國立中興大學精密工程研究所

(National Chung Hsing University, Institute of Precision Engineering)

博士學位論文
(Ph.D. Dissertation)

多穩態撓性機構之設計與分析

Design and Analysis of Multistable Compliant
Mechanisms

指導教授：王東安 Dung-An Wang
研究生：范輝遵 Huy-Tuan Pham

中華民國一百年七月



Design and Analysis of Multistable Compliant Mechanisms

Huy-Tuan Pham
Graduate Institute of Precision Engineering
Doctor of Philosophy

(ABSTRACT)
Multistable mechanisms, which provide multi stable equilibrium positions within
its operation range, can be adopted to design systems with power efficiency and
kinematic versatility, oftentimes two conflicting goals.

Multistable compliant

mechanisms have attracted more and more attention in recent years.

Two new

specified multistable compliant mechanisms are developed in this dissertation: a
compliant quadristable mechanism and a constant-force bistable mechanism.

Finite

element analyses are used to characterize the behavior of these multistable mechanisms
under static loading. A design formulation is proposed to synthesize the shape and size
of these specified compliant mechanisms.
prototypes of them are fabricated and tested.

Millimeter scale polyoxymethylene
The characteristics of these mechanisms

predicted by theory are verified by experiments. The design examples presented in
this investigation demonstrates the effectiveness of the optimization approach for the
design of the multistable compliant mechanism.

The proposed mechanisms have no

movable joint and gain their mobility from the deflection of flexible members.

These

compliant mechanisms have the ease of miniaturization and offer a significant
advantage


in

the

fabrication

of

micro

actuators,

micro

sensors

and

microelectromechanical systems.
Keywords: bistable, quadristable, constant-force bistable, multistable mechanisms,
vibration.
i


ACKNOWLEDGEMENTS
First and foremost, I would like to send my deep gratitude to two universities, Ho
Chi Minh City Nong Lam University, Vietnam where I have been working and National
Chung Hsing University, Taiwan for providing me this valuable scholarship for Ph.D.
degree.


Many people deserve thanks for their contributions to this dissertation and my life.
It is my pleasure to thank my Taiwanese labmates for their help and friendship to
overcome my initial culture and language obstacles.

I must thank Cheng-Hao Ciou, a

master student at Micro/Nano Machining Laboratory in NCHU, who helped me with
meticulous fabrication by using their CNC milling machine. Helpful discussions with
Professor Chao-Chieh Lan of National Cheng Kung University, Taiwan, ROC. are
greatly appreciated

Special thanks to Assoc. Prof. Dung-An Wang, a man I am honored to know as a
teacher, an advisor, and a friend. He has also spent a considerable portion of his time
giving guidance and helping me in countless ways.

I have learned much more than

engineering from him.

Finally, I am very grateful to my parents, my sister and my girlfriend for their love,
for their support and encouragement of my academic pursuits, and for always
expressing confidence in my abilities.
This dissertation was supported by the National Science Council (NSC) ROC,
under grant no. NSC 96-2221-E-005-095.

ii


TABLE OF CONTENTS

ABSTRACT.................................................................................................................i
ACKNOWLEDGEMENTS .......................................................................................ii
TABLE OF CONTENTS............................................................................................iii
LIST OF FIGURES ....................................................................................................v
LIST OF TABLES.......................................................................................................viii
NOMENCLATURE....................................................................................................ix
CHAPTER 1

INTRODUCTION............................................................................1

1.1 Motivation ............................................................................................................1
1.2 Contributions.......................................................................................................2
1.3 Literature Review................................................................................................3
1.3.1 Compliant Mechanism.......................................................................................3
1.3.2 Bistable micromechanism .................................................................................4
1.3.3 Multistable mechanism......................................................................................5
1.3.4 Contant-force bistable mechanism ....................................................................6
1.3.5 Actuation methods of multistable mechanisms.................................................8
1.4 Dissertation Layout .............................................................................................9
CHAPTER 2
2.1 Design

DESIGN OF A BISTABLE MECHANISM ...................................11
...............................................................................................................12

2.1.1 Operational principle .........................................................................................12
2.1.2 Modeling............................................................................................................13
2.1.3 Analysis .............................................................................................................15
2.2 Fabrication and Testing ...................................................................................... 19
2.2.1 Fabrication.........................................................................................................19

2.2.2 Testing

...........................................................................................................20
iii


2.3 Results and Discussions ......................................................................................20
2.4 Summary .............................................................................................................. 23
CHAPTER 3

DESIGN OF A QUADRISTABLE COMPLIANT
MECHANISM..................................................................................41

3.1 Design ..................................................................................................................42
3.1.1 Operational principle .........................................................................................43
3.1.2 Design ...............................................................................................................46
3.1.3 Optimization ......................................................................................................49
3.2 Fabrication and Testing ...................................................................................... 53
3.3 Results and Discussions ......................................................................................54
3.4 Summary ..............................................................................................................58
CHAPTER 4

DESIGN OF A CONSTANT-FORCE BISTABLE
MECHANISM..................................................................................75

4.1 Design ................................................................................................................... 75
4.1.1 Operational principle ..........................................................................................77
4.1.2 Design.................................................................................................................78
4.1.3 Optimization .......................................................................................................83
4.2 Fabrication and Testing ......................................................................................85

4.3 Results and Discussions ......................................................................................85
4.4 Summary ..............................................................................................................88
CHAPTER 5

CONCLUSIONS AND FUTURE WORK......................................100

5.1 Conclusions ...........................................................................................................100
5.2 Future work ...........................................................................................................101
Bibliographies..............................................................................................................103
Publications during Ph.D. studies .............................................................................115
iv


LIST OF FIGURES
Fig. 2.1

(a) A schematic of a BM and a permanent magnet served to actuate
the mechanism (b) Length l and the angle θ with respect to the

y axis ...........................................................................................................25
Fig. 2.2

Two stable equilibrium states of the mechanism.........................................26

Fig. 2.3

Four-step operation of the mechanism.........................................................27

Fig. 2.4


A schematic of a BM ...................................................................................28

Fig. 2.5

A typical f-d curve of a BM.........................................................................29

Fig. 2.6

A schematic of a quarter model ...................................................................30

Fig. 2.7

A mesh for the quarter model ......................................................................31

Fig. 2.8

F-d curve and potential energy curve based on the finite element model ...32

Fig. 2.9

Time responses of the mechanism.

(a) Switching from FSP to SSP;

(b) switching from SSP to FSP ......................................................................33
Fig. 2.10 Fabrication steps ..........................................................................................34
Fig. 2.11 An array of fabricated devices .....................................................................35
Fig. 2.12 An OM photo of a fabricated device ...........................................................36
Fig. 2.13 A schematic of the experimental setup ........................................................37
Fig. 2.14 Experimental apparatus placed under a high-speed camera ........................38

Fig. 2.15 Snapshots for forward motion......................................................................39
Fig. 2.16 Snapshots for backward motion...................................................................40
Fig. 3.1

A ‘ball-on-the-hill’ analogy for a QM, similar to a figure presented
by Chen et al. [2009]......................................................................................61

Fig. 3.2

Operational principle ...................................................................................62

Fig. 3.3

A typical force versus displacement curve of the QM and the
corresponding configurations at displacement a , displacement b ,

v


displacement c , and displacement d , shown in the inlets..........................63
Fig. 3.4

(a) A schematic of a quarter model. (b) Dimensions of the guide
beam and the shuttle mass .............................................................................64

Fig. 3.5

Flowchart of the optimization procedure.....................................................65

Fig. 3.6


A mesh for the finite element model ...........................................................66

Fig. 3.7

Distribution of the population of several generations in the optimization
process .........................................................................................................67

Fig. 3.8

(a) f- δ curve and maximum stress versus displacement curve
for forward motion; (b) strain energy curve for forward motion; (c) f- δ
curve and maximum stress versus displacement curve for backward
motion; (d) strain energy curve for backward motion ...................................68

Fig. 3.9

Photos of a fabricated QM ...........................................................................69

Fig. 3.10 A photo of the experimental setup...............................................................70
Fig. 3.11 Snapshots for forward motion (a-c) and backward motion (d-f) .................71
Fig. 3.12 f- δ curves of the fabricated QM for (a) forward, (b) backward motion....72
Fig. 3.13 (a) Schematic of the inner bistable structure, BS1.

(b) Schematic

of the outer bistable structure, BS2. (c) f- δ curves of BS1 and BS2
based on their individual finite element models ............................................73
Fig. 3.14 f- δ curve and maximum stress versus displacement curve of the
microscale version of the QM for (a) forward motion;

(b) backward motion......................................................................................74
Fig. 4.1

Schematic of a CFBM and its operational principle....................................90

Fig. 4.2

(a) A typical force versus displacement curve of the CFBM and the
corresponding positions at displacement a (b), displacement c (c),
displacement d (d), and displacement g (e) ............................................91

Fig. 4.3

(a) A schematic of a quarter model. (b) Dimensions of the guide
vi


beam and the shuttle mass .............................................................................92
Fig. 4.4

Flowchart of the optimization procedure.....................................................93

Fig. 4.5

A mesh for the finite element model ...........................................................94

Fig. 4.6

(a) A f- δ curve and maximum stress versus displacement curve;
(b) strain energy curve based on a finite element model of the

optimized solution..........................................................................................95

Fig. 4.7

(a) A photo of a fabricated CFBM.

(b) A close-up view of the

flexible hinge .................................................................................................96
Fig. 4.8

A photo of the experimental setup...............................................................97

Fig. 4.9

Snapshots for forward motion (a-c) and backward motion (d-f) .................98

Fig. 4.10 f- δ curves of the fabricated CFBM for (a) forward,
(b) backward motion......................................................................................99

vii


LIST OF TABLES
Table 2-1 Values of the coefficients of the nonlinear spring stiffness function .........24
Table 2-2 Chemical composition and operation conditions for the low-stress nickel
electroplating solution................................................................................24
Table 3-1 Lower and upper bounds on the design variables......................................60
Table 3-2 The values of the design variables of the optimum design........................60
Table 3-3 The values of the design variables of the optimum design of the

microscale QM...........................................................................................60
Table 4-1 Lower and upper bounds on the design variables......................................89
Table 4-2 The values of the design variables of the optimum design........................89

viii


NOMENCLATURE
English symbols
A

planar area of the mechanism

B

magnetic field

Bui

control point of Bézier curve

c

damping coefficient

d

gap between the substrate and the mechanism

D


operational range

E

Young’s modulus

Fm

electromagnetic force on each beam

F

electromagnectic force exerted to the mechanism

Ft + ∆t

effective force

Fi (i = 1..4)

reaction force

F(X i)

objective space

f

force


fc , fd , fe

output forces of the CFBM

h

out-of-plane thickness

hi (i = 1,2)

apex height of the curved beams

I, i

current

ix


i0

amplitude of the applied AC current

k , K (X )

nonlinear spring stiffness

l


length of the hinged beam

L1 , L0 , Ls

length of fexural segment, rigid segment and side beam

L

span of the curved beams

m

mass

m

effective mass

N

number of generations

P

position vector of a point on the Bézier curve

Pui

position vector of the control point Bui


S

specified ratio of the output force f d to f c

t1 , t 0 , t s

in-plane thickness of fexural segment, rigid segment and side
beam

t

time

T

period

U i (i = 1..4)

strain energy

w1 , w2

widths of the outer and inner curved beams

x&

velocity

x


displacement

( xr , y r )

position vector
x


Xi

design space

Greek symbols
a

amplitude of the response

β

phase of the response

δ

displacement

µ

dynamic viscosity


µ1

damping coefficient

ν

kinematic viscosity

νp

Poisson’s ratio

θ

inclined angle of the beam

ρ

density

σ

detuning parameter

ω1 , ω 2 , ω

frequency

Ω


frequency of the external excitation

Abbreviations
ASTM

American Society for Testing and Materials

BM

bistable mechanism

BS

bistable structure

CFBM

constant-force bistable mechanism

xi


CFM

constant-force mechanisms

FSP

first stable position


MEMS

Micro Electro-Mechanical Systems

OM

optical microscope

PDA

personal digital assistant

POM

polyoxymethylene

PRBM

pseudo-rigid-body model

QM

quadristable mechanism

SMA

shape memory alloy

SSP


second stable position

xii


Chapter 1

INTRODUCTION

1.1 Motivation
The desire of using compliant multistable mechanisms for energy saving in the
field of MicroElectroMechanicalSystems (MEMS) has attracted widespread attention
from many researchers and engineers.

While the use of compliant mechanisms would

help reduce cost due to part-count reduction, simplified manufacturing processes and
increased performance by increasing precision, reducing wear (Howell 2002),
multistable mechanisms further enrich their interestingness via maintaining stability
without power consumption and with high repeatability.

Another advantage of

compliant mechanisms is the ease of miniaturized posibilities. All these characteristics
have favored the wide usage of compliant multistable mechanisms in simple
microstructures, actuators, and sensors.
From the last decade, many studies and researches have been committed on
bistable and tristable compliant mechanisms.

However, few mechanisms with four or


more mechanically stable positions have been reported.

The key challenge in

developing multistable mechanisms is the difficulty in their synthesizing and analyzing.
1


Geometry nonlinearities due to large deflections are commonly encountered in
compliant multistable mechanisms.

Modeling of force-deflection characteristics of

compliant mechanisms can be performed by the pseudo-rigid-body model (PRBM)
(Howell 2002).

However, in order to accurately describe the behavior of compliant

mechanisms using PRBM, where to place the added springs and what value to assign
their spring constants are important.
Not only is it essential to synthesize new configurations of multistable
mechanisms but also is it crucial to develop new activating methods.

So far switching

methods of multistable mechanisms can be classified into two main categories: static
and dynamic method. The former method has been widely studied by many reseachers,
while few publications are found on the later.
An effort to develop a new quadristable compliant mechanism and a novel

constant-force bistable mechanism with more versatile synthesis approach and a new
method to switch a bistable mechanism has motivated the present dissertation.

1.2 Contributions
Firstly, a new method to switch a bistable mechanism (BM) by electromagnetic
actuation is presented in this dissertation.
substrate between its stable positions.

Vibration is utilized to drive the BM on a

The feasibility of using vibration to achieve

dynamical switching is confirmed by the derived analytical model and experiments as
well.

The presented switching method provides a simple and efficient means of

activating a BM without on-substrate driving mechanisms such as electrostatic or
electrothermal actuators.
Secondly, a design approach using multiobjective genetic algorithm optimization
to design compliant multistable mechanisms is proposed.
2

The effectiveness of the


methodology is verified by the design of the two new specified compliant multistable
mechanisms.

A new quadristable mechanism (QM) with a bistable structure


embedded in a surrounding beam structure is developed. Three stable equilibrium
positions are within the range of the forward motion of the mechanism, and the fourth
stable equilibrium position can only be reached on the backward motion.

The

characteristics of the mechanism predicted by theory are verified by experiments. This
compliant mechanism has the ease of miniaturization and offers a significant advantage
in the fabrication of micro actuators, micro sensors and microelectromechanical
systems.
Thirdly, a novel constant-force bistable mechanism (CFBM) allowing constant
contact force and overload protection is developed. This mechanism allows constant
contact force and overload protection.

The feasibility of using the mechanism to

achieve constant output force and bistability is confirmed by finite element analyses.
Using the CFBM, sophisticated sensors and control system for force regulation of
machining systems can be eliminated.

1.3. Literature Reviews
1.3.1 Compliant mechanism
Compliant mechanisms are devices which achieve at least some or all of their
functionality from deflection of flexible members. The use of compliant mechanisms
has the advantages of part-count reduction, simple and inexpensive manufacturing
processes and increase performance by increasing precision, reducing wear (Howell
2002).

Compliant mechanisms can be classified as partially and fully mechanism.


These two types are all composed of rigid and flexible segments.

While partially

compliant mechanism makes use of combination of traditional joints and compliant
3


segments to obtain motion, the latter type relies completely on the deflection of flexible
segments.

The motion of compliant mechanisms causes their flexible members to

deflect and store elastic strain energy.

This energy can then be released to execute the

function of the device.
The commonly used design methods for compliant mechanisms are PRBM and
topology optimization methods. While PRBM uses rigid body components which has
the equivalent force-deflection characteristics to model the deformation of flexible
components of conpliant mechanisms (Wilcox and Howell 2005), topology methods use
continuum models (Larsen et al. 1997).

The latter method often requires further

procedure to modify the optimum contour to eliminate the “point hinges” problem from
the final continuum design (Hull and Canfield 2006).
Due to above specified characteristics of compliant mechanisms, certain groups

of mehanisms are favored for appropriate applications.

Some special-purpose

compliant mechanisms studied so far include bistable mechanisms, constant-force
mechanisms, and parallel guiding mechanisms.

This section is also intended to review

some recently developed multistable mechanisms and their actuation methods as well.

1.3.2 Bistable micromechanism
A BM has three locations where no input energy is required to maintain the
device’s position, including two stable equilibria and an unstable “transition state”.
Input energy is only required to change from one stable point to another (Casals-Terre
and Shkel 2005).

Bistable micromechanisms are gaining attention in MEMS

applications such as accelerometers (Hansen et al. 2007), memory cells (Hälg 1990),
switches (Freudenreich et al. 2003; Masters and Howell 2003; Lee and Wu 2005; Yang
et al. 2007; Chen et al. 2009; Liao et al. 2010), relays (Kruglick and Pister 1998; Gomm
4


et al. 2005; Qiu et al. 2005), valves (Wagner et al. 1996), feeding systems (Tsay et al.
2005), microassembly (Wang and Pham 2008), and energy harvesting (Ando et al. 2010;
Stanton et al. 2010).

Low actuation force and power, high cycle life, and predictable,


repeatable motion are required for a BM in MEMS applications.
BMs can also be partially compliant, where the device consists of one or more
flexible segments as well as one or more traditional joints, or fully compliant, where the
mechanism achieves all of its motion and function from the motion of compliant
segments.

Configurations of compliant mechanisms which exhibit bistable behavior

have been classified and presented in Jensen (1998).

1.3.3 Multistable mechanism
Multistable mechanisms, which provide multiple stable equilibrium positions
within their operation range, can be used to design systems with both power efficiency
and kinematic versatility, oftentimes two conflicting goals.

With the concept of

multistable mechanisms, a wide range of operating regimes or novel mechanical
systems without undue power consumption can be created (King et al. 2004).
Substantial interest has focused on design of bistable mechanisms (Gomm et al. 2005;
Qiu et al. 2005; Hansen et al. 2007; Yang et al. 2007; Wang et al. 2009) and tristable
mechanisms (Ohsaki and Nishiwaki 2005; Su and McCarthy 2005; Oberhammer et al.
2006; Pendleton and Jensen 2007; Chen et al. 2009; Chen et al. 2010).
Few mechanisms with four or more mechanically stable positions have been
reported.

Han et al. (2007) developed a planar QM using two pairs of curved beams to

achieve quadristability with two stable positions in each of two orthogonal directions.

The sequence of switching between stable positions can be altered by selectively
actuating the mechanism in one of the two orthogonal directions.
5

Oh and Kota (2009)


have proposed a mathematical approach to synthesize multistable compliant
mechanisms based on a combination of multiple bistable rotational mechanisms.

A

design case study of a QM with four stable rotational orientations is presented.
However a prototype of this QM with an appropriate actuator to validate this design is
still needed. King et al. (2004) proposed a QM consisting of a rotating compliant
beam with an armature magnet attached to it and an array of stator magnets.

Fields of

strain energy, gravitational energy and magnetic energy are all involved in the stability
modes of their mechanism.

The inherently nonlinear nature of the energy storage

elements have proposed complexity for the definition of differential equations in order
to synthesize multiple equilibria in their optimization solution. This may also require a
significant effort to obtain a feasible design.
Hafez et al. (2003) proposed a robotic device with a large number of degrees of
freedom, which can be taken as a large number of stable positions/orientations. The
discrete nature of their mechanism is ensured by the use of bistable mechanisms.

These kind of mechanisms can perform precise, discrete motions without need for
sensing, complex electronics or feedback control.

With complexity of the assembly of

modular parallel platforms and a network of flexible and rigid members with embedded
actuators, their mechanism can be used for tasks which require a robot to operate in a
three-dimensional space, such as camera placement and light positioning.

Despite of

their promising characteristics, actuator technology is still a key challenge for the
implementation of large degrees of freedom binary mechatronic systems.

1.3.4 Contant–force bistable mechanism
Responding to the increasing needs in many systems where a variable output
force is undesirable, mechanisms which provide a near–constant output force over a
6


prescribed deflection range have been developed and are defined as constant–force
mechanisms (CFMs). These mechanisms have been gaining more and more attention
in recent years (Jenuwine and Midha 1994; Howell and Magleby 2006; Berselli et al.
2009; Meaders and Mattson 2010; Lan et al. 2010).

CFMs can be designed for

concrete testing equipment (Jenuwine and Midha 1994), exercise machines (Howell and
Magleby 2006) and electrical contacts (Meaders and Mattson 2010).


A constant–force

actuator based on dielectric elastomers is proposed by Berselli et al. (2009) for
applications in robotics and mechatronics.

Lan et al. (2010) developed a compliant

CFM for force regulation of robot end–effectors operating in an unknown environment.
CFMs can be utilized in systems to reduce the need for complex control
algorithms and feedback loops (Erlbacher 1995; Bossert et al. 1996).

Without

sophisticated control systems, CFMs made of passive mechanisms may minimize
control effort and reduce cost without losing precision.

CFMs have been developed by

various investigators (Howell 2002; Boyle et al. 2003; Nahar and Sugar 2003; Pedersen
et al. 2006; Weight et al. 2007).

Pedersen et al. (2006) used topology and size

optimization to design a transmission mechanism which converts the constant stiffness
of an actuator into constant output force.

CFM can also be explored for the currently

mass using of electrical contact since providing sufficient contact force is a crucial
method to minimize the contact resistance (Jang et al. 2008).


Weight et al. (2007)

proposed a CFM composed of a bent beam and a cam for electrical contacts in personal
digital assistant (PDA) dock stations to improve the reliability of high–cycle electrical
connectors.

Their beam and cam combination provides the strain energy storage

device necessary for constant force behavior.
Boyle et al. (2003) presented a CFM consisting of a rigid link, a flexible
segment and a slider.

His compliant CFM offers the possibility of a new type of spring
7


element for a variety of applications. Nahar and Sugar (2003) designed a double-slider
CFM, where two springs are attached to the sliders.
a micro compliant slider–crank CFM.

They also proposed the design of

However, in order to facilitate these

mechanisms in MEMS devices, monolithic compliant mechanisms which can be
fabricated by microfabrication technologies are favored over the macro devices. With
fewer movable joints, the use of compliant mechanisms results in reduced wear, reduced
need for lubrication, and an increased mechanism precision (Howell 2002).


1.3.5 Actuation methods of multistable mechanisms
Various actuation methods of multistable mechanisms have been proposed
including electrothermal actuation (Qiu et al. 2005; Wilcox and Howell 2005; Yang et al.
2007), electrostatic actuation (Hwang et al. 2003; Freudenreich et al. 2004; Casals-Terre
and Shkel 2004; Receveur et al. 2005; Kwon et al. 2005; Krylov et al. 2008),
electromagnetic actuation (Ko et al. 2006; Cao et al. 2007), optical actuation (Sulfridge
et al. 2002), piezoelectric actuation (Giannopoulos et al. 2007), and shape memory alloy
(SMA) actuation (Barth et al. 2010).

Depending on different application requirements,

an appropriate actuation method should be selected.
Built-in driving mechanisms are usually required for electrothermal and
electrostatic actuations as reported previously (Hwang et al. 2003; Freudenreich et al.
2004; Casals-Terre and Shkel 2004; Kwon et al. 2005; Qiu et al. 2005; Wilcox and
Howell 2005; Yang et al. 2007; Krylov et al. 2008).

Sulfridge et al. (2002) reported an

optical switch for a MEMS bistable beam using a laser light.

The laser being used is

200 mW and a load of 0.6 nN is generated. It might not be convenient for micro
devices requiring actuation forces on the µN scale.

The meso-scale piezoelectric

bistable beam described by Giannopoulos et al. (2007) needs a high driving voltage up
8



to 120 V and a precompression of the beam is needed for snap-through action.
Cao et al. (2007) demonstrated a bi-directional MEMS actuator based on
electrothermal buckling and electromagnetic Lorenz force.

These type of actuators

require relatively low voltages and high currents to operate and can exert large forces on
the mN scale. Electromagnetic actuation can be used in MEMS applications that
require high displacement, high force and bi-directional actuation.

An external

vibration can be utilized to move a BM between its bistable positions based on an
investigation carried out by Kreider and Nayfeh (1998) for a buckled beam under
harmonic excitation.

A harmonic or intermittent snap-through behavior of their

prebuckled beam is observed. The harmonic excitation by electromagnetic forcing
provides a way for motion control of BMs that require high displacement output and
high force actuation.

This kind of actuation will be exploided and investigated in this

dissertation.

1.4 Dissertation Layout
This chapter has given brief introduction on compliant mechanisms and

reviewed researches on two types of special-purpose compliant mechanisms:
multistable mechanisms which include bistable mechanisms, tristable mechanisms, and
quadristable mechanism, and constant-force bistable mechanisms.
Chapter 2 investigates a compliant chevron-type bistable mechanism.

A new

vibration-actuated method to switch this BM by electromagnetic actuation is presented.
An analytical model of the BM is derived in order to analyze its dynamic behavior.
Prototypes of the device are fabricated using an electroforming process. Experiments
are carried out to demonstrate the effectiveness of the dynamical switching of the BM.

9


Chapter 3 describes a design of a new compliant quadristable mechanism.
optimization method is proposed to design the QM.

An

Finite element analyses are

carried out to evaluate the mechanical behaviors of the design obtained by the
optimization procedure.

Prototypes of the device are fabricated using a milling

process. Experiments are carried out to demonstrate the effectiveness of the QM.
Chapter 4 proposes a novel design of a compliant CFBM. An optimization
method is used to design the CFBMs. Finite element analyses are carried out to

evaluate the mechanical behaviors of the design obtained by the optimization procedure.
Prototypes of the device are fabricated using a milling process.

Experiments are

performed to demonstrate the effectiveness of the CFBM.
Chapter 5 summarizes the work of the dissertation. Future researches for the
dissertation are also recommended.

10


Chapter 2

DESIGN OF A BISTABLE MECHANISM

This chapter describes a design of a vibration-actuated bistable micromechanism
(BM).

The vibration exploited to switch the on-substrate BM is provided by an

electromagnetic Lorenz force, requiring no need for built-in driving mechanisms such
as electrothermal or electrostatic actuators. The electromagnetic actuation is based on
the actuation method reported by Cao et al. (2007) and Ko et al. (2006), where a
precompressed beam is moving through the full range of its bi-directional motion (Cao
et al. 2007) or a bistable beam is actuated statically (Ko et al. 2006). Dissimilar to
their design, the BMs are switched dynamically by shaking the device with an
alternating electromagnetic force. An analytical model of the BM is derived in order
to analyze its dynamic behavior.


Prototypes of the device are fabricated using an

electroforming process. Experiments are carried out to demonstrate the effectiveness
of the dynamical switching of the BM.

11