio of the resin material; and
3
12
bd
I 
. Hence,
3 3 3 2
2 2 2
2 (1 ) 12 24(1 ) 24(1 )
T T T
d
E bd E bd E bd
E
R R L


  
      
  

(3.9)
The overall function
dg
Q E E      would be:
32
22
2
sin
()
24(1 ) 2
T
M gS E bd
Lhb q
L
 





(3.10)
g
E  in the last term could be neglected since its magnitude is relatively small compared to the other
two terms in the equation. For example, for a test case with
2 , 0.29 , 0.33 , 10 , L mm h mm d mm b mm    
33
10 / g mm 

 , 2.5 / q J g  , 0.4   ,
2
0.142 Mg  ,
2
9 S mm  . Suppose a bending angle
0
45   . The term
3
( ) 5.8 10 Lhb q J 

 , while the term
6 22
sin
4.5 10
2
M gS
J



. That is,
g
E  in the test case is three orders of magnitude smaller than Q  .
Hence the energy equation can be simplified by neglecting the last term. That is,
32
2
()
24(1 )
T
E bd
Lhb q
L






(3.11)
Accordingly, the relation between the bending angle and the design parameters of a hinge could be
written as:

69

2
3
Lh
K
d
 
(3.12)
where
2
24(1 )
T
q
K
E
   


(3.13)
Note that K is a coefficient related to the temperature and material properties. Physical experiments
can be performed to calibrate its value.
3.3.5 Modeling using the assumption of plastic deformation
Consider the resin material as a perfectly plastic material. Denote u as the unit energy, which can be
calculated as:
u d Y    


(3.14)
where Y is the yield strength of the resin material.
As shown in Fig. 3.6, the areas in the constraint layer have a radius of ' Rr  , ' (0, ) rd  . The
strain
' r
L

  , and
'
Y
u Y r
L

 
. The unit energy varies along ' r . Hence an integral along ' r could
lead to the energy of the deformed hinge. For a small ' r  , the energy would be
2
2
' ' ( ') ' ' ' '
Y Y b
U u V r r b L r Y br r r r
LL

              
(3.15)
Thus the total energy required for the plastic deformation is:
2 2 2 3
2
00
' ' ' '
23
dd
d
Y b Y bd Y bd
E U Y br r r r
LL
  
         


(3.16)

70

Thus the overall function
dg
Q E E      becomes:
2 2 3
22
sin
()
2 3 2
M gS Y bd Y bd
Lhb q
L
 
   
(3.17)
By neglecting
g
E  , the energy equation can be simplified as:
2 2 3
()
23
Y bd Y bd
Lhb q
L

 

(3.18)
Thus the relation between the bending angle and the design parameters of a hinge could be
established as:
3 16
( 1 1)
43
L hq
d Yd

    , or
3'
( 1 1)
4
L K h
dd
   

(3.19)
where
16
'
3
q
K
Y

 .
Since '1 K , the above equation could be approximated using the Taylor equation. That is,
2 3 4
' ' 1 ' 1 ' '
1 1 ( ) ( ) ( )
2 8 16
K h K h K h K h K h
O
d d d d d

     



(3.20)
For the simplicity, only the first order term in the Taylor equation is considered. Hence,
2
3 ' 3 ' 3 '
( 1 1)
4 4 2 8
L K h L K h K hL
d d d d d
      

(3.21)
Accordingly,
2
''
hL
K
d


(3.22)

71

where
3'
''
8
K
K  , which is a coefficient that could be obtained through calibration experiments.
The two models,
2
3
Lh
K
d
 
and
2
''
hL
K
d

, are slightly different by one term
h
d
(i.e.
2
23
'' ''
hL L h h
KK
d d d


     


), which means when hd  , the forms of these two models becomes the
same. Of course, they will have different coefficients.
The design parameters of the body portion of an origami sheet including Length
1
S and
2
S , width a ,
thickness c , top layer thickness
1
d , and bottom layer thickness
2
d . The only two design variables that
need to be further considered are
1
d and
2
d . They should be set values that are not too small; otherwise,
the resin layer may be too thin for blocking the heat transfer from the heating environment to the
embedded polystyrene film. Based on our experiments,
1
d and
2
d can be set to about twice or three times
of the film thickness h. In addition, if M
1
and M
2
are large such that the gravitational load will not be
small compared to the released energy from the hinge, the self-folding angle analysis will need to
consider
g
E  as well.
In the next section, the fabrication process of an origami sheet will be presented. Based on it, the
calibration experiments for identifying K and K
’’
are performed, which will be discussed in Section 3.5.
3.4 Fabrication Process of an Origami Sheet
The cut-before-cure approach is used to fabricate a designed self-folding origami sheet. A 3D
printing process based on a bottom-up Mask Image Projection based Stereolithography (MIP-SL) process
is adopted in curing desired constraint layer on a polystyrene film. In the MIP-SL process, a Digital
Micro-mirror Device (DMD) from Texas Instruments Inc. is used to project designed mask images on the

72

liquid resin. When exposed to the projection light defined by the mask images, liquid resin will be
selectively solidified accordingly.

Figure 3.7 The bottom-up projection based MIP-SL setup as well as a modified chamber design
Various modifications have been made in order to embed the polystyrene film in a built 3D structure.
Fig.3.7 shows the experimental setup, which has a modified curing chamber from our previous MIP-SL
systems. The curing chamber is designed for coating the polystyrene film with desired photocurable resin
layers. The physical structure of the chamber is shown in Fig.3.8. The resin curing chamber is made up of
two components, one is a transparent coated tank and the other is a cover. The tank is used to hold the
resin material. A layer of Polydimethylsiloxane (PDMS) film is coated at the bottom of the tank such that
the cured layer can be detached from the tank. The cover works as the platform on which the film is
attached. Many layers of spacers, each with a standard thickness, can be used on the backside of the cover.
By adding or decreasing the number of spacers, the thickness of the cured layer can be controlled. The
polystyrene film is glued to the cover during the building process. Markers for positioning the tank and
cover are also added such that the film can be aligned with the projection images during the building
process.

73

Figure 3.8 The physical structure of a chamber
The fabrication steps for an origami structure with unidirectional folding (i.e. folding in a single
direction) or bidirectional folding (i.e. folding in both directions) are different. Fig.3.9(a) and 3.9(b)
illustrates the origami sheet designs for the unidirectional and bidirectional folding, respectively. For the
origami sheet with unidirectional folding, only three layers are needed during the fabrication. Note the
thickness of a constraint resin layer may be different from the thickness of a body layer. In comparison,
at least four layers are needed for an origami sheet design with bidirectional folding. In addition, extra
layers can be added on the body layers in each side for additional features such as characters or geometric
shapes. Fig.3.9(c) and 3.9(d) illustrate the origami sheets with one extra layer in both sides for
unidirectional and bidirectional folding, respectively.

Figure 3.9 Origami sheets with unidirectional and bidirectional folding
(a) unidirectional folding design (b) bidirectional folding design
(c) unidirectional folding design
with extra feature layers
(d) bidirectional folding design
with extra feature layers
1
2
3
1
2
3
4
1
2
3
5
4
1
2
3
4
5
6
Constrain layer
Body layer
Extra feature
layer
Polystyrene
film

74

A detail building process of a bidirectional folding design (refer to Fig.3.9(d)) is shown in Fig.3.10.
A total of six layers are required in the designed origami sheet. During its fabrication, the polystyrene
film is first cut into a desired shape based on the outline of the self-folding structure. The cut polystyrene
film is positioned with the spacers and glued on the cover. The tank is then filled with liquid resin. The
cover is positioned on the tank with a controlled gap distance defined by the spacers. As shown in Fig.3.8,
a set of position markers can be used for positioning the cover and the tank together. Next the DMD
device projects a planned mask image for 3 seconds from the bottom of the tank to cure a layer on the
film. The cover with the built structure is then detached from the tank. After the structure as well as the
cover is cleaned, one spacer is removed and the built sheet is positioned back to the cover. The process
repeated for fabricating the next layer. As shown in Fig.3.10, Steps (c) and (f) require the flipping of the
built origami sheet in order to build layers on another side of the film. After the building process, the
fabricated origami sheet is cleaned and positioned in a post-curing chamber for about 20 seconds to
strengthen the attachment between cured resin layers and the polystyrene film.

Figure 3.10 The fabrication process of a bidirectional folding design with extra feature layers
1
3
1
1
3
2
(a) cure the constrain layer 1 (b) remove one spacer, cure body layer 3
(c) flip the structure, cure constrain layer 2 (d) continue to cure body layer 4
1
3
2
4
(e) continue to cure feature layer 5
1
3
2
4
5
(f) flip the structure, cure feature layer 6
5
4
3
2
1
6
Cover
PDMS film
Constrain layer
Body layer
Extra feature
layer
Polystyrene
film
Spacer

75

3.5 Self-folding Experiments
3.5.1 Calibration experiments
As discussed in Section 3.3.4 and 3.3.5, two types of energy models are established based on the
elastic and plastic deformations of the constraint resin layer. They are
2
3
Lh
K
d
 
and
2
''
hL
K
d

. In
order to design hinges based on given folding angles, a set of experiments are performed to determining
the values of K and K
’’
and to verify the models between bending angle  and hinge design parameters (L,
d). In our study, the thickness of the polystyrene film h is fixed (h = 0.29mm).
A set of experiments with different parameter values (L, d) are designed based on the origami sheet
as shown in Fig. 3.5. The origami sheets are then fabricated based on the fabrication process as discussed
in Section 3.4. Some of the built hinge samples are shown in Fig.3.11(a). The samples are then put in a
pre-heated oven with a controlled temperature (120
o
C) for a certain time period (15 seconds). After the
folding completes, the bending angle of each sample is measured. The measured data is shown in Table
3.1.

Figure 3.11 Built samples in the folding experiment

76

Table 3.1 Folding test data based on designs with different ( , Ld ) values

The experimental data is analyzed. Efforts are made to fit the analysis models based on the data. As
mentioned before, the deformation of the constraint layer under the heating condition can be elastic,
plastic, or a combination of both. Hence both the plastic model
2
''
hL
K
d
 as well as the elastic model
2
3
Lh
K
d
  can be used in fitting the experimental data.
Since the polymer used in self-folding origami structures has certain elastic deformation range.
When the folding angle is small, the deformation will fall in the elastic deformation range; while for a
larger folding angle, the deformation tends to be out of the elastic deformation range and the cured layer
will deforms plastically. Accordingly, the elastic model will be used for small bending angles while the
plastic model will be used for large bending angles.
A few trials have been made to identify a folding angle threshold that can divide the two types of
models to fit the measurement data. An empirical value
0
=80  is selected as the threshold between the
elastic and plastic deformations. Accordingly the regression of the experimental data has two segments.
Since the terms of the models on the X axis are different, two separate graphs that present the final data
fitting results are shown in Fig.3.12(a) and 3.12(b), respectively.
In Fig.3.12 (a), the elastic model is used to fit the data with small folding angles. The fitting result is
2
0
3
3.23 26.16
Lh
d

. In the fitted model in the form of
2
0 3
Lh
K
d
 
,
0
 is added to compensate the

77

simplifications that are made during the derivation of the equation. To design a bending angle that is
smaller than
0
 (26.16
o
),
2
3
Lh
K
d
 
could be used. However, the value of K should be recalibrated
using designed experiments with folding angles that are smaller than
0
 . As shown in Table 3.1, the
performed folding experiments have no folding angles that are smaller than
0
 since most applications
require a folding angle that is larger than 30
o
. Further tests on such small folding angles will be
performed in our future study.
Similarly, in Fig.3.12(b), the plastic model is used to fit the data with large folding angles. The fitting
result is
0
2
0.98 75.7
hL
d
   
. In the fitted model that is in the form of
1 2
''
hL
K
d
   
, the term
1
 is
added since the data is split into two parts according to the angle threshold (  = 80
o
).

Figure 3.12 Data fitting using both elastic and plastic model based on the folding angle
Based on the fitted models of a hinge between its design parameters and related folding angles, all
the hinges of an origami sheet can be designed based on given folding angles. For different constraint
materials (e.g. another type of photocurable resins), the aforementioned calibration process needs to be
repeated. Accordingly an appropriate self-folding origami sheet can be designed based on the newly fitted
models.

78

3.5.2 Verification Experiments
Fig.3.13 shows two test cases for verifying the fitted elastic model for small folding angles (  < 80
o
).
Both cases are designed using the first folding angle model
2
0
3
3.23 26.16
Lh
d

. Fig.3.13(a) shows a
rolled tube case, which is a unidirectional folding example. The desired bending angle for the rolled tube
case is 51.4˚. The selected hinge parameter values are L =1.6mm, d =0.23mm. Fig.3.13(b) shows a “Z”
shape case, which is a bidirectional folding example. The desired bending angle for the “Z” shape case is
±64˚. Table 3.2 shows the parameter values of both cases that are based on the measurement of the
fabricated samples. As shown in the table, some variations exist in the designed L and d due to the
fabrication errors. Accordingly the row three in the table is the computed  values using the fitted model
based on the measured ( , ) Ld values. The row four in the table is the measured  values after the folding
experiments. The error of the two  values is generally small (in average ~8%).

Figure 3.13 Two verifying test cases for small angles (α<80
o
)

79

Table 3.2 Parameters of the small angle test cases

Figure 3.14 A verifying test case for large angles (α≥80
o
)
Table 3.3 Parameters of the large angle test case

Fig.3.14 shows a test case for verifying the fitted plastic model for large folding angles (   80
o
). A
lotus design with some extra features (“USC” characters) is used in the test. A folded lotus is also shown
Fig.3.14. Note that the fabrication inaccuracy brings some deviations to the designed parameter values
( , ) Ld . The measured parameter values based on the fabricated samples are shown in Table 3.3. The
computed  values based on the second folding angle model (
0
2
0.98 75.7
hL
d
   
) are shown in the third

80

row of the table. The measured  values after the folding experiments are also shown in the table. The
error of the two  values is quite small (in average ~4.2%).
3.5.3 Discussion on folding angle control
The overall results of the verification experiments are satisfactory. However, some of the bending
angle could have an error as large as 18%. A critical issue in the origami structure design and fabrication
is how to accurately control the self-folding angles. An improved folding angle control method needs to
consider the three main processes: the hinge design, the hinge fabrication, and the heating process. Efforts
should be put into all the three processes in order to achieve well controlled self-folding performance.
(1) In the hinge design process, an important consideration is how to establish better folding models
and how to select appropriate values for the design parameters of an origami sheet. In addition, novel
design features may be added in the hinge design for better folding angle control. Fig.3.15 shows an
angle lock design that can be added based on our 3D-printing-based fabrication process. The designed
angle locks can constrain the max bending angle of the related hinge. Consequently, the design of a hinge
will be less sensitive to its folding error. For example, suppose a desired bending angle  ’ is given for a
hinge. The hinge parameters (L, d) could be set for some target angle  ’’   ’. During the folding process,
the hinge will auto-fold to  ’ and stop there due to the added angle lock design. Hence the folding
behavior of the hinge will be less sensitive to the errors in the fabrication and heating processes. For a
given angle  ’, the thickness of the angle lock layer d
3
could be easily set based on the geometric relation
31
() d d h L      . A test case with the angle lock design is shown in Fig.3.18(b).

Figure 3.15 Angle lock design for self-folding control
h
L

3
d
1
d
Constrain layer
Body layer
Polystyrene film
Angle lock layer

81

(2) In the hinge fabrication process, an important consideration is how to fabricate hinges with the
designed lengths and thicknesses ( L and d ). As shown in Tables 3.2 and 3.3, the fabricated hinges have
some variations from the designed values. Such variations need to be better controlled. In addition to
improving the mask image planning in the MIP-SL process, the manual operations in the current
fabrication process needs to be automated. In our future study, an automated fabrication testbed will be
built to reduce the fabrication errors.
(3) In the heating process, an important consideration is how to control the heating environment such
that the temperature inside the oven can be homogenous with small variations. An oven with multiple
thermocouples is built in our study. The temperature distribution inside the oven is measured. Efforts are
made to identify the positions inside the oven where the temperature distribution is the most
homogeneous. Hence each hinge of an origami sheet can have the same heating conditions during the
self-folding process. Better heating devices with improved temperature sensors and controllers will be
considered in our future study.
3.6 Applications
3.6.1 Self-folded Origami structures
Self-folding origami structures can be used for building complex geometry that may be difficult to be
fabricated by other manufacturing processes including 3D printing processes. For example, the test cases
as shown in Fig.3.17 and Fig.3.18 all require complex support structures in the MIP-SL process. In
comparison, no supports are required in the 2D origami sheet fabrication process since the complex 3D
structures can be achieved by the self-folding process. In addition to avoiding support structures, the
fabrication process of a 2D origami sheet is much simpler and faster compared to directly printing the
related 3D structures. In addition to the polystyrene films, the presented folding mechanism and models
can also be applied to other types of materials and micro-scale objects.

82

Some more complex test cases are presented as follows to demonstrate the capability of the design
and fabrication methods for self-folding structures. Fig3.16 shows a “USC” letter case, which is based on
the string-type folding. The designed models of each letter are shown in Fig.3.16(a). For each joint of the
letters, the values of design parameters (L, d) are selected based on the aforementioned folding angle
models and the desired angles in the letters. The fabricated origami strings are shown in Fig.3.16(b).
After the strings are put in a heated oven, the folded letters are shown in Fig.3.16(c).

Figure 3.16 A string test case using letters of “USC”
Fig.3.17 shows a designed structure with eight folded “legs” (four on each side). The shape of the
structure is motivated by a virus structure in the biology. To fabricate such a shape, two origami sheets
(refer to Fig.3.17(a)) are designed and fabricated based on the processes as described in Sections 3.4 and
3.5. Appropriate hinge parameter values are selected for their desired folding angles in the related legs.
Two fabricated origami sheets are glued together by curing a small amount of liquid resin at the center of
the structures. The fabricated origami sheet is shown in Fig.3.17(b). Accordingly, the folded origami
structure is also shown in Fig.3.17(b).

83

Fig.3.18 shows two more self-folding structures with additional features. A crane test case is shown
in Fig.3.18(a). Both the front and back sides of the 2D origami sheet is shown in Fig.3.18(a)-left. Note
some extra features (two “USC” letters) are added in their wings. Such features are hard to be fabricated
on the related 3D structure. The self-folded structure after putting the origami sheet in a heated oven is
shown in Fig.3.18(a)-right. Fig.3.18(b) shows a cube test case. Both the 2D origami sheet and the self-
folded 3D structure are shown in the figure. Note the angle lock design is added at each hinge (refer to
the front side). The test results illustrate that the angle lock design is effective in eliminating any over-
folding of the hinges in the 3D origami structure (i.e. the self-folding angle  is ensured to be less than  ’
related to the angle lock design).

Figure 3.17 A test case of an origami structure with eight “legs” - four in each side

(a) Designed models
(b) Fabricated structure and structure after folding
Constrain layer
Body layer
Polystyrene film
Glue layer

84

Figure 3.18 Two self-folding origami structures (a crane and a cube) with letters (‘‘USC’’)
A YouTube video of the presented origami structure design and fabrication method can be found in
the link of [54].
3.6.2 Self-folded 3D Circuit Design
Another application of the method developed in this study is the fabrication of 3D circuit designs.
3D circuit design has a lot of applications in electrical devices such as antenna, 3D wireless charging
devices as well as wearable devices. 3D circuit design has a lot of specific advantages over 2D circuit
design in the way that 3D circuit design is compact and the spatial layout gives potentially better
performance. Traditionally, the method of fabricating 3D circuit is through assembling and wiring, where
the circuit is made up of different components and is connected using connectors or soldered wires. With
the development of 3D printing technology, more and more functionality are added to the printed parts,
one of them is conductivity, where conductive traces are printed and circuit designs are embedded in the
3D object fabricated. The method decreases the steps of assembling needed in the fabrication process,
however the printing requires complex path planning due to the nature of combining the circuit printing
within the 3D printing process.
By using the 4D printing method developed in this study, a 3D design can be achieved through
deforming a 2D design. Similar idea of using folding to achieve 3D circuits can be found in other research,
however, the folding is manually operated. In this study, a self-folding mechanism based on thermal

85

responsive material is developed to realize 4D printing process. By carefully designing the constraint
patterns and hinge patterns, different structures can be folded using this method. Direct ink writing
process is used to print conductive traces on the 2D foldable structure. After the printing of the circuit, the
structure is put into an oven, and the structure will deform into the desired 3D shape, electric components
can be assembled onto the circuit to realize more functions. Fig.3.19 shows an example of the folded 3D
antenna design. It's really difficult to fabricate this 3D antenna using other approaches.

Figure 3.19 A self-folded 3D spiral antenna design
There are four main steps in the process of self-folding 3D circuit designs, they are: 1) Unfolding of
a 3D circuit design; 2) Fabrication of the 2D foldable structures; 3) Direct Ink Writing of the circuit traces;
4) Folding the 2D circuit into a 3D circuit. Details of the four steps are as follows:
1) Unfolding of a 3D circuit design
Given a 3D circuit design, the first step is to unfold the design into a 2D flattened design. As shown
in Fig.3.20, the designed 3D circuit is embedded with a crane model. To unfold a 3D circuit design, both
the 3D shape as well as the circuit pattern needs to be flattened. For the 3D shape represented using 3D
triangular mesh, there are a lot of algorithms that could be used to unfold it. The one used in this paper is:
1) For each triangle, rotate it locally to align with global Z direction; 2) Match the corresponding edges
with each other; 3) Translate each triangle to the same global plane; 4) Combine the neighboring triangles
by rotation.

86

Figure 3.20 Unfolding of a 3D circuit design
To align the 3D circuit traces with the 2D flattened mesh, mesh parameterization method is used,
here are the steps: 1) Find the position of the vertices in the 3D circuit traces in the 3D mesh using ; 2)
Calculate the Barycentric Coordinates of each vertices relative to the triangles they are in; 3) Find the
corresponding vertices of the circuit traces in the unfolded 2D mesh; 4) draw the circuit path in the 2D
mesh.
2) 2D Foldable Structure Design
The self-foldable structure we developed previously is a constraint based sandwiched structure as
shown in Fig.3.21(a), where a thermal responsive polystyrene film works as an active material, a photo
curable resin material is coated on both sides of the film; at the hinge portion, one side of the film is
coated with a resin layer functioning as the constraint layer, one side of the film is not coated. When the
structure is heated, the unconstrained side will shrink more, hence generate bending.

Figure 3.21 Foldable structure design

87

The key parameters in the sandwiched design that affects the folding angle are the length of the gap
L , the thickness of the constraint layer d , the thickness of the film h , which is fixed in this study.
To combine the circuit design, a cavity pattern is left on the body layer to leave room for the printed
circuit trace as shown in Fig. 3.21. The fabrication steps are exactly the same as mentioned in Section 3.4.
3) Direct Ink Writing of circuit design
The Direct Ink Writing device used in the study is a CNC based ink printer as shown in Fig.3.22. The
CNC kit from Zen Toolworks is a XYZ-stage, an extruder is designed and mounted on the Z-axis. The
conductive material is filled in the syringe, the material used in this study is PELCO Conductive Silver
Ink from TED PELLA, Inc, the piston is controlled with a lead-screw mechanism. G code of the designed
circuit traces will be uploaded into the TinyG controller, the controller drives all the motors of the axes to
do the required motion such as extruding the silver ink material and drawing the circuit traces on the 2D
structure we have fabricated.

Figure 3.22 CNC based ink printer

88

4) Folding the 2D circuit into a 3D circuit
Since we changed the design of the hinge, also we added silver ink trace on the back of the hinge
structure, folding tests are done to study the relationship between designed parameters ( ,, L d h ) and the
folding angle  . Based on our previous study, there are two phases of the design, when the folding angle
is smaller than 80 degree, the elastic model
2
10 3
Lh
K
d
    is used to guide the design, otherwise,
the plastic model
20 2
hL
K
d
    is used.
In the equation above,  is the folding angle,
12
, KK are the coefficients need to be calibrated, L is
the length of the gap, d is the thickness of the constraint layer, h is the thickness of the film
( 0.29 h mm  ),
00
,  are the relative angles that needs to be calibrated. Fig.3.23 shows the folded hinges,
Table 3.4 shows the collected data.

Figure 3.23 Folding Test
Table 3.4 Folding test result

89

Based on the test results, the relationship of the folding angle can be calibrated as: for angle
0
80   ,
2
0
3
5.1379 5.25
Lh
d
    , for angle
0
80   ,
0
2
0.534 68.96
hL
d
    . These calibrated equations
are based on fitted linear regression model and can be used to guide the structural design of hinges with
printed silver ink.
After the calibration of folding angles, parameters of the self-foldable design can be calculated and
used. A LED Cube is made to demonstrate the feasibility of this process. As shown in Fig.3.24, the 3D
circuit design is first transformed into a 2D layout, then conductive traces will be designed to implement
the function of the 3D circuit; after that, a 2D foldable structure is fabricated and conductive traces are
printed on the 2D foldable structure; the structure is then put into an oven, when the temperature rises
above 120 degree, it transforms into a 3D shape, LED components as well as connecting wires are
assembled afterwards, the LED can light up sequentially with a microcontroller when the wiring of the
LEDs are separated as shown in Fig. 3.25.

Figure 3.24 A LED Cube case

90

Figure 3.25 Sequential lighting of a LED Cube
The method presented in this section uses 4D printing as well as folding to achieve 3D circuit
designs, the method is fast and simple compared with other methods, especially in the design and
fabrication of customized 3D circuits, however, this method has certain limitations. One of the limitations
would be that the method proposed can only fabricate shell structures due to the nature of folding
mechanism. The method is not suitable for some solid parts with embedded circuits. Another thing is that
the assembling of the electrical components is not automatic. There does exist some automatic ways to
assemble the components to the 2D PCB boards, however, here the concerns are that some electrical
components cannot be put into the heating environment during folding, so right now it's still need certain
degree of assembly unless the printed traces can be used directly as a complete circuit, such as antenna,
charging coil etc.
3.6.3 Mesh based triangulated shape fabrication
So far we have only implemented the designs that fold along single hinge, in this section, designs
with multiple hinges in the same spot will be implemented. Most of these designs are in mesh based
triangulated shapes as shown in Fig. 3.26 and Fig.3.27. In the one ring patch design as well as two ring
patch design, the folding hinges share one single point, to make sure there is no stress concentration at
that point during folding, a small hole is drilled at that intersection point. The folding can be realized
successfully, by changing the design parameters such as the width of the hinge gap, different folding

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angles are achieved in the design. Comparison of the folded model with the design models shows that the
self-folding method is pretty accurate.

Figure 3.26 One ring patch model

Figure 3.27 Two ring patch model
Some optimization work has been done along this line to do the mesh unfolding such that any given
shapes can be self folded (Kwok, 2015). Following are some test cases we made.

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Figure 3.28 A face mesh model with optimized interior cut design

Figure 3.29 A wave shaped model. (a) The fillets in the input model make the model non-flattenable.
(b) The edges in the optimized shape are sharpened to improve its flattenability, and (c) the mask image
that only includes the sharp edges. (d) The fabricated result.

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Figure 3.30 A flower blade model
3.7 Summary
In this chapter, a bilayer self-folding mechanism that can quickly respond to thermal conditions has
been presented. A 3D-printing-based fabrication approach for building related 2D origami sheets has been

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developed. In addition to constraint layers, the developed fabrication method enables complex features
and 3D shapes to be incorporated in related self-folding structures. Heuristic models based on the folding
angle analysis have been established for designing parameter values of hinges. Accordingly a 2D origami
sheet can be designed with desired self-folding performance. A novel angle lock design is presented that
can be incorporated in a 2D origami sheet to improve its folding angle control. Various experiments have
been performed for structures with different complexity. The experimental results verify the effectiveness
of the presented design and fabrication method for building self-folding structures with controlled folding
behavior. Applications such as origami structures, 3D circuit designs, mesh based triangulated geometry
fabrication are also discussed.

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Chapter 4 Design and Fabrication of Smooth Curved Surface Using
Controlled Self-Folding
In Chapter 3, we discussed the design and fabrication method for traditional origami based structures
that fold along pre-defined hinges, and the neighboring facets of which are folded to transform planar
surfaces into three-dimensional (3D) shapes. In this chapter, we present a new self-folding design and
fabrication approach that has no folding hinges for building 3D structures with smooth curved surfaces.
This four-dimensional (4D) printing method uses a thermally responsive mechanism, where the
polystyrene film is used as the active material and the photocurable material SI 500 is used as the
constraint material on the film. When the structure is heated, the two sides of the film will shrink
differently due to the distribution of the constraint material on the film. Consequently, the structure will
deform to a 3D surface that has no folding hinges. By properly designing the coated constraint patterns,
the film can be self-folded into different shapes. The relationship between the constraint patterns and their
correspondingly self-folded surfaces has been studied. For a given 3D shell structure with smooth curved
surfaces, our 4D printing method presents a simple approach to quickly fabricate it by designing an
accordingly programmed two-dimensional (2D) structure.
4.1 Overview
In this study, we presents a method to self-fold thin shell structures with smooth curved surface using
the constrained thermal deformation, we name the folding method as "curved folding". The principle of
the method is illustrated in Fig.4.1. A bilayer structure design is used in the thermal responsive
mechanism, where a photocurable resin material (thickness ~0.1mm) is coated on the pre-strained

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polystyrene film (thickness ~0.3mm) using Mask Image Projection based StereoLithgraphy(MIP-SL)
process, where a pattern mask image is projected by a commercial projector onto one layer of liquid resin
and get it solidified. The material used in our study is called SI 500 from EnvisionTEC Inc. Normally, the
polystyrene film shrinks almost uniformly in the XY plane under homogeneous heating environment.
When the resin material is coated on one side of the film, it provides extra physical constraint to the film.
Consequently, when the bilayer structure is heated, the resin material functions as the constraint material
with small shrinking ratio, while the polystyrene film functions as the active material that can have a
maximum shrinking ratio of 45%. Different shrinking ratios in the two sides of the film generate a curved
deformation of the film towards the side that has no constraint material. A bi-directional folding can be
achieved by coating the constraint material on both sides of the film. Different constraint patterns will
lead to varying folding behaviors, and thus, different three-dimensional (3D) shapes.

Figure 4.1 An illustration of the principle for self-folding shapes with smooth curved surfaces.
An example of a flower model using the aforementioned self-folding principle is shown in Fig.4.2.
The major challenge is how to design two-dimensional (2D) constraint patterns such that the printed film
can achieve the desired self-folding behavior to fabricate 3D shapes with designed curved surfaces. To
address the problem, we have developed a design method by mapping a given 3D mesh into a set of
surface patches and generating 2D constraint patterns based on three basic folding features. A number of
experiments have been performed to identify the proper constraint patterns that can control the folding
behaviors of the film including the folding axis, curvature, and orientation. A simulation tool to predict

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the deformed 3D shape has been developed based on an established analytic model. The simulation
results have been validated by comparing them with the physical testing results that were captured by a
3D scanner. The rest of the chapter is organized as follows. Section 4.2 introduces a mapping method
based on three basic folding types and other folding parameters. Section 4.3 discusses the effect of
different constraint patterns and how to use them to achieve curved surfaces. A developed simulation is
also introduced in the section. Afterwards, Section 4.4 describes the self-folding design and fabrication
method and presents the experimental results of two test cases. Section 4.5 introduces a computational
framework we developed to generate the constraint pattern automatically. Finally a short summary is
given in Section 4.6.

Figure 4.2 A test case of a self-folding flower. (a) A double-sided coated flower model and the self-
folded object; (b) the simulation result based on a designed constraint pattern.
(a)
(b)
Front side Back side

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4.2 Mapping 3D Thin Shell Structures
4.2.1 Process Overview
The goal of our study is to develop a self-folding method that can fabricate 3D thin shell structures
with smooth curved surfaces. We focused on 3D surfaces that are smooth (i.e., C
1
-continuity over the
surface) without sharp features or high curvatures; otherwise, a hinge-based self-folding method could be
incorporated. Fig.4.3 shows the main steps of the developed design and fabrication method. For a given
3D thin shell structure, the first step is to unfold the CAD model into a 2D structure with designed
constraint patterns through feature mapping. The second step is to fabricate the 2D foldable structure
based on the designed constraint patterns. The third step is to fold the fabricated 2D structure into a 3D
structure using raised temperature as the self-folding stimuli. Afterwards, an optional step of post-
processing can be used, such as coloring, polishing, or assembling multiple 3D structures to form more
complex 3D structures.

Figure 4.3 Main steps of the process
4.2.2 Folding Types and Parameters
A given 3D curved surface can be divided into a set of surface patches based on the idea of shape
parameterization and shape matching (refer to Fig.4.4(a)), and each of the surface patches is referred as a
folding unit in our study. When the surface patch is small, it can be classified into three basic folding
types including: (1) flat, i.e., no folding, (2) one-axis, and (3) dual-axis (refer to Fig.4.4(b)). A mapping

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method was developed for a given curved surface based on this classification. In addition, three folding
parameters to define the behavior of a folding unit include folding orientation (flat, upwards, or
downwards), folding axis (i.e. the axis along which the structure folds), and folding curvature (i.e. how
much the flat surface patch folds up). They are shown in Fig.4.4(c)-4.4(e), respectively.
In our study, folding curvature (denoted as ) is defined as the ratio between the depth d (i.e., the
height of the surface patch folds up) over the width w of the folding unit. The curvature for a flat folding
unit is defined as zero. For the type of one-axis folding, the curvature is the depth-to-width ratio of the
folded curve along the direction that is perpendicular to the folding axis. For the type of dual axis folding,
two curvatures ( 
1
and 
2
) can be defined along the two folding directions. In this study, we assume the
dual-axis folding along the two folding axes is symmetrical. Hence the folding curvature of the surface
patch is simplified as the average of 
1
and 
2
.

Figure 4.4 Folding unit and the four folding parameters.
A set of codes are defined to label each surface patch according to its aforementioned folding
properties. Table 4.1 shows the codes that are used in the paper to label a surface patch. A square
represents the folding unit, and a solid line inside the square represents the folding axis. The curvature 
folding unit
(a) a grid of surface patches
(b) three basic folding types
flat
one axis dual axis
(d) folding axis
(e) folding curvature
d
w
 
d
w
dual axis
one axis
w
d
(c) folding orientation
folding curvature
upward downward flat

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is recorded inside the square, and an arrow is used to indicate whether the folding unit folds upwards or
downwards. A horizontal double-sided arrow indicates the flat ones.
Table 4.1 Illustration of folding codes for labeling folding units

The steps of mapping a 3D structure and generating codes based on the aforementioned classification
are shown in Fig.4.5. To map a 3D curved surface, the first step is to divide the given surface into a mesh
grid based on the idea of mesh parameterization. The patch size can be set according to users. Generally,
the smaller the size, the more accurate the mapping, however, the requirements of the fabrication
resolution for the constraint pattern feature size is higher. The mesh grid defines a set of small surface
patches that will be deformed into the 3D curved surface. Based on the defined codes, each surface patch
is labeled by its folding type, folding orientation, folding axis, and folding curvature. Fig.4.5(c) and
Fig.4.5(d) show the labels of the mesh grids using the codes in Table 4.1. The constructed surface patches
and the accordingly defined folding codes on them are the key elements of our self-folding structure
design method. We will discuss how to design 2D constraint patterns for each surface patch in Sections
4.3.

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Figure 4.5 Illustration of mapping a curved surface.
4.3 Folding Control Using Constraint Patterns
After coded surface patches are generated, we discuss the design and fabrication of the constraint
patterns for them in this section. The main challenge here is how to convert the folding code of each
surface patch to a constraint pattern such that the fabricated 2D structure can be self-folded as designed
when heated. As mentioned in Section 4.1, our method is based on the thermo-responsive self-folding
mechanism using a bilayer structure design. That is, a pre-strained polystyrene film serves as the active
material, and cured resin is used as the passive material that selectively constrains the shrinkage of the
film. Both the active and passive materials contribute to the structure deformation. As shown in our
previous work, heating will release the potential energy that introduced by the residual stress inside the
film during its manufacturing process and cause it to shrink to bend the 2D structure in a certain angle. In
this section, our shrinkage study of a polystyrene film is first presented, followed by a discussion of the
deformation principle and a correspondingly developed simulation. Finally the main factors that control
the self-folding behavior are discussed.
(a) designed model
(b) generated mesh grids
(c) label surface patch using the codes (d) make the grid flat
0
0
0
0
2

3

8

9

1

5

6

11

12

7

10

4

0
0
0
0
2

3

5

1

6

4

11

12


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4.3.1 Shrinkage Study of Polystyrene Film
The polystyrene film is produced by stretching under heat into a certain thickness and cooling down
rapidly to maintain its stretched shape. Consequently, the film stores a large potential energy due to
residual stress of stretching in its final shape. When the temperature is raised above its glass transition
temperature, the film will release the stored potential energy and shrink to the most stable configuration.
If the pre-stressed polystyrene film is uniformly stretched, it will shrink uniformly on the film plane under
heat. Due to the non-uniformity processing condition, the stored potential energy of film may not be
uniform. Hence the two sides of the film may shrink differently.
The polystyrene film used in our study is the inkjet shrink film (clear) purchased from Grafix (Maple
Hts, OH). Tests were first performed to calibrate its shrinkage ratio by measuring the length of both sides
of the film when it is heated to different temperatures. Fig.4.6 shows the measured lengths of both sides
of the polystyrene film, which has an original length of 20mm. When the temperature is raised up above
98
o
C, the film starts to shrink, and one side of the film (denoted as Side A, red curve) shrinks slightly
more than the other side (denoted as Side B, blue curve). The difference leads to slight bending of the
film at the temperature of 106
o
C (refer to Fig.4.6(b)). When the temperature keeps increasing, the
shrinkage of Side B catches up with that of Side A; hence the difference becomes smaller. Eventually, the
potential energy is totally released when the temperature reaches ~120
o
C, and both sides shrink similarly
to get a flat film in a smaller size (~9mm). For the temperature setting between 98
o
C and 120
o
C, each
temperature has the corresponding shrinking ratio, and the reason is that the polymer trains inside the
material is not uniform, so the the phase transition is gradually introduced with the increased temperature
until it's totally changed above 120
o
C. If the temperature increased to over 120
o
C, the film would become
soft or even be melted.

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Figure 4.6 Shrinking behavior of the polystyrene film.
In our 4D printing method, we will design 2D patterns to constrain one side of the film to control its
bending towards another side. It is desired to have small shrinkage difference between both sides of the
film such that its effect could be minimized in the pattern design. In addition, if the shrinkage of the film
is too much, the shear stress induced between the film and the coated material would be large and the
constraint material may be peeled off from the film. Consequently, the shrinkage ratio in our tests is kept
smaller than 25% by using a lower temperature. Based on the curve shown in Fig.4.6(a), the raised
temperature should be below 110
o
C. In our study, the oven temperature is set at 108
o
C, at which the
related shrinking difference in both sides is relatively small.

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4.3.2 Deformation Principle and a Simulation
Constraint patterns are designed to cause the polystyrene film to shrink differently on both sides. The
shape of the coated constraint material will determine how the fabricated 2D structure will self-fold. The
moment of inertia is one of the main parameters to evaluate how a 2D surface patch will be bent. As
shown in Fig.4.7, for a surface patch with thickness h , width b and length a , the moment of inertia I
around the X and Y axes is
3
12
x
bh
I  and
3
12
y
ah
I  , respectively.

Figure 4.7 Folding axis analysis.
As the thickness of the constraint layer ( h ) is fixed, the 2D structure tends to bend around the axis
that has a smaller I value. For example, if b << a , the surface patch will bend around the X axis. In
other words, assuming the film portions that are coated with constraint material are protected from
heating and constrained by the coated material from any shrinkage, the two sides of the film will shrink
differently. Hence the distribution of the coated material will lead to inhomogeneous deformation that
causes the film to bend around the axis that is orthogonal to the distribution of the constraint material.
A simulation based on the analyzed deformation principle can be developed to predict the deformed
3D shape of a designed 2D structure. Similar to the finite element method, we subdivide a design domain
into a set of small elements, e.g., small cells as shown in Fig.4.8(c). When the elements are sufficiently
small, the contraction and deformation can be approximated linearly. In the simulation, we assume the
side of a shrinking film without coated material will shrink to a new length
RL 
linearly from the
original length
L
as illustrated in Fig.4.8(a) with a 2D view.

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Figure 4.8 Deformation principle used in simulation and the developed simulation.
Given the shrinking ratio
R
, which can be obtained through calibration tests as shown in Fig.4.6(a),
the target shape of each element can be computed based on the configuration of allocated constraint
material. For example, when both sides of the element are constrained, this element will stay in same
shape throughout the deformation. When one side of the element is empty and another side is constrained,
it is deformed like the one shown in Fig.4.8(a). However, the target shapes are computed individually for
each element. When the target shapes of the neighbor elements are not compatible to each other, the
conflicts have to be resolved by connecting the elements together and at the same time approaching their
own target shapes. Therefore, the simulation is done by projecting a set of vertices onto the target shape
by minimizing the sum of the squared distances of the vertices to the corresponding constraint set. This
minimum is computed through shape matching, i.e. by finding the least squares fit of the constraint shape
onto the set of vertices. Let V be a vector that stacks all the vertices of the elements (V
1
,…, V
n
) and V
i V
be the vertices of the i-th element. A new function is developed for the simulation:

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(4.1)
where with being a matrix with all element equal to 1, and V
i
’
is the
projected vertices computed by the target shape. Equation (4.1) can be rewritten to a linear equation
system that can be solved by a least square solution:

(4.2)
where A is a 8m×n matrix combines all the mean-centered vertices and p integrates all projections,
and the solution of Equation (4.2) will be the vertex positions of the simulation mesh such as the one
shown in Fig.4.8(c). In other word, it is trying to maintain the rigidity of the transformation between the
target and the current shape of the elements as shown in Fig.4.8(b). The computation scheme used in our
simulation is adopted from the ones that have been used in other engineering applications [35, 36]. Based
on the developed simulation tool, an input 2D structure in Fig.4.8(c) will lead to a 3D shape as shown in
Fig.4.8(d). Hence, we can predict the behavior of a designed constraint pattern. We will discuss the
constraint patterns that can be used to achieve the four folding parameters of a surface patch in Sections
4.3.3 and 4.3.4.
4.3.3 Folding Type and Axis Control Using Constraint Patterns
Since the folding type and the axis direction are highly related, we will discuss them together. As
mentioned in Fig.4.7, a simple 2D bar (b << a ) can be used as the constraint pattern if a folding axis is
defined on the film. The direction of the constraint bar (i.e. the direction of the longer edge) should be
perpendicular to the folding axis. Similarly, a 2D cross shape can be used as the constraint pattern for a
dual-axis folding. Fig.4.9 shows the designed constraint patterns and related experimental results for both
one-axis and dual-axis folding. Five constraint patterns were tested, and the feasibility of using them to

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achieve the three basic folding types has been demonstrated. In the designs as shown in Fig.4.9, the grey
portion is the polystyrene film, and the yellow portion is the designed constraint pattern, which is printed
using the stereolithography (SL) process in our study. The black lines on the film were drawn in order to
position the film during the fabrication process.
As shown in the testing results, the folded shapes of both one-axis and dual-axis cases are close to
the desired shapes. Simulation results were also computed for the tests. The steps of the comparison
analysis are shown in Fig.4.10. The folded samples are scanned using a SLS-2 3D Scanner (David Vision
Systems GmbH, Germany) with a resolution of 0.06mm, and the scan data is compared with the
simulated data. Since the simulated model is a 3D object with certain thickness but the scanned data is a
mesh surface, only the related exterior surface of the simulated model is used in the comparison analysis.
Hausdorff distance is used to evaluate the difference of the two meshes at different data points, which is
computed using the publicly available software system - Metro (Cignoni, 1998). For the test samples with
the size of 10mm 10mm, the maximum error is around 0.8mm. That is, the maximum ratio of difference
between simulated and scanned data is around 8%. It can be noticed that the majority of the comparison
color map is in blue color, while the boundaries of the patches have large error, which may be due to
different heating conditions along the boundary.

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Figure 4.9 An illustration of the constrain patterns

Figure 4.10 Comparison analysis of the folded model vs. simulated model

109

Some additional experiments were performed to study the folding performance of the one-axis
folding type. In the tests, the single constraint bar is subdivided into two and three parallel bars by
keeping the total areas of the constraint patterns the same. Fig.4.11 shows the designed patterns and the
corresponding folding results. The blue dashed line in the figure indicates the folding axis. After the
folding, we evaluated the performance of folding by evaluating the straightness of the curve along the
folding axis, which is defined as the axial curve. Theoretically, if the sample is perfectly folded along the
axis, the axial curve is a straight line. However, due to the constraint material, the coated portion will
curve up and form a "bump". When the constraint pattern is divided into smaller parts, smaller "bumps"
will form and the overall smoothness of the structure is improved. The results show that the more
constraint bars that the 2D structure has, the better overall smoothness it can obtain. However, the
constraint pattern cannot be unlimitedly divided into smaller ones due to the fabrication limit on feature
resolution. In our study we used three bars as the 2D constraint pattern for the one-axis folding type.

Figure 4.11 Folding performance of one axis folding using different distributions of materials.
4.3.4 Folding Curvature and Orientation Control Using Constraint Patterns
Another important parameter to control the folding of a surface patch is the folding curvature. The
factors that may affect the curvature of a surface patch include the shape of the constraint pattern, the

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property of constraint material, the thickness of the constraint layer, and the temperature used in self-
folding. This paper fixes all the factors except the shape of the constraint pattern to study the relationship
between the folding curvature and the pattern shape. The effects of other factors will be explored in our
future work.
In a folding unit, a constraint pattern for a surface patch can have a wide variety of designs including
its shape, position, and scale. We limited the pattern designs in our study and chose two patterns for the
one-axis and dual-axis folding, respectively. As shown in Fig.4.12, a parallel bar pattern is used for the
one-axis folding, and a cross shape pattern is used for the dual-axis folding. Fig.12 also shows the pattern
size and position that are considered in our study. The edge length of a unit surface patch is denoted as L .
The control parameter in these designs is the width of the constraint bar, that is,
1
l in Fig.4.12(a) and
2
l in
Fig.4.12(b). We experimentally studied how to set the design parameters to achieve the desired folding
curvatures.

Figure 4.12 Two examples of constraint patterns for two base types.

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Figure 4.13 Curvature control with parallel bar pattern.
A set of designed tests were performed to calibrate the relationship between
1
l ,
2
l and their
corresponding curvatures. The fabricated samples and the folded results are shown in Fig.4.13 and
Fig.4.14. Similar to Fig.4.10, the comparison analysis of the experimented and simulated results were
performed. In addition, the values of the depth and width ( , ) dw as discussed in Section 4.2.2 were
measured on the folded test samples using a caliper. Table 4.2 shows the measurement results. In the tests,
the size of each surface patch is 10mm × 10mm. Fig.4.15 shows the plotted curve based on the data in
Table 4.2. The experimental results illustrate that the constraint patterns for both one-axis and dual-axis
folding types can be used to control the folding curvatures of the polystyrene film. Increasing the
parameter
1
l and
2
l will increase the curvatures of the corresponding surface patch. In addition, for a

112

polystyrene film without any constraint material (i.e. the cases when
1
l and
2
l equals zero), the curvature
is very small compared to the ones with constraint layers. Hence it can be regarded as the flat folding type.

Figure 4.14 Curvature control with cross shape pattern.
The relationship between the folding curvature and the parameters of the constraint pattern can be
used in designing the required constraint patterns for a given 3D shell structure. For example, for a folded
3D structure with a specific curvature value, we can determine the parameters
1
l (or
2
l ) by the curves in
Fig.4.15. When there is no exact point for a given value, the parameter is approximated by the linear
interpolation between two neighboring data points.

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Table 4.2 Results of the folding curvature and bar width from Fig.4.13 and Fig.4.14

Figure 4.15 Curvature control curves.
From the measured data, the curvature is ranging from 0.044 to 0.313. Using our method, it would be
difficult to fabricate sharp features that have large curvatures unless the folding units of the related
features are further subdivided into smaller surface patches. However, using small surface patches will

114

require a fabrication process that has an even higher feature resolution. The SL process used in our study
enables the smallest feature size of the constraint pattern to be 0.5-1mm.
Finally, the last folding parameter of a folding unit is the folding orientation. The constraint material
can be coated on either side of the film. When the constraint pattern is coated on one side of the film, the
film will bend towards the other side when heated. Hence, the folding orientation can be easily controlled
by coating the resin on the appropriate side of the film.
4.4 Constraint Pattern Design and Fabrication
As discussed in Section 4.3, a 2D film with varying constraint pattern designs can have different
folding performances that are defined by four folding parameters on surface patches. Our 4D printing
approach approximates each surface patch by a smooth surface patch represented by its curvature.
Accordingly, the design process to generate the constraint patterns based on the coded surface patches is
shown in Fig.4.16. The first step is to calculate the curvatures of each surface patch. A number of points
are sampled along the boundary and the center of each surface patch to measure its width and depth in
different directions. The direction that has the minimum curvature variation along the sampling direction
is selected as the folding axis. If the curvature variation in the orthogonal direction is large (i.e., >0.044 in
the test), the additional direction will be selected as the second folding axis, and the dual-axis pattern will
be used for the surface patch. To achieve the measured curvature of each surface patch, the curves shown
in Fig.4.15 are used to determine the parameters
1
l and
2
l . Accordingly, the constraint patterns can be
designed based on the two patterns that are used for the one-axis and dual-axis folding types (refer to
Fig.4.12). Finally, a mask image is generated for coating the constraint material on the polystyrene film
that is cut with the unfolded 2D shape.

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Figure 4.16 The constraint pattern design process.
Fig.4.17 shows the fabrication system that was used in our study to print the photocurable resin on
the polystyrene film. The fabrication process is based on an additive manufacturing process named mask-
image-projection-based stereolithography (MIP-SL). During the fabrication process, a mask image is
projected by a digital micromirror device (DMD) onto the printing chamber. The polystyrene film is
positioned on the bottom of the chamber, and a layer of liquid resin is spread on top of the polystyrene

116

film. After that, a transparent cover coated with PDMS film is used to form a thin layer, and the layer
thickness is controlled by the selected spacers. When the resin is exposed to the projected mask image,
the material gets solidified to form the constraint pattern on the polystyrene film. The resin used in our
study is SI500 resin from EnvisionTEC Inc. (Dearborn, MI).

Figure 4.17 A fabrication system based on MIP-SL.
Fig.4.18 shows the fabricated film with the designed pattern using the MIP-SL process. After
positioning the fabricated film inside an oven that is pre-heated to 108
o
C, the structure is self-folded to its
3D shape as shown in Fig.4.18. The self-folded curved surface was captured using the SLS-2 3D scanner
and compared with the designed CAD model. The color map of Hausdorff Distance shows that the shapes
of the designed and folded models are close to each other. In addition, the folded 3D structure has the
desired curve surface that is smooth. The self-folded curved surface has no folding hinges, or stair-
stepping effect that is typical in layer-based AM processes. The fabricated 3D structure can be used as a
tool to transfer the shape of the curved surface into other materials such as silicone rubber. In addition, the
folding process takes less than 10 seconds, which is much shorter than the fabrication time that is required
for building the 3D structure using a 3D printer such as SL or fused deposition modeling (FDM).

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An additional test case based on “USC” letters is shown in Fig.4.19. The one-axis folding pattern
design was used in the test. Compared with the layer-based 3D printing of these 3D structures, our
method does not require using additional support structures. The fabrication time is also largely reduced.
Based on the experimental results, the feasibility of using the developed 4D printing process to build 3D
thin-shell structures with smooth curved surfaces has been verified.

Figure 4.18 A test case of a bowl.

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Figure 4.19 A test case of “USC” letters.
4.5 Computational framework of the constraint pattern design
A computational framework is developed to generate the constraint pattern for the designs
automatically. There are two major steps involved, the first step is to unfold the 3D shape into a 2D mesh,
the second step is to generate constraint patterns on the 2D mesh based on mesh parameterization.
4.5.1 Unfolding of a 3D Mesh
To obtain the folding pattern, a given 3D triangle mesh is first unfolded into a 2D plane. Since we
are focusing on simple 3D curved features, we can assume that the given 3D triangle mesh can be flatten
into 2D without a cut. Then the 2D mesh is calculated as follows:
1) Local rotation of each triangle.
For a triangle (v1, v2, v3), its rotation axis is first calculated, around which the triangle can rotate to
be parallel to the X-Y plane of the coordinate system. Assume v2 has a Z height less than v1 but bigger
than v3, then the rotation axis must pass through v2 and is the intersection line of the triangle and the

119

horizontal plane. The rotation angle is the angle between the z axis and its normal, its sign is determined
by the dot product of the rotation axis vector and cross product vector of z axis (positive direction) and
triangle normal. When the dot product is positive, the rotation angle is positive, otherwise negative. After
that, the rotation matrix can be established based on the rotation axis and angle.
2) Corresponding edge matching.
Each triangle is stored separately and the common edge between two neighboring triangles needs to
be identified after the local rotation in the step 1. For two neighboring triangles, each vertex in one
triangle is compared to all the vertices in the other one, and the indexes of the corresponding vertices in
two triangles are recorded.
3) Translation to the reference plane.
For two neighboring triangles t1 and t2, t1 is fixed and t2 is translated to t1, coinciding at the starting
point of their common edge. The same will be done on all the neighboring triangles of t1.
4) Combine neighboring triangles by rotation.
For the two neighboring triangles t1 and t2, t2 will be rotated further around the coinciding point
between them. The rotation axis is unit vector (0,0,1) and rotation angle is the angle between the
identified common edges in step 2. After the rotation, the alignment between t1 and t2 is finished, and
triangle t2 will be labeled as “done”. All the neighboring triangles of t1 will be rotated to align with t1.
A unfolded "CS" letter test case is shown in Fig.4.20.

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Figure 4.20 A unfolding "CS" letter test case
4.5.2 Mesh Parameterization &Constraint Pattern Generation
After unfolding of a given 3D mesh, A mesh parameterization routine is done to get square mesh and
then calculate the curvature of each patch unit, based on the curvature, draw the constraint pattern in the
2D mesh. Later, the 2D pattern can be projected to coat photocurable materials on the Shrinking film.
The detailed steps are as follows:
1) Use a 2D grid to contain the flattened mesh;

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2) Calculate the Barycentric coordinates of the grid points according to their positions in the triangle
mesh. Judge each grid point to see whether they are inside, on or outside of the mesh.
3) For the grid points inside or on the mesh, use the Barycentric coordinates to calculate their 3D
coordinates with the coordinates of the points in original 3D mesh.
4) Draw the square mesh in 3D and display;
The square mesh of the "CS" letter case is shown below in Fig.4.21.

Figure 4.21 Square mesh of the "CS" letter case

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5) Calculate the curvature of each grid cell;
The curvature is calculated in using a custom-defined curvature as shown in Fig.4.22.

Figure 4.22 A custom-defined curvature calculation diagram
To calculate the curvature of a single square unit, five points are needed as shown In Fig.4.22, the
Center point C, the middle points on each edge M,N,P,Q. To calculate the folding curvature along one
axis, for example, folding along Y-axis, use the triangle CMN, define the curvature as the distance
between C and MN divided by the length of MN. Similarly, the folding curvature along X-axis is the
distance between C and PQ divided by the length of PQ.
6) Draw the constraint pattern based on the calculated curvature
By changing the width of the constraint bars, different curvature could be get, this is proven through
experiment. Shown below in Fig.4.23 is the generated constraint patterns for the "CS" letter test cases.
For "C", curvature variation could be seen obviously through the constraint pattern; For "S", there are two
sets of images since "S" has a dual orientation folding.

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Figure 4.23 Generated constraint patterns for "CS" case
4. 6 Summary
In this chapter, we present a new 4D printing approach to fabricate 3D thin shell structures with
smooth curved surfaces. To control the self-folding process based on a thermo-responsive mechanism, a
curved surface is divided into a set of small surface patches as individual folding units. Each folding unit
is classified into three basic folding types: the flat patches, the one-axis folding patches, and the dual-axis
folding patches. Three additional parameters are then presented including folding axis, curvature, and
orientation. The effects of these four parameters and the accordingly developed controlling methods have
been presented. In addition, a simulation tool has been developed to predict the deformation of given
constraint patterns. A computational framework is introduced to generate the constraint pattern
automatically. The comparison between the simulated and fabricated shapes shows good agreement.

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Several test cases have been presented to demonstrate the effectiveness of the developed 4D printing
method.
There are several limitations in the presented design and fabrication method. Firstly, the degree of
bending is determined by the shrinkage of the polystyrene film. Due to the limit on the shrinkage ratio of
the polystyrene film, our method cannot be used to fabricate shapes with high curvature. Secondly, the
thickness of the constraint layer needs to be well controlled. If the constraint layer is too thick, the surface
patch will be too stiff that limits its bending; however, if the constraint layer is too thin, the constraint
provided to the film is not strong enough to constrain its shrinkage. A proper thickness of the constraint
layer based on the selected film is between 0.1-0.2mm. A concept of digital material may be used to
address the limitations, that is, pixelized constraint materials can be distributed on the polystyrene film.
By using different composition of rigid and soft materials, the printed constraint patterns may have certain
flexibility to enable the polystyrene film to have a larger folding curvature range and a wider layer
thickness. Finally, the approach we used to map the 3D shape is based on local shapes of each patch, it's
an approximation method for design purpose, with the simulation developed, we do have the capability to
calculate the global shape, we can further study the pixelized constraint material as well, which is
impossible by using localized shape mapping.

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Chapter 5 Sequential Folding Structures By Silver Ink Printed
Polystyrene Film
In Chapter 3 and Chapter 4, we introduced the process to fabricate self-folding structures based on
projection based Stereolithography, the process is simple and the structures fabricated can fold in a well
controlled manner, however, it's not that easy to realize sequential folding. As we've discussed before,
sequential folding can add more functionality to the structures as well as more design freedom. In this
chapter, we will present a new way to fabricate self-folding structures using polystyrene film by printing
conductive silver ink on top of the polystyrene film using Direct Ink Writing (DIW) process. The
polystyrene film shrinks almost uniformly along XY plane when the temperature rises above its glass
transition point under uniform heating condition, silver ink traces printed on one side of the film can
provide local joule heat by conducting current in order to modify the shrinking behavior of the film along
thickness, thus achieving folding performance. Parameters affecting the folding process are identified, they
are the current, the unit resistance of the ink as well as the time. Sequential folding could be achieved by
using printed ink traces of various width as well as decoupled circuit designs. Theoretical analysis are done
to guide the design of the folding process. Programmable structures are achieved to test the feasibility and
potential application of this method.
5.1 Folding behavior of the polystyrene film activated by current.
The process developed in this chapter is really simple, first step is to print the conductive ink traces on
the polystyrene film, the second step is to fold it by conducting current. As shown in Fig.5.1(a) and
Fig.5.1(b), a cube model is folded with printed triggering circuit when current is applied. The folding
behavior of the polystyrene film under current is critical for this process. We will introduce this in detail.

126

As we've already known the polystyrene film is pre-strained due to the stretching and rapid cooling in
the manufacturing process, when the temperature rises above its glass transition temperature, the material
will return to its most stable state and the film shrinks along XY plane and expands in thickness. The
shrinking ratio of the film is directly determined by the temperature. Fig. 5.2(a). shows the shrinking ratio
of the film along with the temperature. The film will start to shrink at around 102
o
C, the glass transition
temperature of the film, then the shrinking ratio will continue to increase until the temperature reaches
around 120
o
C, where the material starts to become soft and the shrinking ratio becomes stable; the physical
sample is shown in Fig. 5.2(b), when the temperature rises, the sample will first shrink, then becomes
stable, when the temperature goes above 120
o
C, the film reaches its max shrinking capability and will
become soft, the thickness of the film is increased. For a certain temperature between 102
o
C and 120
o
C, the
shrinking ratio is fixed, the reason is that to enable the film to shrink, energy is needed to trigger the phase
transition, however, the heat transfer between the heating environment and the film will always becomes
stable with certain fixed temperature setting so that the energy absorbed by the film is fixed in that
temperature. Once the energy is large enough for the entire film to go through phase transition, the film
becomes soft.
Printed silver ink provides heat source to the film, the heat conduction causes a shrinking ratio
difference along thickness in the film. By adjusting the current given to the silver ink trace, different source
temperatures could be achieved, thus generating different folding angles as shown in Fig.5.2(c). Heat
conduction is really important in deciding the folding process, some of the governing equations regarding
the thermal analysis is shown below. With the model shown in Fig.5.1(c) and Fig.5.1(d), the heat
conduction problem can be regarded semi-infinite surface heat conduction. The assumptions we made in
the analysis are that the temperature field is same along Y-axis, and the surface diffusivity can be ignored
since it's much smaller than the heat conduction through Z-axis, the thickness direction. Eq.(5.1) is the
thermal conduction differential equation for the semi-infinite surface heat conduction, where T is the
temperature field, t is the time, a is the thermal diffusivity of the film,
2a
b
ch 

is the heat diffusion

127

coefficient, c is the specific heat capacity of the material,  is the density, h is the thickness of the film.
Since the surface diffusivity can be ignored, the term bT  can be removed, Eq.(5.1) becomes Eq.(5.2). By
solving the equation, we have the temperature distribution function as shown in Eq.(5.3), in the equation,
0
Q is the joule heat generated by the circuit,  is the thermal conductivity of the film, L is the length of the
silver trace, r is the distance between the target point and the heating source
22
r x z  .

Figure 5.1 Principle of the self-folding structure. (a) A cube model. (b) A folded cube by conducting
current (c) Modeling of the folding structure. (d) Design parameters of the self-folding structure. (e)
Thermal models.

22
22
()
T T T
a bT
t x z
  
  
  

(5.1)

128

Here two models could be used regarding the heating source, the single point model and the multi-
point model. In the single point model, the heating source is regarded as a concentrated single point.
Eq.(5.3) is the expression of the temperature field under single point model. In multi-point model, however,
the ink trace is regarded as several heating points, the heat is divided uniformly along the width of the ink
trace, so
0 s
Q n Q  , where
s
Q is the divided heat regarding the n heating sources, so in the multi-point
model, the temperature for a certain location becomes the sum of each heating sources, expressed in Eq.
(5.4), where
1
...
n
rr is the distance between the target location and the corresponding heating sources,
denoted as * r in Fig. 1d. The isothermals could be drawn based on Eq.(5.4) as shown in Fig.5.1(d), from
which we can see the locations with the similar temperature. The multi-point model is more general than
the single point model, for simplicity, we will use single point model to guide the design of our experiment.
Since joule heat
2
0
Q I R t  , by plugging in this in the Eq.(5.3), we have Eq.(5.5).
We can get the max temperature in the single point model as
2
max
4
IR
T
L 
 , in order for the folding to
happen, max temperature should be bigger than the glass transition temperature, so
max
102
o
g
T T C  ,
We can also get the temperature of the bottom surface location ( 0, x z h  ) for a certain amount of time

22
22
()
T T T
a
t x z
  

  

(5.2)

2
0
exp( )
44
Q r
T
Lt at 

(5.3)
2 22
12
1
( ) exp( ) exp( ) ... exp( )
4 4 4 4
n
sn
i
i
Qr rr
T T r
Lt at at at 


       




(5.4)

22
exp( )
44
I R r
T
L at 

(5.5)

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*
t ,
22
*
exp( )
44
yield
I R h
T
L at 
 , according to the thermal model we derived, this location is the point that
has the highest temperature on the bottom side; in order for the folded shape to hold the shape, this
temperature should be smaller than soften temperature 120
o
C, so we have 120
o
yield soft
T T C  . The
max
T
and
yield
T can be used to guide the setting of current I . So far we already know that the shrinking ratio of
the film s is determined by the temperature () s f T  , also, the folding angle  is determined by the
shrinking ratio of the structure () gs   , so folding angle  is determined by the factors that affecting the
temperature, which is ( , , , I R L t ), the current I , the unit resistance / RL , and the time t .
A set of tests are done to study the relationship between the folding angle and the current, as well as
unit resistance, the samples are of the same size 10mm. Fig.5.2(c). shows the folding angle curves for
various samples with different resistance. In this test, the time can be regarded as a fixed very long time,
we wait for long enough till the folding angle becomes stable. From the curve, we can see that with higher
resistance, the structure folds at a lower current, and folds faster. The folding angle will reach a maximum
value and then, with the increasing of current, the angle will bounce back a little. This is because the heat
conduction has cause the bottom side of the film to shrink as well, when the bottom side shrinks more than
the top side, the folding angle will start to bounce back, it will reach a stable folding angle at certain
current value, this is when the bottom side and the top side stops shrinking. The bouncing back is less
obvious with smaller resistance, the reason is that for a smaller resistance, the printed ink trace is always
thick and wide, which makes the heat conduction to the bottom side easier so that the bottom/top difference
is smaller. The folding angle is smaller as well.

130

Figure 5.2 Folding behavior of the self-folding structure. (a) Shrinking ratio curve. (b) Shrinking of
the film. (c) Folding angle vs. current. (d) Folding angle test.
5.2 Printing parameters optimization
The printing platform is shown in Fig.5.3(a). It's a CNC stage with XYZ axis control. A printing head
is designed and mounted on the Z axis. Another motor is added to drive the extrusion of the printing head.
Syringe is used to load the printing material. The physical set up can be found in Fig.3.22.

131

Figure 5.3 Printing platform (a) XYZ stage (b) Printing head (c) Printed Traces with varied width (d)
Resistance as well as temperature of different traces.
There are several parameters during the printing can be used to optimize the printing quality, they are
the nozzle size, printing speed, extrusion speed, the distance between nozzle and printing surface (referred
as nozzle height). By changing the printing parameters, printing traces with different width as well as
resistance can be achieved as shown in Fig.5.3(c). With printed traces in different resistance, if we pass the
same current to the circuit, the temperatures of the traces will be different due to the different amount of
heat generated. Blue curve in Fig.5.3(d) shows the temperature of the printed traces when we apply a DC
current of 0.8A. Generally, the trace with higher resistance will have higher temperature and vice versa.
The nozzle size needs to be selected carefully because if it's too small, the extrusion is not smooth or even
cannot extrude material due to high pressure drop inside the nozzle such as the one shown in Fig.5.4(a)

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with nozzle size of 160 micron, it's almost impossible to extrude the material out; if it's too big, the printed
trace is big so extrusion resolution is not good enough. In our experiment, we used 279 micron inner
diameter nozzle, the best printing resolution can achieve 350-500 micron as shown in Fig.5.4(a). The ink
material used in this study is PELCO Conductive Silver Paint, the material has good conductivity as well
as mechanical strength.

Figure 5.4 Printed traces. (a) Nozzle size study. (b) Printing speed study.
The printing speed and extrusion speed, nozzle height affect the printed trace width and trace
thickness, hence affecting the resistance of the trace. One of the properties of the conductive traces that
need to be controlled well is resistance per unit length. Fig.5.5 shows a model of the syringe extruder for
analysis of the extrusion.

133

Figure 5.5 Extruder model.
When the extruder starts to print material, the ink is pushed out by the syringe through the nozzle,
there is compression of the material inside the syringe, Denote the volume decreased inside the syringe in
the amount of time t  as V  , we have:
Also, assume the printed trace has uniform width and thickness, volume extruded out of the nozzle is:
Denote the density of the ink material inside the syringe as
1
 , the density of the ink material out of
the nozzle as
2
 , we have:
From Eq.(5.6)~Eq.(5.8), we have:

2
1
1
4
V V t 

    

(5.6)

3
' V V w d t      

(5.7)

12
' VV    

(5.8)

3 2
2
1 1 1
14 V
w d V


  


(5.9)

134

To calculate the resistance over length, based on the resistance equation:
We have:
 is the resistivity of the ink material.
From Eq.(5.11), we can see the resistance per unit length of the printed trace is positively relevant
with the feed rate of
3
1
V
V
because we know the density ratio of the ink material
2
1


is changing due to
pressure change within the syringe. A validation experiment is done to study the relationship between
resistance per unit length and the feed rate, the result in shown in Fig.5.4(b). A positive relevant, nearly
linear relationship can be identified from the plot.
To study the effect of nozzle height, different nozzle heights are tested during the printing. The
general understanding is that nozzle height should be selected properly, if it's too small, the ink material
will be squeezed during the printing such that the width of the printing is too big as shown in Fig.5.6. If the
nozzle height is too large, the extruded material will grow and accumulate on the nozzle tip first, until it
becomes big enough to tough and land on the printing surface, the resulting printed trace is irregular, not
uniform. In this study, we set the nozzle height around 220 micron. One thing to notice is that the nozzle
height will not affect the unit resistance since the material extruded out is always the same amount and the
nozzle height will affect the thickness of the trace, however, with larger width of the trace, the thickness is
decreased, so the overall intersection area of the printed trace remains the same, thus the resistance is the
same.
L
R
wd
 


(5.10)

3 2
2
1 1 1
14 V R
L w d V



     


(5.11)

135

Figure 5.6 Printed trace width vs. Nozzle height.
5.3 Sequential folding using single circuit loop
Sequential folding designs can be made from this method of current induced folding. Two different
approaches are studied in this paper, the first approach is folding using ink trace in various unit resistance
in a single circuit loop, the second approach is folding using multiple circuits with uniform ink traces. Here
we will discuss the first approach.
As shown in Fig. 5.7(a), ink traces with varied unit resistance can be achieved by adjusting printing
parameters such as printing speed, nozzle height and material feed rate. Based on the observations we have,
it's easy to see that with the same current amplitude in a single circuit, the edges with larger unit resistance
will reach the glass transition point faster than the ones with lower unit resistance and start to fold first. In
the designed sample shown in Fig.5.7(a), the length of each edge is 18mm, the resistances for three varied
ink traces are 1.7Ω, 1.0Ω and 0.6Ω, the trigger current for each edge to fold is tested as 0.82A, 1.11A,
1.40A. By adjusting the current to different ranges, sequential folding of the design is realized. This is the
principle used in the first approach. As we discussed before, there is a bouncing back effect which will stop
the structure from holding its shape, so there is a scenario that when the following edges start to fold, the
previously folded edge will continue to fold and when the current raises above it bouncing back point, the
structure will start to bounce back, which is not what we need in the design. So a structural design

136

combining angle locks and constraint layer is used to address this problem, which will be discussed in
Section 5.3.1 and 5.3.2; the combined design is shown in Fig.5.7(b), for varied edges with same length, one
of which is with a resistance of 1.1Ω, the other is 0.5Ω. When the current provided increases to around
1.0A, the 1.1Ω hinge will start to fold first, when it reaches around 90
o
, the folding stops due to the
blocking effect of angle locks (the yellow pieces on each side of the hinge); then continue to increase the
current to a value around 1.5A, the 0.5 Ω edges will start to fold and finally form a box.

Figure 5.7 Sequential folding in a single circuit loop. (a) Circuit traces in various unit resistances (b)
Two-step folding of a box model
5.3.1 Angle lock design
There are two design features that could be used to change the folding angle, the angle locks and the
constraint layer. Shown in Fig.5.8(a), angle lock design is composed of two blocking structures that
aligned with the ink trace, the angle block is made of photocurable resins, added to the structure through
projection based stereolithograpy; when the hinge folds, the two blocks will contact and stop the structure
from folding further, the angle lock design could be used to constrain the maximum folding angle allowed
for a certain parameter setting. Parameters that affect the blocking angle are shown in Fig.5.8(c), they are

137

the height of the blocks D , the width of the gap
1
L between them and the distance of the outer edge
2
L and
the thickness of the polystyrene film h . The folding angle can be formulated as Eq.(5.12), where K and b
are linear coefficients that needs to be fitted.
The model is more suitable for designs with larger block gap
1
L because when the two blocks are too
close to the printed ink, they will squeeze the ink traces during the folding when the film starts to shrink as
shown in Fig.5.8(b), the behavior of the folding is more difficult to predict due to the squeezing effect. For
larger gap value
1
L , there is no squeezing effect, thus the folding behavior is more predictable; Fig.3d gives
a linear fitting of the formulated function, it shows a very good correspondence with the model. Using
Eq.(5.12), we can define the maximum folding angle for a certain hinge design. However, the current
added to the structure should be smaller than the value that will cause bouncing back effect.

Figure 5.8 Self-folding structure with angle lock design. (a) Angle lock effect. (b) Angle lock test. (c)
Design parameters of angle lock. (d) Modeling of the angle lock design.

12
180
2( )
LL
Kb
Dh



   


(5.12)

138

5.3.2 Constraint layer design
Constraint layer design could be used to make the folding stabilized within a range of given current,
which helps the folding angle lock design to work well. Fig.5.9(b) shows the design with constraint layer,
where a very thin layer of material is coated at the bottom side of the hinge using the projection based
stereolithography process, underneath the portion where we printed silver ink trace. The constraint layer
gives a physical constraint to the structure, decreases the shrinking ratio of the bottom side such that the
bouncing back effect can be decreased. However, since the constraint layer adds the strength to the hinge
portion, the folding angle will become smaller than the designs with no constraint layer as shown in
Fig.5.9(a). The relationship between folding angle and the current can be studied, Fig.5.9(d) shows the
result. The unit resistance of the four samples are quite similar, the samples with constraint layer coated
shows a slower slope of growing, where at certain point, it is stabilized, then it will start to bounce back
when the current is too high. For the samples with no constraint layer, the stabilized stage is really short,
and then the structure will start to bounce back. In general, constraint layer will make the folding curve
"flatter" and enlarges the stabilized stage such that we can adjust different current within the corresponding
range, however the folding angle remains the same. For example, for the sample shown in red curve with
constraint, we can set the current from 1.6A to 1.9A, the folding angle will be always around 50
o
. This
feature is really useful in designing sequential folding structures, which will be discussed in detail in the
following section. We define the zone that gets shrink as affected zone, from Fig.5.9(c), the affected zone
for the samples with constraint layer is much smaller than the ones with no constraint, which verifies that
the constraint layer does provide physical constraint to the film that stops it from shrinking.

139

Figure 5.9 Self-folding structure with Constraint layer. (a) Constraint layer effect. (b) Sample with
constraint layer. (c) Affected zone of samples. (d) Folding angle curve with and without constraint layer.
5.4 Sequential folding using decoupled multiple circuit
The second approach is more straightforward by using multiple circuits to trigger the folding in
different sequence, Fig.5.10 shows a structure that locks itself using sequential folding. There are three
folding hinges in the structure, at two sides are two features designed for the locking, A small piece
material on the left side of the structure is the "lock", where the piece with an opening on the right side is
the "handle", in the folding process, the piece that has the "lock" feature will fold first, then the piece on
the right with the "handle" feature folds secondly to enable the "lock" go into the "handle", finally the
"lock" piece will fold and lock the structure by itself. This type of structure cannot be made using other
approaches other than sequential folding because careful calculation is needed in order for the "lock" to go
into the "handle" precisely.

140

Figure 5.10 A sequentially folded self lock structure (a) model of the folding sequence (b) physical
test case of the design
Two other cases are fabricated using the same approach, as shown in Fig. 5.11. Fig. 5.11(a) shows a
demo case with an "inverted F" antenna as well as "USC" lettered circuit boards. The structure is
composed of two categories of circuits, one of them are the functional circuits that provides functionality
such as the "inverted F" antenna portion in the design Fig.5.11(a), the other are folding circuits, the circuits
that are added specifically for self-folding purposes. the folding circuits can be printed either on the same
side of the functional circuits, or on the other side to minimize interference, it depends on the application.
Self-folded circuit designs have great potential in application such as 3D antenna, robotics and wearable
devices. For the 3D antenna, since most of the devices right now are using 2D circuit boards, and antenna
takes a lot of space in that piece of circuit boards, which makes our products such as cell phones bigger and
bigger if we want to add more functionalities to the circuit board; while with 3D antenna or 3D circuit
designs, the product could be more compact and small, which is more convenient for daily use. Self-
folding circuits also make it easier for the transportation of the designed structures, because they can
remain in 2D during transportation and can turn into 3D when reaching the location of installation.

141

Figure 5.11 Self-folding origami structures. (a) An "inverted F" antenna demo case. (b) Origami
crane model using multiple circuits folding.
Fig. 5.11(b) shows an origami crane model made using the method proposed, the structure uses
multiple circuit designs as mentioned before so that complex shapes can be achieved with steps of simple
folding. The folding current for each hinge can be calibrated using the folding angle curve with current
once we know the unit resistance of the ink trace on each folding hinge.
As we might have noticed that for simple circuit folding such as the one shown in Fig.5.11(a), the
design is relatively simple, however, for the designs with multiple circuits, as shown in Fig.5.11(b), there
would be a lot of connection pins, so the design of the circuit layout needs to be studied to make the design
more suitable for standard pin connection with controller.
5.4.1 Decoupled circuit design through circuit "jump"
To make the connection between the self-folding structure and the controller easier, circuit design
layout should be studied to make the design neat and clean. Several designs have been tried to realize the

142

design of multiple hinge folding in one structure. Shown in Fig.5.12 are some of the structures we tried in
this study. To realize folding along multiple hinges in one structure, the circuit has to be designed in a way
that each hinge can fold successfully. Fig.5.12(a) shows a hand model with parallel connection of the
circuit hinge. It turns out that the difference of the resistance between the hinge portion and the other
portion is not big enough and the first hinge will always short the other hinges and fold, the other hinges
will not fold. Hand model in Fig.5.12(b) uses a serial connection of each hinge circuit such that there is
always current passing through the hinge portion, so the hinges in the structure will all fold, however,
another issue arises that since the circuit traces will all generate heat, the portion with denser circuit lines
will accumulate more heat than the others so that it will cause the polystyrene film to deform and generate
some distortion. Fig.5.12(c) is a design with circuits separated, we call it decoupled circuit design, the
circuits will share one edge, while the others are separated, the way they are separated will affect the
folding, in the case of Fig.5.12(c), the portion of the film that has paralleled circuit traces will not fold for
the bottom most hinge since there is too much material left on the hinge portion that will provide too much
constraint that stops the hinge from folding, the outmost hinge, will fold well. To solve the constraint
problem introduced by extra material, we came up with two other designs as shown in Fig.5.12(d) and
Fig.5.12(e). The one in Fig.5.12(d) uses a sharp corner at the hinge portion, trying to decrease the amount
of extra material on that hinge, however, it turns out to be not good because there is heat generated at that
corner that will cause the film to shrink and melt. Also, this structure is not easy to extend to more hinges
because in that way the corner has to become larger and larger. The other one shown in Fig.5.12(e) solves
our problem by using a jump mechanism, the two circuits are decoupled in a way that the outmost circuit
will pass across the bottom most circuit by using pin holes and conductive ink connections from the back.
This design can be used for more hinges. One issue is that the folding sequence of the design has to be
from outmost to the bottommost, because we do not want to damage the outmost circuit when we fold the
bottom most first, however it works just well in the reversed order because we do not care about the
damage to the hinge circuits after they are folded already.

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Figure 5.12 Circuit design layouts for multiple hinge structures (a) A parallel circuit design (b) A
serial connection circuit design (c) decoupled circuit design in parallel layout (d) sharp corner decoupled
circuit design (e) decoupled circuit "jump" design.
5.4.2 Updated angle lock design.
Now that we have already figured out how to design structures with multiple hinges, the next thing is
how to control the folding angle for the folding of each hinge. In section 5.3.1 we used angle lock design to
realize the angle control, however the controlled angle range is limited. here, we use the same idea and
update the angle lock design to be more suitable for both smaller angles as well as larger angles. The angle
lock design is shown in Fig.5.13.

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Figure 5.13 Angle lock design and its variation for angle control. (a) Angle lock design (b) Angle
lock design variations (c) Illustration of the relationship between folding angle and the design parameters
The angle lock design has two pieces of blocks (we denote them as first block (in blue color) and
second block(in yellow color) in the followed analysis) that will contact with each other during folding to
constrain the maximum folding angle allowed as shown in Fig.5.13(a). Design parameters can be adjusted
to achieve different folding angles as shown in Fig.5.13(b), in the first design, a block feature is added by
add some extra material on the first block so that the other block can contact with this block in a smaller
angle with the range of 0
o
to 45
o
. The relationship between the extended length s and the folding angle 
can be seen in Fig.5.13(c) part 1; in the second design, the height of the second block is adjustable, by

145

decreasing the length of the height, larger folding angles could be achieved between 45
o
to 90
o
, the
relationship between the height of the second block and the folding angle can be seen in Fig.5.13(c) part 2;
in the third design, we add a gap between the first block and the folding axis, by adjusting different
distance of the gap, various folding angles ranging from 45
o
to 135
o
degree can be achieved, the
relationship between the distance of the gap and the folding angle could be seen in Fig.5.13(c) part 3. For
angles larger than 135
o
, we will not use angle lock anymore because the folding angle cannot achieve that
large without bouncing back. The idea of using angle lock is to constrain the folding angle before its
bouncing back.
The tested results are shown in Fig.5.14. The experimental results aligns really well with the
theoretical angles with a max error around 5%.

Figure 5.14 Calibration of the folded angle controlled by angle lock (a) Angles ranging from 0
o
to
45
o
(b) Angels ranging from 45
o
to 90
o
(c) Angles ranging from 45
o
to 135
o
. (d) Samples from 0
o
to 45
o
(e)
Sample from 45
o
to 90
o
(f) Samples from 45
o
to 135
o

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5.5 A twp-phase 3D antenna case design
A two-phase 3D antenna design is implemented using the sequential folding method developed in this
study as shown in Fig.5.15. The antenna is in a 2D layout during transportation to be more compact,
however, when it arrives at its service location, it will be folded into 3D layout to enhance the signal
transmission. The designed 3D antenna has two phases; in the first phase, the four petals of the antenna
will fold along the first outmost hinge to form a 45 degree folding with the help of angle lock features, in
the second phase, the four petals will continue to fold along the second hinge for another 45 degree, so the
total folding degree of the antenna petals are 90 degree. The two-phase design of the antenna gives more
functionality of the structure such that it can change the signal transmission range by transforming its shape.

Figure 5.15 A two phases antenna design.(a) 2D model of the antenna. (b) 45 degree folding model (c)
90 degree folding model (d) 2D antenna sample (e) 45 degree folded antenna (f) details of the folding
hinge (g) 90 degree folded antenna.
5.6 Summary
In this chapter we have demonstrated the self folding of polystyrene films using electricity triggered
silver ink printed traces. To control the self-folding process, thermal models are established to analyze the

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temperature field of the structure, key factors such as current and unit resistance of the ink traces are
identified to affect the folding angles; folding angles are also calibrated with various current and unit
resistance. Two methods of sequential folding are studied, they are sequential folding with single circuit
loop as well as multiple circuit loops. Design features such as angle lock is developed to control the folding
angle. several test cases have been presented to demonstrate the effectiveness and potential application
such as 3D antenna of the developed self-folding method.

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Chapter 6 Conclusions and recommendations
Self-folding structures have attracted more and more attention as well as research interest in different
disciplines and fields due to their great potential in the application such as biomedical devices, packaging,
sensing, 3D circuit designs as well as wearable devices. In previous chapters, we mainly focused on the
development of two new processes to realize the fast fabrication of self-folding structures, the self-folding
of smooth curved structures as well as simple manner of sequential folding. In this chapter, we will review
the research questions and hypothesis presented in Chapter 1 and discuss main contributions of our work in
the dissertation and give recommendations for future research that could move the technology forward.
6.1 Answering the Research Questions and Testing Hypothesis
To verify the three main hypotheses, we subdivided the three main research questions into three sub-
questions and came up with a sub-hypothesis corresponding to each sub-question. Each hypothesis is tested
in prior chapters as follows:
Hypothesis 1.1 A sandwiched structural design based on bilayer structure could be used in the self-
folding structure.
Hypothesis 1.2 Theoretic model as well as physical design features could be used to guide the design
of the folding angle .
To verify hypothesis 1.1, the structural design of the self-folding structure based on thermal
responsive mechanism was presented in Chapter 3.2. Its fabrication process was discussed in Chapter 3.4.
Validation test cases as well as application cases were shown in Chapter 3.5 and Chapter 3.6. The
sandwiched self-folding structure can be used to realize self-folding.
To verify hypothesis 1.2, a mechanical analysis of the folding behavior of the structure under heat was
analyzed in Chapter 3.3, design features such as angle locks were also discussed in Chapter 3.5. Folding

149

angles of the structure were measured and compared with the theoretical angles, the results aligned well
with each other.
Hypothesis 2.1 A surface discretization method can be used to map curved 3D surface into 2D design
with folding parameters.
Hypothesis 2.2 Constraint patterns can be identified and designed to control the corresponding
folding parameter that can realize the deformation control of each folding unit.
To verify hypothesis 2.1, a mapping method was discussed in Chapter 4.2 to transform 3D designs
into 2D design with defined patch codes based on the folding parameters such as folding type, folding
orientation, folding axis and folding curvature. The global shape based on local deformation was compared
with the simulated results in Chapter 4.4, showing that this method works well.
To verify hypothesis 2.2, certain constraint patterns were discussed in Chapter 4.3 to control the
folding parameter. A computational framework was also introduced based on the method developed to
generate constraint patterns automatically in Chapter 4.5. The folded structure based on the designed
constrain pattern aligns well with the design.
Hypothesis 3.1 Factors that affecting the folding angle can be analyzed and calibrated to control the
folding angle with the help of angle lock.
Hypothesis 3.2 Decoupled circuit design can be used to heat up the self-folding structure locally to
achieve sequential folding.
To verify hypothesis 3.1, thermal models as well as experimental tests were covered in Chapter 5.1.
The factors that affecting the folding angle were identified and studied, they were the temperature, unit
resistance and the current as well as time. Angle lock designs were developed also to better control the
folding angle in Chapter 5.3.1 and Chapter 5.4.1. Details of the printing parameters control and
optimization can be found in Chapter 5.2.

150

To verify hypothesis 3.2, decoupled circuit designs were discussed in Chapter 5.4 to implement
sequential folding through locally sequential heating. Test cases such as self-lock structure, origami crane
as well as a two-phase antenna design were shown in Chapter 5.4 and Chapter 5.5 to verify the feasibility
of this method.
6.2 Contributions and Intellectual Merit
Main contributions of our work can be summarized as follows:
(1) Developed a 4D Printing process to design and fabricate self-folding structures using projection based
stereolithography with polystyrene film.
(2) Developed a design method to realize self-folding of smooth curved structures.
(3) Developed a new process to fabricate sequential folding structures with silver ink printed polystyrene
film using Direct Ink Writing process.
(4) Developed design features such as angle lock, constraint layer to better control the folding angle of the
self-folding structures.
(5) Established analytical models for main process parameters and provided parameter design methods for
the process. Applied the process in fabricating origami designs as well as 3D circuit designs like 3D
antenna.
6.3 Recommendations for Future Work
Self folding structures have great potential in so many fields, 4D printing process is a promising
technology in implementing self-folding designs. In future, more work can be done in the following
aspects.
(1) Process automation. The process developed in our study, although it's a simple and fast process, there

151

are still a lot of manual steps involved, which might introduce fabrication errors as well as slow down
the process. Specific set-ups could be developed to fabricate the self-folding designs used in this study.
In this way, more complex structures could be fabricated and integrated with the self-folding designs,
for example, structures with complex 3D features could be built on the self-folding sheet so more
interesting designs could be achieved.
(2) Regarding the self-folding of smooth curved shell structures, more general constraint patterns could be
studied, right now we just identified two patterns that could be used for the folding control purpose.
There would be more design freedom if more general constraint patterns could be used, for example,
digitalized constraint pattern with details going down to each pixels could be used for the self-folding
purpose, in that way, a more powerful simulation tool would be developed as well to randomly
generate the constraint patterns or to use machine learning methods to automatically reverse the shape
and generate the constraint pattern for the self-folding structures.
(3) More materials could be tested using the developed methods, so far, we mainly use polystyrene films
as the experimental material, actually there are more polymer materials that can shrink under heat or
other stimulis, by identifying more material choices or developing our own material that can directly
be printed using a 3D printer, that would bring in more design freedom in the future work. Another
thing I would like to mention is that all the designs we made can only deform along one way instead
of reversing the shape back, this gave us a lot of limitations in using the design in real application.
(4) For the sequential designs in our study, there is a lot of other materials that we can use for printing the
circuits to achieve various unit resistance, especially flexible materials because we require the
structure to fold during the process. We've tried some materials such as Nickel Ink, Carbon based Ink,
they were too brittle to fold. If more flexible conductive materials can be identified for the self-folding
purpose, the circuit could be much simpler and more applications can be identified as well.

152

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Abstract (if available)

Abstract Self-folding structures have been extensively studied over the past few decades due to their potential application in areas such as biomedical devices, reconfigurable robots, packaging, micro grippers, etc, especially with the emerging concept of 4D printing since 2013. Different self-folding mechanisms as well as processes have been developed for different self-folding designs, most of them require complex material preparation procedures

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Asset Metadata

Creator Deng, Dongping (author)

Core Title 4D printing of self-folding structures using polystyrene film

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Industrial and Systems Engineering

Publication Date 08/09/2017

Defense Date 12/13/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 4D printing,OAI-PMH Harvest,polystyrene film,self-folding structures

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Chen, Yong (committee chair), Khoshnevis, Behrokh (committee member), Wu, Wei (committee member)

Creator Email ddeng@usc.edu,dengdongping999@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-332721

Unique identifier UC11258363

Identifier etd-DengDongpi-5016.pdf (filename),usctheses-c40-332721 (legacy record id)

Legacy Identifier etd-DengDongpi-5016.pdf

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Document Type Dissertation

Rights Deng, Dongping

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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