(Đồ án hcmute) analysis and optimization design new 1 dof compliant stage based on additive manufacturing method with circular hinge for highly position accuracy

8 Mechanisms with Linear Leaf Flexures a and Compound Linear Spring Mechanisms b [5] .... Bearing joint a; flexure hinge b Compliant mechanisms utilize flexures as a crucial component in

MINISTRY OF EDUCATION AND TRAINING

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION

FACULTY FOR HIGH QUALITY TRAINING

ADVISOR:

STUDENT:

GRADUATION PROJECT MAJOR MECHANICAL ENGINEERING TECHNOLOGY

DR DANG MINH PHUNG NGUYEN QUOC HUY

DO PHAN TUONG VY

S K L 0 0 9 9 1 9

RESEARCH AND IMPLEMENTATION OPTIMIZATION DESIGN NEW 1-DOF COMPLIANT STAGE BASED

ON ADDITIVE MANUFACTURING METHOD

WITH CIRCULAR HINGE FOR HIGHLY POSITIONING

ACCURACY

HO CHI MINH UNIVERSITY OF TECHNOLOGY AND EDUCATION

FALCUTY FOR HIGH QUALITY TRAINING DEPARTMENT OF MACHINERY MANUFACTURING TECHNOLOGY

BACHELOR THESIS

RESEARCH AND IMPLEMENTATION OPTIMIZATION DESIGN NEW 1-DOF COMPLIANT STAGE BASED ON ADDITIVE MANUFACTURING METHOD WITH CIRCULAR HINGE FOR HIGHLY POSITIONING ACCURACY

SUPER VISOR: M.E DANG MINH PHUNG

STUDENT NAME: NGUYEN QUOC HUY

HO CHI MINH UNIVERSITY OF TECHNOLOGY AND EDUCATION

FALCUTY FOR HIGH QUALITY TRAINING DEPARTMENT OF MACHINERY MANUFACTURING TECHNOLOGY

BACHELOR THESIS

ANALYSIS AND OPTIMIZATION DESIGN NEW 1-DOF

MANUFACTURING METHOD WITH CIRCULAR HINGE FOR HIGHLY POSITIONING ACCURACY

SUPER VISOR: M.E DANG MINH PHUNG

STUDENT NAME: NGUYEN QUOC HUY

CỘNG HOÀ XÃ HỘI CHỦ NGHĨA

VIỆT NAM

Độc lập - Tự do – Hạnh phúc

PHIẾU NHẬN XÉT ĐỒ ÁN TỐT NGHIỆP

(Dành cho giảng viên hướng dẫn)

Họ và tên sinh viên: Nguyễn Quốc Huy MSSV:18144022 Hội đồng: 02

Họ và tên sinh viên: Đỗ Phan Tường Vỹ MSSV:18144061 Hội đồng: 02

Tên đề tài: NGHIÊN CỨU THIẾT KẾ ĐỊNH VỊ 01 BẬC TỰ DO TÍCH HỢP CƠ CẤU KHUẾCH ĐẠI CHUYỂN VỊ SỬ DỤNG CƠ CẤU MỀM CHO HỆ THỐNG ĐỊNH VỊ CHÍNH XÁC

Ngành đào tạo: Mechanical Engineering Technology

Họ và tên GV hướng dẫn: ThS Đặng Minh Phụng

Ý KIẾN NHẬN XÉT

1 Nhận xét về tinh thần, thái độ làm việc của sinh viên:

2 Nhận xét về kết quả thực hiện của ĐATN

2.1.Kết cấu, cách thức trình bày ĐATN:

2.2 Nội dung đồ án:

(Cơ sở lý luận, tính thực tiễn và khả năng ứng dụng của đồ án, các hướng nghiên cứu có thể tiếp tục phát triển)

2.3.Kết quả đạt được:

2.4 Những tồn tại (nếu có):

3 Đánh giá:

tối đa

Điểm đạt được

1 Hình thức và kết cấu ĐATN 30

Đúng format với đầy đủ cả hình thức và nội dung của các

mục

10

Mục tiêu, nhiệm vụ, tổng quan của đề tài 10

Khả năng ứng dụng kiến thức toán học, khoa học và kỹ

thuật, khoa học xã hội…

5

Khả năng thực hiện/phân tích/tổng hợp/đánh giá 10

Khả năng thiết kế chế tạo một hệ thống, thành phần, hoặc

quy trình đáp ứng yêu cầu đưa ra với những ràng buộc thực

tế

15

Khả năng sử dụng công cụ kỹ thuật, phần mềm chuyên

CỘNG HOÀ XÃ HỘI CHỦ NGHĨA

VIỆT NAM

Độc lập - Tự do – Hạnh phúc

PHIẾU NHẬN XÉT ĐỒ ÁN TỐT NGHIỆP

(Dành cho giảng viên phản biện)

Họ và tên sinh viên: Nguyễn Quốc Huy MSSV:18144022 Hội đồng: 02 STT: 28

Họ và tên sinh viên: Đỗ Phan Tường Vỹ MSSV:18144061 Hội đồng: 02 STT: 28 Tên đề tài: NGHIÊN CỨU THIẾT KẾ ĐỊNH VỊ 01 BẬC TỰ DO TÍCH HỢP CƠ CẤU KHUẾCH ĐẠI CHUYỂN VỊ SỬ DỤNG CƠ CẤU MỀM CHO HỆ THỐNG ĐỊNH VỊ CHÍNH XÁC

Ngành đào tạo: Mechanical Engineering Technology

Họ và tên GV phản biện: PGS.TS Phạm Huy Tuân

Ý KIẾN NHẬN XÉT

1 Kết cấu, cách thức trình bày ĐATN:

2 Nội dung đồ án:

(Cơ sở lý luận, tính thực tiễn và khả năng ứng dụng của đồ án, các hướng nghiên cứu có thể tiếp tục phát triển)

3 Kết quả đạt được:

4 Những thiếu sót và tồn tại của ĐATN:

5 Câu hỏi:

6 Đánh giá:

tối đa

Điểm đạt được

1 Hình thức và kết cấu ĐATN 30

Đúng format với đầy đủ cả hình thức và nội dung của các

mục

10

Mục tiêu, nhiệm vụ, tổng quan của đề tài 10

Khả năng ứng dụng kiến thức toán học, khoa học và kỹ

thuật, khoa học xã hội…

5

Khả năng thực hiện/phân tích/tổng hợp/đánh giá 10

Khả năng thiết kế, chế tạo một hệ thống, thành phần, hoặc

quy trình đáp ứng yêu cầu đưa ra với những ràng buộc thực

tế

15

Khả năng sử dụng công cụ kỹ thuật, phần mềm chuyên

ACKNOWLEDGMENT

We would like to express my sincere gratitude for Dang Minh Phung, my guidance, through all his support on our academic journey His vast knowledge and expertise have inspired us to strive for excellence and have made a significant impact on my growth and development as a student

We are grateful for the time and effort my advisor put into providing us with a challenging and stimulating learning experience His passion for the subject and his dedication to teaching have made the classes enjoyable and memorable

Thank you for being a mentor, a role model and a source of inspiration Your encouragement and support have been invaluable and I am grateful to have had the opportunity

to learn from my advisor, M.E Dang Minh Phung

ABSTRACT IN VIETNAMESE

Ngày nay, công nghệ đang phát triển một cách nhanh chóng, công nghệ nano hiện đang được ứng dụng trong mọi mặt của cuộc sống, đặc biệt là trong ngành công nghiệp vũ trụ và y sinh Với yêu cầu cao về độ chính xác trong giai đoạn gia công, trong trường hợp đó, chúng ta phải sử dụng phương pháp nanoindentation, được sử dụng để kiểm tra độ biến dạng và hành vi

cơ học của vật liệu sinh học với một giá trị khối lượng rất nhỏ Tuy nhiên, một số bộ định vị trước đây có giới hạn trong việc thực hiện thử nghiệm vật liệu Do đó, nghiên cứu này giới thiệu một cấu trúc được thiết kế mới theo tiêu chuẩn 1 bậc tự do với độ chính xác cao hơn Do đó, bài viết này thiết kế một kết cấu mới sử dụng phương pháp mô phỏng phần mềm Đầu tiên, bộ thiết

bị 1 bậc tự do được thiết kế với hai mô-đun, bao gồm bộ khuếch đại dịch chuyển với mười cần

và cơ chế đối xứng Thứ hai, một sơ đồ động học của mô hình được xây dựng bằng phương pháp vật thể giả cứng Để tăng khả năng khuếch đại, giai đoạn thiết kế cấu trúc được tối ưu hóa thông qua thuật toán RSM Kết quả cho thấy tỷ lệ khuếch đại lý thuyết rơi vào khoảng 14 lần Kết quả

lý thuyết gần với mô phỏng đã được xác minh Trong nghiên cứu sắp tới, nguyên mẫu sẽ được chế tạo bằng phương pháp gia công đắp dần hoặc phương pháp cắt dây vi tính hóa để kiểm chứng kết quả phân tích bằng kết quả thực nghiệm

ABSTRACT IN ENGLISH

Nowadays, technology changing every day, nanotech is now applying in every aspect of our life, especially in the space industrial and Biomedical With an excessive requirement of accuracy in machining, in that case, we must use nanoindentation, which is use for testing the deformation and mechanical behavior of bio-material with a very small volume of value However, the previous structural of positioning stage have a limited on perform the material testing As the consequent, this research paper introduces a new designed structural of a compliant 1 Degree of Freedom (1-DoF) with faster response and higher accuracy As a result, this article designs a new structural using software with technology algorithm Firstly, the 1-DoF stage is design with two modules, including a displacement amplifier with ten levers and a symmetric parallelogram mechanism Secondly, a kinetostatic diagram of the stage is built by pseudo-rigid-body method In order to speed up the response of the indentation system, the structural stage is optimizing via the Response Surface Method (RSM) The result showed that the theoretical amplify ratio is found at about 14 Theoretical consequences are nearby to the verified simulation In an upcoming study, the prototype will be fabricated by additive manufacturing method or a computerized wire cutting method in order to verify the analytical results with experimental results

TABLE OF CONTENT

ACKNOWLEDGMENT i

ABSTRACT IN VIETNAMESE ii

ABSTRACT IN ENGLISH iii

TABLE OF CONTENT iv

TABLE OF ABBREVIATION vi

LIST OF TABLES vii

LIST OF FIGURE viii

MISSION OF THESIS xi

CHAPTER 1 INTRODUCTION 1

1.1 Flexure and compliant mechanism 1

1.1.1 Definition 1

1.2 Advantages and disadvantages 10

1.3 Application 14

1.3.1 Micro compliant mechanisms 14

1.3.2 Macro Compliant Mechanisms 17

1.4 Review of the Literature on the Compliant Positioning Stage 19

CHAPTER 2 DESIGN 1 DOF COMPLIANT STAGE 21

2.1 Pseudo –Rigid Body model 23

2.2 Theory of Response Surface Method (RSM) 23

2.3 Types of RSM 24

2.4 Design of Experiment (DOE) 25

2.5 Designing 1 DoF stage 27

CHAPTER 3 EXPERIMENTS SETUP 34

3.1 Static structural 34

3.2 Design of Experiments 37

3.3 Optimization 40

CHAPTER 4 SIMULATION RESULT AND ANALYZATION 1 DOF STAGE 42

4.1 Dynamics Establishment for 1 DoF stage 42

4.2 Design of experiments 44

4.3 Optimization 45

4.4 Simulation result 47

CHAPTER 5 MANUFACTURING AND EXPERIMENT 61

5.1 Manufacturing method 61

5.2 Experiment 63

CHAPTER 6 CONCLUSION 67

REFERENCE 68

TABLE OF ABBREVIATION Abbreviation Meaning

1 DoF 1 Degree of Freedom

MEMS Micro Electro Mechanical System

SEM Scanning Electron Microscope

TEM Transmission Electron Microscope

ANFIS Adaptive neuro-fuzzy inference system

EDM Electrical Discharge Machining

RSM Response Surface method

RSR Response surface regression

DOE Design of Experiment

PRBM Pseudo-Rigid Body Model

LAM Lever Amplification Mechanism

LIST OF TABLES

Table 1 Material properties 32

Table 2 Dimension properties 33

Table 3 Design of experiments data points and computational results 44

Table 4 Bounds of the response surfaces 46

Table 5 Candidate parameter 46

Table 6 Measuring experiments data 66

Table 7 Error comperasion 66

LIST OF FIGURE Figure 1

Figure 1 1 Mechanisms use joints Bearing joint (a); flexure hinge (b) 1

Figure 1 2 Ancient Greece catapult [https://www.theclassroom.com/greek-scientists-invented-catapult-11142.html] 2

Figure 1 3 Elegant Flexible System 3

Figure 1 4 Crimping mechanism [2] 3

Figure 1 5 Flexure classification 4

Figure 1 6 Flexure with single-axis 4

Figure 1 7 Example of Cantilever Beam [5] 5

Figure 1 8 Mechanisms with Linear Leaf Flexures (a) and Compound Linear Spring Mechanisms (b) [5] 6

Figure 1 9 Flexure of the notch kind 6

Figure 1 10 (a) Basic Notch Hinge Flexure Assembly, (b) Compound Notch Spring Assembly [5] 7

Figure 1 11 Mechanisms with double compound springs [5] 7

Figure 1 12 The Cantilever beam Structure 8

Figure 1 13 Crossed strip flexure (a), monolithic flexure (b), and cruciform angle flexure (c) 8

Figure 1 14 Example for flexure with Multi-axis 9

Figure 1 15 Flexure with two axis 9

Figure 1 16 Two degree of freedom flexures 10

Figure 1 17 (a) Compliant running clutch (b) Disassembled rigid body mechanism [2] 11

Figure 1 18 Stress-strain relationship 12

Figure 1 19 Rigid-link parallel-guiding mechanism [2] 13

Figure 1 20 Example consumer products that use a parallel-guiding mechanism: (a) desktop lamp, (b) tackle box, and (c) playground swing 13

Figure 1 21 Young's mechanism [7] 15

Figure 1 22 Micro pin joint that is compliant 15

Figure 1 23 Pantographs with micro-compliance 16

Figure 1 24 A Silicon microgripper [10] 16

Figure 1 25 An aluminum microgripper [11] 17

Figure 1 26 SMA microgripper [12] 17

Figure 1 27 Brake of Bicycle 18

Figure 1 28 A compliant switch 18

Figure 1 29 Piezo-driven parallel micro positioning 1 DoF [18] 20

Figure 1 30 Micro positioning for 1 DoF [1] 20

Figure 2: Figure 2 1 Beam (a) and it PRBM (b) 23

Figure 2 2 RSM flowchart 24

Figure 2 3 DOE process chart 26

Figure 2 4 A scheme of proposed nanoindentation [32] 28

Figure 2 5 Flowchart for 1-DOF stage proposed method 29

Figure 2 6 Dimensional schematic of proposed stage 30

Figure 3: Figure 3 1 Adding material properties to project 34

Figure 3 2 Creating simulate model 35

Figure 3 3 Simulate 1 DoF stage mesh in ANSYS 35

Figure 3 4 Sizing properties 36

Figure 3 5 Choosing material for simulation 36

Figure 3 6 Define input displacement 37

Figure 3 7 Define parameter 38

Figure 3 8 Choosing type of design 38

Figure 3 9 Determining method 39

Figure 3 10 Set up boundaries for simulate parameters 39

Figure 3 11 Creating response surface 40

Figure 3 12 Select model to simulate 40

Figure 3 13 Go to optimization function 41

Figure 3 14 Choose parameter that need to optimize 41

Figure 4:

Figure 4 1 Pseudo-rigid-body diagram for the 1-DOF stage 43

Figure 4 2 Parameter of circular hinge 44

Figure 4 3 Flexure leaf hinge dimension 44

Figure 4 4 Total deformation of 1 DoF stage 54

Figure 4 5 Deformation Probe result 55

Figure 4 6 The safety factor result 56

Figure 4 7 Response simulation affected on deformation P9 58

Figure 4 8 Response simulation affected on safety factor 60

Figure 5: Figure 5 1 Water Jet cutting 61

Figure 5 2 Wire cutting theory 62

Figure 5 3 Sample of 1 DoF stage 63

Figure 5 4 Setting up the experiment 64

Figure 5 5 Measuring the 1 DoF stage 65

MISSION OF THESIS

to a cantilever beam Unlike traditional revolute joints which rely on sliding and rolling, flexure joints are based on the deflection of bending The key determinant in designing the desired motion using flexure hinges is the material's modulus of elasticity, or Young's modulus

Figure 1 1 Mechanisms use joints Bearing joint (a); flexure hinge (b)

Compliant mechanisms utilize flexures as a crucial component in their design These joints, also referred to as flexure-based mechanisms, have a long history of being utilized for generating motion Examples of early compliant mechanisms include bows and catapults, which harness the strain energy of flexible materials and convert it into kinetic energy Bows were among the earliest known forms of compliant mechanisms, and catapults were widely utilized in ancient wars to propel missiles over great distances The design of these early

catapults consisted of flexible wooden members that stored energy and released it upon activation

Figure 1 2 Ancient Greece catapult

[https://www.theclassroom.com/greek-scientists-invented-catapult-11142.html]

Compliant mechanisms, also known as flexure-based mechanisms, are utilized in various forms of common devices that are prevalent in our daily life Such examples include tweezers, paper clips, nail scissors, safety scissors and belt locking tools These mechanisms employ the principle of deflection, where the application of force results in the bending of flexible elements, enabling the device to perform its intended task For instance, tweezers utilize the flexibility of two beams to grasp small objects, while paper clips rely on the flexibility of their material to attach papers Similarly, nail scissors utilize the deflection of the upper beam to close the gap and cut the nail The functionality of belt locking tools is also based on the deflection of beams

Figure 1 3 Elegant Flexible System The Figure depicts a crimping mechanism, a prototypical illustration of a compliant mechanism, as shown in Figure 1.4 The mechanism exploits the malleability of its flexible members to transfer the input force to the output port via hand grip, enabling the storage of strain energy The use of compound and simple flexures in the mechanism enables the attainment of the least amount of closure at the output port with the application of human force Further elaboration on the various flexure types will be expounded upon in the subsequent subsection [2]

Figure 1 4 Crimping mechanism [2]

1.1.2 Classification of Flexural Elements and Mechanisms Based on Flexure

Classification of Flexures: As depicted in Figure 1-5, Flexures are categorized into three forms Single-axis flexures only offer linear or angular motion, whereas multiple-axis and two-axis flexures offer both linear and angular motion [1]

Figure 1 5 Flexure classification

Single-axis flexures: These are flexures that are designed to be compliant in a single

axis, which is referred to as the sensitive or compliant axis, as depicted in Figure 1-6 They are utilized in two-dimensional (planar) mechanisms

Figure 1 6 Flexure with single-axis Single-axis flexures are further divided into two groups, linear and angular flexures Linear flexures afford solely linear movement while angular flexures afford solely rotary movement

Linear flexures are a category of single-axis flexures that are designed to provide linear

motion The basic form of this type of flexure is the cantilever beam, which is depicted in

Figure 1.7 Although linear flexures are simple to design, they are prone to instability, buckling, and twisting, particularly if the actuation force is misaligned This can lead to substantial parasitic deflections, which can compromise the functionality of the mechanism Efforts are ongoing to develop novel linear flexure mechanisms that can overcome these limitations and improve their performance [5]

Figure 1 7 Example of Cantilever Beam [5]

Mechanisms with multiple-flexure arrangements, such as leaf-spring flexures, exhibit improved resistance to torsional deflection, as demonstrated in Figure 1.8a These mechanisms offer greater rigidity in torsion and a larger mounting area for specimens, but suffer from decreased stiffness in directions other than the driving axis, leading to parasitic deflections The rotational axis around the Z-axis is the primary weak point of these mechanisms To combat these parasitic errors, compound leaf spring mechanisms, depicted

in Figure 1.8b, have been devised This design entails connecting a simple linear spring mechanism to the underside of another linear spring mechanism The parasitic deflections of platform B cancel out those of platform A, resulting in more precise linear motion This mechanism, when subjected to the same force, experiences twice the deflection of a single linear spring mechanism

Figure 1 8 Mechanisms with Linear Leaf Flexures (a) and Compound Linear Spring Mechanisms (b) [5]

Flexures with "notch hinges" were developed to address the limitations of leaf spring mechanisms in high precision applications Leaf springs tend to exhibit parasitic deflections

in the form of an S-shaped deflection, which can be countered by straightening or reinforcing the beam centers, but this results in a trade-off between buckling resistance and drive stiffness The notch hinge, as depicted in Figure 1.9, is a type of flexure with two closely spaced holes that operates similarly to elastic rotary bearings [5]

Figure 1 9 Flexure of the notch kind Figure 1.10a depicts a simple mechanism constituted of notch-hinge flexures The curvature is constrained by the tensile stress concentrated in the notch hinge portions, thereby rendering the deformation amenable to precise calculation through work-energy methods.’Despite being restricted by Euler buckling, the load capacity of leaf-type flexures experience variations in their stiffness when subjected to loading, whereas notch-type flexures

are susceptible to variations in stiffness as a result of loading [5]’ In Figure 1.10b, a type compound spring mechanism is devised to augment the torsional rigidity of notch-type mechanisms Similar to the linear-type compound mechanism, the notch-type compound mechanism boasts half the stiffness of the simple mechanism, thus inducing twice the deformation in response to the same stress applied to the compound mechanism [5]’

notch-Figure 1 10 (a) Basic Notch Hinge Flexure Assembly, (b) Compound Notch Spring Assembly [5]

Double compound spring mechanisms aim to exhibit exceptional rectilinear performance Figure 1.11a displays a double compound mechanism of the leaf type, and Figure 1.11b exhibits a double compound mechanism of the notch type Due to their symmetrical configuration, these mechanisms also mitigate errors caused by thermal expansion [5]

Figure 1 11 Mechanisms with double compound springs [5]

The utilization of Angular flexures is necessitated in scenarios demanding limited rotary angular motion The rudimentary form of such flexures is depicted as a brief cantilever beam,

as illustrated in Figure 1.12, which was first employed by Eastman in 1937 The extended and

broader cantilever flexures provide a wider angular motion range The fundamental drawback

of straightforward cantilevers is that their center of rotation shifts with the degree of rotation

Figure 1 12 The Cantilever beam Structure Figure 1.13 depicts various forms of angular flexures, including the crossed strip flexures invented by Haringx in 1949, which include a formula for axis shift with angular displacement Monolithic flexures, developed by Young in 1989, exhibit higher resistance to parasitic errors compared to other types of angular flexures Additionally, Jones in 1955 designed cruciform angle flexures, which are beams that twist about their longitudinal axis

Figure 1 13 Crossed strip flexure (a), monolithic flexure (b), and cruciform angle flexure

(c)

Multi-axial flexures: depicted in Figure 1-14, exhibit a versatile rotational geometry

and exhibit multiple compliant axes The compliant axis is situated on the thinnest sectional region, however, it lacks a specified orientation, thereby allowing for utilization in three-dimensional applications where the orientation of rotation is immaterial

cross-Figure 1 14 Example for flexure with Multi-axis

Two-axis flexures: These flexures are engineered to provide bi-dimensional movement

to the mechanism, and are utilized in three-dimensional (spatial) contexts As depicted in Figure 1.15, they have two conforming axes, with the secondary axis exhibiting a slightly lower degree of compliance compared to the primary conforming axis

Figure 1 15 Flexure with two axis Paros and Weisbord devised a means of generating two-axis flexures by arranging single-axis flexures in series Nonetheless, these flexures require additional spatial real estate

to arrange the flexures in a serial manner In Figure 1.16a, two perpendicular notch hinge flexures are coalesced to produce dual-axis motion, while Figure 1.16b depicts the creation

of a universal circular flexure for the same purpose

Figure 1 16 Two degree of freedom flexures

1.2 Advantages and disadvantages

Advantages

Compliant mechanisms are highly prized for their application in a multitude of settings requiring elevated precision This is due to their monolithic design, which is composed of a single piece of material This construction imparts several advantages over traditional mechanisms with numerous joints, including reduced clamping stiffness, joint creep, wear, and weight This renders them suitable for utilization in aerospace and other domains that necessitate lightweight systems [5] Moreover, their deployment results in a decrease in the quantity of components required to accomplish a task, thereby simplifying the manufacturing, assembly, and costs For instance, as depicted in Figure 1.17a, the construction of a compliant running clutch mechanism demands fewer parts than the rigid body mechanism depicted in Figure 1.17b [2]

Figure 1 17 (a) Compliant running clutch (b) Disassembled rigid body mechanism [2]

- The lack of articulations in compliant mechanisms eliminates the need for lubrication and eliminates backlash between joints

- The smooth, consistent displacements and ability to provide minimal rotations make compliant mechanisms ideal for high precision applications

- Symmetry provides resistance to fluctuations caused by temperature changes

- Proper design allows for easy control of compliant mechanisms through prediction of motion using modeled spring characteristics, enabling simple motion control

- Compliant mechanisms are easily miniaturized, as the reduction of components and joints contributes to their suitability for fabrication of micro mechanisms through micro electro mechanical system (MEMS) techniques

Disadvantages

Despite their advantages, compliant mechanisms also pose certain challenges and limitations in specific applications

The analysis and design of compliant mechanisms is challenging due to the complexity

of their mechanics, requiring knowledge of mechanism analysis, synthesis techniques, and deflection of flexible elements The geometric nonlinearities caused by significant deflections

result in invalidity of linear beam equations, and traditional trial-and-error methods for simple systems are only effective for small displacements A pseudo-rigid-body model, which models compliant components as multiple rigid bodies connected via pin joints, is utilized for modeling these mechanisms

The performance of compliant mechanisms is also dependent on the modulus of elasticity of the material used, which can be difficult to control and often requires post-manufacture calibration Any deviation from the elastic deformation region of the material into the plastic deformation range can result in hysteresis, due to dislocation movements in the material, leading to plastic deformation and permanent distortion This can be seen in the Figure 1.18 when the mechanism's yield strength is exceeded

Figure 1 18 Stress-strain relationship Compliant mechanisms are vulnerable to buckling under excessive loads, which may result in fatigue, devastating failures, and permanent deformation Additionally, it is imperative that the drive axis aligns with the desired motion, as the out-of-plane stiffness is low, whereas the stiffness along the drive direction is high [2, 5]

1.1.3 Parallel mechanism

A parallel-guiding mechanism is one in which two opposing links remain parallel throughout the motion of the mechanism The motion of the rigid-link parallel-guiding mechanism is depicted in Figure 1.19 The mechanism is a simple four-bar mechanism with opposing links of equal length, forming a parallelogram

Figure 1 19 Rigid-link parallel-guiding mechanism [2]

One of the simplest mechanisms to comprehend is the rigid-link parallel-guiding mechanism The path of an arbitrary point, P, along the coupler link can be easily described

by the following simple equations:

1.3.1 Micro compliant mechanisms

Micro compliant mechanisms are a subclass of Micro Electro Mechanical Systems (MEMS), which feature the integration of electrical and mechanical components on the microscale Fabricated through specialized techniques, such as etching, lithography, and surface micromachining, these mechanisms exhibit minute size on the order of micrometers and are thus virtually invisible to the naked eye Their minuscule movements are similarly imperceptible Examples of their application include parallel compliant stages utilized in the microcosm:

Bi-stable Mechanisms: Compliant bi-stable mechanisms are those that are capable of

maintaining two steady states within their operational range The motion from one equilibrium position to the other is achieved through the deflection of flexible components These micro bi-stable mechanisms are utilized in micro applications like micro valves and micro switches, and the movement is activated by thermal influence and the bending of the flexible links An illustration of this is shown in Figure 1.21, with the mechanism transitioning from its first stable position in Figure 1.21 to its second in Figure 1.21 b

Figure 1 21 Young's mechanism [7]

Pin joints: The floating pin joints depicted in Figure 1.22 have been engineered using

two layers of polysilicon and produced through multi-layer MEMS fabrication processes These joints have the capacity for both rotational and translational motion, and have been applied as joints in bi-stable mechanisms [8]

Figure 1 22 Micro pin joint that is compliant

Micro compliant pantographs: The creation of Micro Pantographs was a research

endeavor undertaken in the facilities of Brigham Young University The visual representation

of these micro-devices can be seen in Figure 1.23 [9]

Figure 1 23 Pantographs with micro-compliance

Microgrippers: Microgrippers are compliant tools that allow for the manipulation of

minute particles in the micro and Nano ranges They are characterized by their lack of joints,

as the motion is generated by the deformation of their beams One example of such a tool is

a silicon-based micro gripper, as depicted in Figure 1.24, manufactured through etching and lithography techniques, with thin arms measuring 1 micrometer in width and 3 micrometers

in length

Figure 1 24 A Silicon microgripper [10]

Microgrippers can be fabricated utilizing a micro wire electrical discharge machine (EDM), as depicted in Figure 1.25a The construction of this microgripper involves the utilization of aluminum and spring steel, both of which are amenable to EDM fabrication techniques The actuation of this microgripper is achieved through the employment of piezo motors, as illustrated in Figure 1.25b [11]

Figure 1 25 An aluminum microgripper [11]

Figure 1.26 depicts an alternative form of microgripper that employs a shape memory alloy and grips a 140 micrometer diameter optical fiber The gripper, made of a TiNi alloy, measures 2mm x 5.8mm and was constructed using [12] Shape memory alloys are suitable for use in compliant mechanisms as they possess the ability to recall their geometry, which is facilitated by the material's property of returning to its original shape at a specified temperature after undergoing deformation The metals' ability to recover from significant strain allows for the generation of substantial movement through actuation

Figure 1 26 SMA microgripper [12]

1.3.2 Macro Compliant Mechanisms

When the demand for accurate motion is substantial, macro compliant mechanisms are utilized These mechanisms are larger in scale and more perceptible and functional compared

to micro compliant mechanisms This section will present several instances of macro compliant mechanisms

Compliant Bicycle Brakes: Figure 1.27 illustrates a bicycle brake project produced by

Larry L Howell and his pupils They used flexible beams to replace the bicycle brake joints Complimentary brakes provide exact parallel motion while minimizing noise and wear It also

takes care of the lubrication problem

Figure 1 27 Brake of Bicycle

Bi-stable switches: Macro-scale compliant mechanisms, which are more readily visible

and manipulable than their micro counterparts, can also serve as a viable solution when precision motion is sought These mechanisms come in the form of bistable designs, like those described in the previous section on micro bi-stable mechanisms, and are utilized in a range

high-of applications, including as switches, breakers, clamps, snap hinges, closures, positioning devices, and so on One such example of a macro compliant switch is depicted in Figure 1.28 These mechanisms can be actuated by an external force to transition between their two stable positions, and they do not require any holding energy to maintain their state once in either

position, making them relatively inexpensive and straightforward to fabricate [16]

Figure 1 28 A compliant switch

1.4 Review of the Literature on the Compliant Positioning Stage

Parallel mechanisms, unlike serial mechanisms, have rigorous structures that are necessary for high precision and can minimize the buildup of error As a result, the literature has several methods to the design of high precision micro positioning stages Some of these micro positioning stages, according to the literature, are compliant mechanisms with distinct flexure kinds They've all worked hard to develop the most accurate and controlling mechanism possible for their intended uses

Yang, M.; Zhang, X.; Zhang, C.; Wu, H.; Yang, Y [18] created a unique piezo-driven parallel kinematic, micro positioning 1-DoF stage, as seen in Figure 1.29 Their design consists of three levers (two parallel and one for output) coupled by flexure hinges Piezo actuators were employed to move the system The theoretical analysis, finite element method, and experiment were used to analyze the system's kinematic performance, and the motion linear equation was computed utilizing the linear fitting equations of three approaches The investigation findings revealed that the system had strong strength and dynamic characteristics, as well as high accuracy and linearity in its motion This research has some implications for the design and performance of micro-drive systems

a)

b)

Figure 1 29 Piezo-driven parallel micro positioning 1 DoF [18]

Dang, M.P.; Le, H.G.; Tran, N.T.D.; Chau, N.L.; Dao, T.-P [19] focuses on the design

of a 1-DOF micro positioning stage, which has a novel design for enhanced motion flexibility and simpler force conveyance, as shown in Figure 1.30 The stage is composed of two modules: a displacement amplifier with six levers and a symmetric parallelogram mechanism

To evaluate the kinematics and dynamics of the stage, an analytical approach is used To begin, a kinetostatic diagram is constructed using the pseudo-rigid-body approach The Lagrange technique is then employed to develop a dynamic equation The RSM is used to improve the reaction speed of the indentation system during the optimization of the stage's structure

Figure 1 30 Micro positioning for 1 DoF [1]