Luận án tiến sĩ design and analysis of multistable compliant mechanisms

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. 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. Millimeter scale polyoxymethylene prototypes of them are fabricated and tested. 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. 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. 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. ii TABLE OF CONTENTS ABSTRACT.ii TABLE OF CONTENTS.iii LIST OF FIGURES .v LIST OF TABLES.ix CHAPTER 1 INTRODUCTION.4 Contant-force bistable mechanism .5 Actuation methods of multistable mechanisms.9 CHAPTER 2 DESIGN OF A BISTABLE MECHANISM .2 Fabrication and Testing .3 Results and Discussions.

23 CHAPTER 3 DESIGN OF A QUADRISTABLE COMPLIANT MECHANISM.2 Fabrication and Testing .3 Results and Discussions .58 CHAPTER 4 DESIGN OF A CONSTANT-FORCE BISTABLE MECHANISM.2 Fabrication and Testing .3 Results and Discussions .88 CHAPTER 5 CONCLUSIONS AND FUTURE WORK.103 Publications during Ph.115 iv LIST OF FIGURES Fig.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 .2 Two stable equilibrium states of the mechanism.3 Four-step operation of the mechanism.4 A schematic of a BM .5 A typical f-d curve of a BM.6 A schematic of a quarter model .7 A mesh for the quarter model .8 F-d curve and potential energy curve based on the finite element model .9 Time responses of the mechanism. (a) Switching from FSP to SSP; (b) switching from SSP to FSP .11 An array of fabricated devices .12 An OM photo of a fabricated device .13 A schematic of the experimental setup .14 Experimental apparatus placed under a high-speed camera .15 Snapshots for forward motion.16 Snapshots for backward motion.1 A ‘ball-on-the-hill’ analogy for a QM, similar to a figure presented by Chen et al.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.4 (a) A schematic of a quarter model. (b) Dimensions of the guide beam and the shuttle mass .5 Flowchart of the optimization procedure.6 A mesh for the finite element model .7 Distribution of the population of several generations in the optimization process .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 .9 Photos of a fabricated QM .10 A photo of the experimental setup.11 Snapshots for forward motion (a-c) and backward motion (d-f) .12 f- δ curves of the fabricated QM for (a) forward, (b) backward motion.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 .14 f- δ curve and maximum stress versus displacement curve of the microscale version of the QM for (a) forward motion; (b) backward motion.1 Schematic of a CFBM and its operational principle.3 (a) A schematic of a quarter model. (b) Dimensions of the guide vi beam and the shuttle mass .4 Flowchart of the optimization procedure.5 A mesh for the finite element model .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.7 (a) A photo of a fabricated CFBM. (b) A close-up view of the flexible hinge .8 A photo of the experimental setup.9 Snapshots for forward motion (a-c) and backward motion (d-f) .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.2 Contributions Firstly, a new method to switch a bistable mechanism (BM) by electromagnetic actuation is presented in this dissertation.

Vibration is utilized to drive the BM on a substrate between its stable positions. 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.

The effectiveness of the 2 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 Compliant mechanism Compliant mechanisms are devices which achieve at least some or all of their functionality from deflection of flexible members.