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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" in the Micro/Nano World May 3-8, 2010, Anchorage, AK Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 1 University of Florida, Gainesville, FL

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 Analytical and Pseudo-Rigid-Body Model (PRBM) l ti l d P d Ri id B d M d l (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 2 University of Florida, Gainesville, FL

OPTICAL FORCE SENSOR • Device is designed so that input loads are applied to a movable structure • The stiffness of the structure is calculated • I Interferometry determines the displacement of the structure f d i h di l f h • Force is computed using Hooke’s law: F = kx • Many methods to implement interferometry – Michelson k – Fabry-Perot – Sagnac F – Diffraction based Diffraction based (linear optical encoder) • Diffraction method – 2 types [Zhang] – Amplitude diffraction Amplitude diffraction – Phase diffraction • preferred due to higher optical efficiency Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 3 University of Florida, Gainesville, FL

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 photodiode • Displacements cause the index p grating to translate and vary the intensity of the diffracted orders • Changes in intensity measured via F photodiodes h t di d x 0.5*period index grating index grating scale grating light source Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 4 University of Florida, Gainesville, FL

OPTICAL SENSOR CHARACTERISTICS First Order Diffraction Intensity 120 • Sensitivity: change in intensity N = 10 N = 2 with respect to a unit displacement 100 I o ity (%): Normalized to I o • Dynamic Range: total range of 80 motion for which the position can 60 be determined Intensity • Trade off between the two 40 • Both are determined by the 20 number the grating periods under g g p 0 0 illumination 0 20 40 60 80 100 Displacement ( µ m) • Controlled by grating pitch and laser light source diameter g • Sensitivity can be enhanced mechanically [Zhang] Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 5 University of Florida, Gainesville, FL

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 MEMS sensors provide a solution id l ti – Small device and feature sizes – High sensitivity for very small sensing ranges Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 6 University of Florida, Gainesville, FL

WHY OPTICAL MEMS SENSORS • C Capacitive force sensors are available with high i i f il bl i h hi h resolution and on the chip integration • Sun et al . have developed an capacitive force sensor with sub- µN resolution and range of g µ 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 F – With small gap heights or large bias voltages, k pull-in becomes a problem – The voltage-displacement relation is non-linear near pull-in ll i • Optical interferometry provides a means to decouple conflicting design goals • Allows incorporation of capacitive elements for p p self-calibration Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 7 University of Florida, Gainesville, FL

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 emitting laser) i i l ) [Zhang, 2004] – Silicon p-n junction photodiodes – Short distances eliminate needs Sh t di t li i t d for large lenses Advanced Photonix Inc. Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 8 University of Florida, Gainesville, FL

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( w 3 ) • 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 9 University of Florida, Gainesville, FL

ANALYSIS OF 4-BEAM DESIGN • Analytical A l i l – Hooke’s law: F = kx 192 EI  k 3 l • 2-D FEA Comparison of Models: 4 Beam Design 0.012 – Elastic beam elements Elastic beam elements analytical analytical FEA – Zero mass, DC or very low 0.01 frequency operation 0.008 – Nonlinear solver used ce (N) Force 0.006 0.006 • Able to handle large deflections 0.004 • Geometric non-linearities k = 10.8 N/m 0.002 – Static analysis using load steps Static analysis using load steps 0 0 10 20 30 40 50 60 70 Displacement ( µ m) Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 10 University of Florida, Gainesville, FL

A COMPLIANT SOLUTION • Unchangeable parameters  4 – Structural material: LPCVD silicon nitride (Si 3 N 4 )   n t 1  shift • Good optical and stress qualities – In-plane thickness: 1.5 µm • Refraction properties P-P’ *not shown: substrate and scale grating Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 11 University of Florida, Gainesville, FL

ROBERT’S MECHANISM • 4 bar mechanism designed for straight line motion • Certain geometric constraints are necessary: BC     0 AB DC BP CP • Compliant version compatible with coupler point surface micromaching – Revolute joints difficult to Revolute joints difficult to implement in surface micromachining – Issues include • Alignment • Wear • Debris Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 12 University of Florida, Gainesville, FL

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 13 University of Florida, Gainesville, FL

PSEUDO RIGID BODY MODEL • D Developed to bridge rigid-body l d b id i id b d 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 PRBM coefficients ffi i – Characteristic radius factor (  ) – Stiffness coefficient ( K θ ) – Dependent boundary conditions of Dependent boundary conditions of compliant beam EI   2 K K  l [Howell] [ ] Space, Automation, and Manufacturing Mechanisms (SAMM) Laboratory 14 University of Florida, Gainesville, FL