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Mechanism Approach for Enhancing the Dynamic Range and Linearity of MEMS y g y Optical Force Sensing

Gloria J. Wiens

Space, Automation and Manufacturing Mechanisms Laboratory Department of Mechanical and Aerospace Engineering University of Florida, Gainesville, FL

2010 IEEE ICRA 2010 IEEE - ICRA International Conference on Robotics and Automation

Workshop: "Signals Measurement and Estimation Techniques Issues in the Micro/Nano-World"

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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in the Micro/Nano World

May 3-8, 2010, Anchorage, AK

OUTLINE

• Introduction and background of MEMS force sensors and interferometry
• Motivation – Why are these devices beneficial
• A look at a current device – focusing on limitations and drawbacks
• A new design that builds upon previous devices

– Analysis techniques

A l ti l d P d Ri id B d M d l (PRBM)

• Analytical and Pseudo-Rigid-Body Model (PRBM)
• FEA
• Optimization
• Latin hypercube design of experiments

– Comparison to other designs

• Integration into systems
• Conclusions

– Discussion of results – Future work

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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OPTICAL FORCE SENSOR

• Device is designed so that input loads are applied to a movable structure
• The stiffness of the structure is calculated

I f d i h di l f h

• Interferometry determines the displacement of the structure
• Force is computed using Hooke’s law: F = kx
• Many methods to implement interferometry

– Michelson – Fabry-Perot – Sagnac Diffraction based

F k

– Diffraction based (linear optical encoder)

• Diffraction method – 2 types

– Amplitude diffraction

[Zhang]

Amplitude diffraction – Phase diffraction

• preferred due to higher optical efficiency

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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OPTICAL DIFFRACTION

• Uses 2 constant period gratings to

change the intensity of a light source

• The scale grating is fixed while
• The scale grating is fixed, while

the index grating is free to move

• The index grating is fabricated

above the scale grating above the scale grating

• While no input is applied the

gratings are aligned

• Displacements cause the index

photodiode

p grating to translate and vary the intensity of the diffracted orders

• Changes in intensity measured via

h t di d

F

photodiodes

index grating scale grating 0.5*period index grating

x

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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light source

OPTICAL SENSOR CHARACTERISTICS

• Sensitivity: change in intensity

with respect to a unit displacement

100 120 First Order Diffraction Intensity Io N = 10 N = 2

• Dynamic Range: total range of

motion for which the position can be determined

60 80 ity (%): Normalized to Io

• Trade off between the two
• Both are determined by the

number the grating periods under

20 40 Intensity

g g p illumination

• Controlled by grating pitch and

laser light source diameter

20 40 60 80 100 Displacement (µm)

g

• Sensitivity can be enhanced

mechanically

[Zhang]

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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MOTIVATION

• Biomedical research

– In vivo experiments (i.e. RNA interference) p ( )

• Determination of required injection forces to

penetrate membrane

• Minimizing cell damage and preserving specimens

– Cancer cell research Cancer cell research

• Investigate mechanical properties of cancer cells
• Compare with healthy cells to distinguish
• Microassembly

– Fabrication yields numerous small parts that require assembly – Assembly forces can range from mN to µN

MEMS id l ti

• MEMS sensors provide a solution

– Small device and feature sizes – High sensitivity for very small sensing ranges

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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WHY OPTICAL MEMS SENSORS

C i i f il bl i h hi h

• Capacitive force sensors are available with high

resolution and on the chip integration

• Sun et al. have developed an capacitive force

sensor with sub-µN resolution and range of µ g about a half a mN

• Some applications may require same µN

resolution over a range of tens or hundreds of mN mN

• Conflicting design goals in the electrical domain

are a drawback for capacitive sensors

– Sensitivity increases with decreasing gap height and increasing bias oltage and increasing bias voltage – With small gap heights or large bias voltages, pull-in becomes a problem – The voltage-displacement relation is non-linear ll i

k F

near pull-in

• Optical interferometry provides a means to

decouple conflicting design goals

• Allows incorporation of capacitive elements for

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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p p self-calibration

INTEGRATION OF OPTICAL COMPONENTS

• A majority of optical sensors

use “off the chip” components

• Emerging technologies can be

applied to realize integrated systems

– VCSEL (vertical cavity surface i i l ) emitting laser) – Silicon p-n junction photodiodes Sh t di t li i t d

[Zhang, 2004]

– Short distances eliminate needs for large lenses

Advanced Photonix Inc.

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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CURRENT STATE-OF-THE-ART DESIGN

• Index grating is suspended by 4 simple beams
• Force-displacement relation is linear for small displacements: ~ 10% of L
• During small deflections bending is the dominant mode

g g

– Function of area moment of inertia (I): ƒ(w3)

• Beyond small deflections axial stretching becomes dominant

– Function of cross-sectional area (A): ƒ(w) Function of cross sectional area (A): ƒ(w)

• Thicker beams have more linear characteristics than thinner beam, but are

also much stiffer

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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ANALYSIS OF 4-BEAM DESIGN

A l i l

• Analytical

– Hooke’s law: F = kx

• 2-D FEA

Elastic beam elements

0.012 Comparison of Models: 4 Beam Design analytical

3

192EI k l 

– Elastic beam elements – Zero mass, DC or very low frequency operation – Nonlinear solver used

0.006 0.008 0.01 ce (N) analytical FEA

• Able to handle large

deflections

• Geometric non-linearities

– Static analysis using load steps

0.002 0.004 0.006 Force k = 10.8 N/m

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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Static analysis using load steps

10 20 30 40 50 60 70 Displacement (µm)

A COMPLIANT SOLUTION

• Unchangeable parameters

– Structural material: LPCVD silicon nitride (Si3N4)

• Good optical and stress qualities

1

4

shift

n t    

– In-plane thickness: 1.5 µm

• Refraction properties

P-P’

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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*not shown: substrate and scale grating

ROBERT’S MECHANISM

• 4 bar mechanism designed for

straight line motion

• Certain geometric constraints are

necessary:

AB DC 

BP CP 

BC  

• Compliant version compatible with

surface micromaching

– Revolute joints difficult to

coupler point

Revolute joints difficult to implement in surface micromachining – Issues include

• Alignment
• Wear
• Debris

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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COMBINATIONS OF THE MECHANISM

• Combination in series eliminates need for

revolute connection at coupler point

• Allows entire device to be monolithically

fabricated

• Index grating can now rotate and translate
• Adding mechanism in parallel eliminates

g p rotational degree of freedom

• Mirroring device reduces errors in straight-

line motion caused by structural errors y

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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PSEUDO RIGID BODY MODEL

D l d b id i id b d

• Developed to bridge rigid-body

mechanism theory to compliant mechanisms

• Analytical method to model compliant

y p mechanisms using typical rigid-body kinematics

• Replaces compliant members with

equivalent system of rigid links equivalent system of rigid links, revolute joints and torsional springs

• Resulting mechanism has the same

force-displacement relation PRBM ffi i

• PRBM coefficients

– Characteristic radius factor () – Stiffness coefficient (Kθ) – Dependent boundary conditions of Dependent boundary conditions of compliant beam

2 EI K K l 





[Howell]

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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[ ]

APPLYING PRBM

   

3 2 2 2 3 3 3

cos cos sin cos 1 2

S

• r

x N r b               

     

32 2 42 32 4 42 32 3 3 2 2 32 3 3 3

2 2 1 2 sin sin cos 2

T S

h h h h h F N K r N r h b                               

NS number of Robert’s mechanisms in series (2 in this case) final angle of link i (i = 2,3,4) initial angle of link i (i = 2,3,4)

i



io

 NT total number of Robert’s mechanisms (8 in this case)

   

2 4 2 32

sin sin r h r      

   

2 3 2 42

sin sin r h r      

x F

i

  change in ith link angle from initial position (i = 2,3,4)

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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 

3 3 4

sin r   

 

4 3 4

sin r   

FEA MODELS

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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OPTIMIZATION

P ti l ti i ti (PSO)

• Particle swarm optimization (PSO)

is a population based stochastic method

• Objectives to minimize

Objectives to minimize

– Stiffness: slope of the force- displacement curve – Non-linearity: adjusted R-square value (ARS) best fit metric value (ARS), best fit metric

• Constraints

– Max stress < yield stress – Feasible configuration g – Geometric

( ) * (1 )*(1 )

b

f X slope ARS      

3 3 2

( ) (1 ) (1 ) [ , , , , ]

• bj
• f

X slope ARS X w l r b     

   

3 3

, , 1 ,300 1 ,10 l r b m m w m m      

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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20 ,90

• 

   

 

I i i l i i i d d f 70

OPTIMIZATION RESULTS

• Initial optimization conducted for 70 µm

displacement range

– 1.53, 222.0, 108.3, and 261.0 µm for w, l, r3 and b3, respectively – Initial angle for link 2 (θ2o) = 72.5° – Stiffness: 0.26 N/m – ARS: 0.9997 – Max displacement before failure: 200 µm Max displacement before failure: 200 µm

• Non-linearity

– Measured in % of full scale output (%FSO) R i f i d i i d

F

– Ratio of maximum deviation compared to

• verall range for a set of data

– Generally 3%FSO or below is acceptable

disp

100% maximumdeviation NL full scaleoutput  

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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EFFECTS OF GEOMETRY

FEA Comparison: Changing Widths 3 3.5 4 x 10

−5

FEA Comparison: Changing Widths w=1µm w=2µm w=1.53µm NL = 0.071%

w (µm) Max displacement (µm) Max Force (µN) FEA stiffness (N/m) NL (%FSO)

1.5 2 2.5 Force (N) NL = 0.020%

1.53 200 53.4 0.26 2.8

10 20 30 40 50 60 70 0.5 1 Displacement ( m) NL = 0.024%

change variable change stiffness w

─ ─

2.0 170 98.6 0.57 1.73 2.5 138 153 1.10 0.98

Displacement (µm)

l

+ ─

r3

─ ─

b3

+ ─

3.0 118 222 1.88 0.74

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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PARAMETRIC STUDY

−5

FEA Comparison: Varying Length L

−5

FEA Comparison: Varying Length r 6 7 8 9 x 10

−5

FEA Comparison: Varying Length L L 1.2*L 1.1*L 0.9*L 0.8*L NL =1.5 %FSO 5 6 7 x 10

−5

FEA Comparison: Varying Length r

3

r3 1.2*r3 1.1*r3 0.9*r3 0.8*r3 NL =2.2 %FSO NL =14.1 %FSO 2 3 4 5 Force (N) 2 3 4 Force (N) 0.8*r3 50 100 150 200 1 Displacement (µm) NL =2.5 %FSO 50 100 150 200 1 Displacement (µm) 7 x 10

−5

FEA Comparison: Varying Length b

3

8 x 10

−5

FEA Comparison for Varying Initial Angle of Link 2: θ2o 4 5 6 (N) b3 1.2*b3 1.1*b3 0.9*b3 0.8*b3 NL =4.8 %FSO 5 6 7 e (N) θ2o= 72.5deg θ2o= 77.5deg θ2o= 75.0deg θ2o= 70.0deg θ2o= 67.5deg NL =3.0 %FSO NL =42 %FSO 1 2 3 Force (N NL =2.5 %FSO 1 2 3 4 Force (

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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50 100 150 200 Displacement (µm) 50 100 150 200 Displacement (µm)

REVISED OPTIMIZATION

• Parametric study revealed optimal design

dependent on displacement range

• Refinement of optimization algorithm

p g

– Initial PSO employed FEA within algorithm – Expensive function and time consuming – Latin hypercube design of experiments used

 

min 1 300

sensor

k l b

Latin hypercube design of experiments used to eliminate FEA and approximate NL

• Define a cubic polynomial in 4 variables
• 3 link lengths and width selected

   

3 3

, , 1 ,300 1 ,10 l r b m m w m m      

• 35 unknown coefficients, 70 FEA simulations
• Polynomial ARS = 0.95
• Adjustment to problem statement

2

72.5 3%

• calc

failure

    



j p

– Modified objective function – Placed non-linearity as constraint – Changing constraint tolerance generates

3% NL 

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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g g g Pareto chart

PARETO OPTIMAL RESULTS

• New optimization conducted for 200 µm

displacement range

• Non-linear constraint varied from 3 to 0.5%FSO in

0.5 increments

• Non-linear constraint: 3 to 1%FSO

– 1, 300, 80, and 300 µm for w, l, r3 and b3,

 

3 3

min , , 1 ,300

sensor

k l r b m m   

3 3

respectively – All geometric constraints active – NL and max stress constraints not active

   

3 3 2

, , , 1 ,10 72.5 w m m       



– Stiffness: 0.029 N/m

• Non-linear constraint: < 1%FSO

– 1, 295, 116, and 300 µm for w, l, r3 and b3,

2

72.5 3%

• calc

failure

NL     

3 3

respectively – NL constraint has become active – Stiffness: 0.033 N/m

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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COMPARISON OF DESIGNS

NEW DESIGN ATTRIBUTES

• Larger linear range

x 10

−3

FEA Comparison of Designs

• Very small stiffness without

compromise of linearity

– Higher sensitivity

i i i li i

3 3.5 4 Roberts 4−Beam

• Minimizes compliance in

remaining 5 DOF

– Reduces optical errors

• Combination of mechanisms

1.5 2 2.5 Force (N) linear range of 4−beam design

• Combination of mechanisms

reduces measurement error due to structural variations

• Over etching of compliant

0.5 1

Over etching of compliant members can be compensated via experimental calibration

5 10 15 20 25 30 35 −0.5 Displacement (µm)

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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CONCLUSIONS

• Optical force sensor

– Compliant mechanisms enhances sensor characteristics Compliant mechanisms enhances sensor characteristics

• Increased linear range
• High sensitivity via smaller stiffness
• Allows optics to be setup for greater dynamic range
• Robustness with respect to fabrication errors
• Reduction in cross-axis sensitivity

– Versatile platform

• Selection of geometric parameters can yield devices with varying characteristics
• Foundation for potential use in other areas such as microassembly

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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FUTURE WORK

• Experimental validation

– Verify FEA results – Test effects of fabrication process

• Dynamic analysis

– Update model to include mass properties – Determine natural frequency and resonance modes Determine natural frequency and resonance modes – Feasibility for high frequency applications and actuation

• Integration of components

Eli i t l l d l – Eliminate large laser source and lenses – Single or multi-chip design – Allow for inclusion in a lab-on-chip setup

l hi h d f f d

• Explore higher degree of freedom sensors

– 2DOF, 3DOF or 6DOF

• Patent Application in progress

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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pp p g

System Integration of Sensing

DEVELOPMENT OF A COMPLIANT ROTARY DEVELOPMENT OF A COMPLIANT ROTARY-

• TO

TO TRANSLATIONAL TRANSMISSION TRANSLATIONAL TRANSMISSION TO TO-TRANSLATIONAL TRANSMISSION TRANSLATIONAL TRANSMISSION MECHANISM FOR A MICRO MECHANISM FOR A MICRO-

• PARALLEL

PARALLEL KINEMATIC MECHANISM KINEMATIC MECHANISM

Jessica R. Bronson Jessica R. Bronson1, Gloria J. Wiens , Gloria J. Wiens2, Irene Fassi , Irene Fassi1

1 ITIA CNR I

tit t f I d t i l T h l i d A t ti

1 ITIA-CNR, Institute of Industrial Technologies and Automation

National Research Council, Italy irene.fassi@itia.cnr.it

2 Department of Mechanical and Aerospace Engineering

U i it f Fl id USA

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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University of Florida, USA: gwiens@ufl.edu

3DOF Micro-PKM

• Goal: 3DOF micromanipulator

for precise micro/nano positioning

• Applications: manufacturing,

assembly, teleoperation, biomedical devices, and optical , p positioning

• Challenges: adhesion, friction,

dimensional inaccuracies and

• 1DOF

electrostatic actuator

dimensional inaccuracies and binding in the joints

• Approach: Integrate electrostatic

rotary actuator into micro PKM

• 3DOF PKM
• Compliant

linkage design

Fig 4. Rigid body slider- crank transmission

rotary actuator into micro-PKM device using a rotary-to- translation transmission based on a compliant slider-crank

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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transmission mechanism.

a compliant slider crank mechanism.

Transmission Design

Actuator Performance and Sensing Actuator Performance and Sensing Compliant Slider Compliant Slider-

• Crank Design

Crank Design

• Evaluate actuator

f

• Transmission ratio for

crank-linkage

• Robert’s mechanism

slider system performance using PRBM and FEA

• Incorporate optical

sensing into slider for control feedback

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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Design of Fixturing and/or Manipulation Devices

THRUST: Development of a technology suite for micro/mesoscale manufacturing utilizing micromanipulation and positioning devices – mechanisms / robotics

• Material Handling and Fixturing

– Precision Positioning and Manipulation – Mechanically Adaptive Tooling – Dynamic Fixturing – Integration of MEMS Devices

Pin 2a Tol, Wiens, Schueller, 2003 Culpepper 1b

1a

2a 2b

Pin 1b

Pin 2a Pin 2b Pin 4

Memspi.com 0.8 mm x 0.8 mm Pin 1b

[Wiens & Gustavo, 2007]

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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Bi and Zhang, 2001

Mechanically Adaptive Tooling – Monolithic

Micro-manipulator Monolithic Design Features:

Modular fixture elements – minimize fabrication errors (e.g., joints) Mechanically adaptive – governed by the underlying physics of the compliant elements and parallel kinematics elements and parallel kinematics Mechanically adjusting the fixture device enables tuning of the kinematics and dynamics  passive and active control

M i l t

  Micro machine tool stage courtesy of Jun Ni S.M. Wu Manufacturing Research Center The University of Michigan, Ann Arbor, MI

Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory University of Florida, Gainesville, FL

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y p

• f tool-part interface dynamics

Macro-manipulator