displacement-amplifying compliant mechanisms for sensor

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  • DISPLACEMENT-AMPLIFYING COMPLIANT MECHANISMS FOR SENSOR APPLICATIONS

    A Thesis

    Submitted for the degree of

    Master of Science (Engineering) IN THE FACULTY OF ENGINEERING

    By

    Girish Krishnan

    DEPARTMENT OF MECHANICAL ENGINEERING INDIAN INSTITUTE OF SCIENCE

    BANGALORE-560012 INDIA

    DECEMBER 2006

  • Dedicated

    To

    My Parents

  • i

    TABLE OF CONTENTS

    ABSTRACT___________________________________________________________ v

    AKNOWLEDGEMENT_________________________________________________ vi

    LIST OF FIGURES ___________________________________________________viii

    LIST OF TABLES ____________________________________________________ xiv

    1. INTRODUCTION___________________________________________________ 1.1

    1.1 Displacement amplifying Compliant Mechanisms __________________ 1.1

    1.2 Evaluation and selection of DaCM topologies ______________________ 1.2

    1.3 Topology Optimization for DaCMs_______________________________ 1.3

    1.4 High-Sensitivity Micro-g Resolution Accelerometers ________________ 1.4

    1.5 A Minute Force sensor Using a DaCM ____________________________ 1.5

    1.6 Organization of the thesis_______________________________________ 1.6

    2. LITERATURE REVIEW ____________________________________________ 2.1

    2.1 Displacement amplifying Compliant Mechanisms (DaCMs) 2.1

    2.1.1 Compliant mechanisms _________________________________________ 2.1

    2.1.2 Displacement amplifying compliant mechanisms (DaCMs) _____________ 2.3

    2.1.3 Optimal Design of Compliant Mechanisms__________________________ 2.4

    2.1.4 Use of DaCMs for sensor applications _____________________________ 2.5

    2.2 Micro-g Accelerometers 2.6

    2.2.1 Introduction to Accelerometers ___________________________________ 2.6

    2.2.2 Micro-g Accelerometers _______________________________________ 2.10

    2.2.3 Force feedback in Accelerometers (Bao, 2000)______________________ 2.11

    2.2.4 Noise in Accelerometers _______________________________________ 2.14

    2.2.5 Evolution of high-resolution, high sensitivity accelerometers __________ 2.15

    2.2.6 Electronic Circuitry for capacitance detection_______________________ 2.25

    2.2.7 Need for mechanical amplification for accelerometers ________________ 2.27

  • ii

    2.3 Force sensor for micro-manipulation of Cells 2.27 2.3.1 Introduction to force sensors for micro-manipulation _________________ 2.27

    2.3.2 Use of DaCMs as force sensors __________________________________ 2.29

    2.4 Closure 2.29

    3. OBJECTIVE COMPARISON OF VARIOUS DACMS FOR SENSOR APPLICATIONS _____________________________________________________ 3.1

    3.1 Introduction ___________________________________________________ 3.1

    3.2 DaCMs for Sensor applications ___________________________________ 3.2

    3.3 Spring-mass-lever Model of a sensor with a DaCM___________________ 3.3

    3.4 Objective comparison of some DaCMs _____________________________ 3.8

    3.4.1 Comparison criteria ____________________________________________ 3.8

    3.4.2 Specification for Analysis ______________________________________ 3.11

    3.4.3 Observations and insights ______________________________________ 3.12

    3.4.4 Figure of merit _______________________________________________ 3.18

    3.4.5 Selection vs. Optimization ______________________________________ 3.19

    3.5 Closure ______________________________________________________ 3.23

    4. DESIGN OF A MICRO-G ACCELEROEMTER WITH A DACM __________ 4.1

    4.1 Introduction__________________________________________________ 4.1

    4.1.1 General layout of an accelerometer with a DaCM _________________ 4.1

    4.2 Capacitance detection__________________________________________ 4.3

    4.3 Selection of a DaCM for an accelerometer_________________________ 4.7

    4.3.1 Selection of a DaCM for Chea et al.s (2004) micro-g accelerometer __ 4.8

    4.3.2 Selection of a DaCM for a bulk-micromachined accelerometer for the

    DRIE process ____________________________________________________ 4.12

    4.4 Design of an accelerometer with a DaCM for a given chip area ______ 4.15

    4.4.1 Suspension stiffness ( sk ) ___________________________________ 4.15

    4.4.2 Proof mass ( M ) __________________________________________ 4.15

    4.4.3 Size of the mechanism ( mechl )________________________________ 4.16

  • iii

    4.4.4 Optimization of the accelerometer for a given chip-area ___________ 4.17

    4.5 Design of sense combs and external suspension____________________ 4.18

    4.5.1 Cross-axis Sensitivities _____________________________________ 4.18

    4.5.2 Design of the sense combs __________________________________ 4.20

    4.5.3 External sense-comb suspension______________________________ 4.24

    4.6 Analysis of the accelerometer designs____________________________ 4.27

    4.7 Closure _____________________________________________________ 4.28

    5. SYSTEM LEVEL SIMULATION OF A MICRO-G BULK-MICROMACHINED ACCELEROMETER __________________________________________________ 5.1

    5.1 Introduction__________________________________________________ 5.1

    5.2 Mechanical components: Mode-Summation Method ________________ 5.2

    5.2.1 Calculating the Damping Coefficients __________________________ 5.6

    5.2.2 Mechanical noise in the system _______________________________ 5.7

    5.3 Capacitance detection circuit____________________________________ 5.8

    5.4 Closed-loop response _________________________________________ 5.10

    5.4.1 Feedback combs __________________________________________ 5.10

    5.4.2 Design of the PID controller (Kraft, 1997)______________________ 5.13

    5.5 Closure _____________________________________________________ 5.22

    6. TOPOLOGY OPTIMIZATION OF DACMS FOR SENSORS______________ 6.1

    6.1 Introduction__________________________________________________ 6.1

    6.2 Topology optimization for sensor applications _____________________ 6.2

    6.2.1 Objective functions and constraints used for topology optimization ___ 6.3

    6.3 Optimality Criterion with non-linear constraints ___________________ 6.7

    6.3.1 Sensitivity analysis for the Objective functions and constraints ______ 6.9

    6.4 Numerical Examples__________________________________________ 6.12

    6.4.1 Topology optimization of DaCMs with constraints on cross-axis

    displacement and natural frequency ___________________________________ 6.14

  • iv

    6.4.2 Topology optimization of DaCMs for accelerometer applications____ 6.17

    6.5 Closure _____________________________________________________ 6.23

    7. A DISPLACEMENT-AMPLIFYING COMPLIANT MECHANISM AS A MECHANICAL FORCE SENSOR ______________________________________ 7.1

    7.1 Introduction__________________________________________________ 7.1

    7.2 Use of DaCMs as force sensors __________________________________ 7.2

    7.3 Vision based force sensing in micromanipulation of cells_____________ 7.3

    7.4 Force sensor for laparoscopic surgery ____________________________ 7.5 7.4.1 Topology optimization of DaCMs for force sensor application _________ 7.6

    7.4.2 Fabrication Process of the mechanism ____________________________ 7.8

    7.4.3 FEM Analysis of the mechanism using COMSOL__________________ 7.10

    7.4.4 Displacement Sensing Technique (Hall-effect Sensor) ______________ 7.11

    7.5 Experimental set-up to calibrate the force sensor and the DaCM _____ 7.13 7.5.1 Force required to rupture an inflated balloon ______________________ 7.14

    7.6 Closure _____________________________________________________ 7.16

    8. CONCLUSIONS AND FUTURE WORK _______________________________ 8.1

    8.1 Summary ____________________________________________________ 8.1

    8.2 Contributions_________________________________________________ 8.2

    8.3 Future Work _________________________________________________ 8.3

    A. EFFECT OF FABRICATION LIMITATIONS ON THE RESOLUTION OF AN ACCELEROMETER _________________________________________________ A.1

    B DRIE WITH SOI PROCESS FOR FABRICATING THE ACCELEROMETER WITH A DACM ______________________________________________________B.1

    R REFERENCES ____________________________________________________ R.1

  • v

    ABSTRACT The thesis deals with Displacement-amplifying Compliant Mechanisms (DaCMs),

    which use the input force applied at a point to a give amplified output displacement at

    another point with a single elastic continuum. We developed a spring-mass-lever

    model to capture the static and dynamic behavior of DaCMs. We used this model for

    evaluating the topologies of DaCMs for sensor applications based on several criteria,

    and used a combined figure of merit for selection. When none of the DaCM

    topologies in the database are able to meet all the requirements of a new sensor, we

    synthesize a new DaCM using topology optimization. This involves nonlinear

    constraints that were linearized to incorporate them into the optimality criteria

    method, which is used to solve the topology optimization problem. Two applications

    of DaCMs, namely, a bulk-micromachined high-resolution accelerometer and a

    minute mechanical force sensor are pursued in this work.

    (i) The addition of a DaCM to a micromachined accelerometer increases the

    sensitivity along the intended axis by an order of magnitude or more. But it has the

    undesirable side-effect of increasing the cross-axis sensitivit