Gyroscope Notes and draft

7/27/2019 Gyroscope Notes and draft

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M E 381 I N T R ODUCT I ON T OM I CR O E L E CT R O M E CH AN I C AL SYST EMAARON BURGAZEEM MERUANIBOB SANDHEINRICHMICHAEL WICKMANN

MEMS GYROSCOPESAND THEIRAPPLICATIONS

A STUDY OF THE ADVANCEMENTS IN THEFORM, FUNCTION, AND USE OF MEMSGYROSCOPES


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Table of ContentsINTRODUCTION .......................................................................................................... 3Gyroscope History ...................................................................................................... 3Traditional Gyroscope Function ................................................................................. 3The Move to MEMS ................................................................................................... 3Draper Tuning Fork Gyroscope ...................................................................................... 4Piezoelectric Plate Gyroscope ........................................................................................ 6Introduction ................................................................................................................. 6Physical Description ................................................................................................... 6Fabrication .................................................................................................................. 6Functional Description ................................................................................................ 7Conclusion .................................................................................................................. 8

Laser Ring Gyroscopes ................................................................................................... 9Micro-Laser Gyro ..................................................................................................... 10Absolute Angle Measurement using MEMS Gyroscope.............................................. 12Applications .................................................................................................................. 14Bibliography ................................................................................................................. 18Biographical Sketches................................................................................................... 20

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INTRODUCTION

Gyroscope History

In order to discuss MEMSgyroscopes we must first understandgyroscopes in general and what role theyplay in science. Technically, agyroscope is any device that canmeasure angular velocity. As early asthe 1700.s, spinning devices were beingused for sea navigation in foggyconditions. The more traditionalspinning gyroscope was invented in theearly 1800.s, and the French scientistJean Bernard Leon Foucault coined theterm gyroscope in 1852 [14]. In the late1800.s and early 1900.s gyroscopeswere patented for use on ships. Around1916, the gyroscope found use in aircraftwhere it is still commonly used today.Throughout the 20th centuryimprovements were made on the

spinning gyroscope. In the 1960.s,optical gyroscopes using lasers were firstintroduced and soon found commercialsuccess in aeronautics and militaryapplications. In the last ten to fifteenyears, MEMS gyroscopes have beenintroduced and advancements have beenmade to create mass-produced successful

products with several advantages overtraditional macro-scale devices.

Traditional Gyroscope Function

Gyroscopes function differentlydepending on their type. Traditionalspinning gyroscopes work on the basisthat a spinning object that is tiltedperpendicularly to the direction of thespin will have a precession. Theprecession keeps the device oriented in avertical direction so the angle relative tothe reference surface can be measured.Optical gyroscopes are most commonlyring laser gyroscopes. These devicessend two lasers around a circular path in

opposite directions. If the path spins, aphase shift can be detected since thespeed of light always remain constant.Usually the rings are triangles orrectangles with mirrors at each corner.Optical gyroscopes are a greatimprovement to the spinning massgyroscopes because there is no wear,greater reliability and smaller size andweight.


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The Move to MEMS

Even after the introduction oflaser ring gyroscopes, a lot of propertieswere desired. MEMS vibrating mass

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gyroscopes aimed to create smaller,more sensitive devices. The two maintypes of MEMS gyroscope, discussed inMicromachined Vibrating Gyroscopes:Design and Fabrication, are the tuningfork gyroscope and the vibrating ringgyroscope. In this paper, we will look attwo other types of gyros; the macro laserring gyroscope and the piezoelectricplate gyroscope.

Draper Tuning ForkGyroscope

Advancements andApplications

One of the most widely usedmicro-machined gyroscopes is the tuningfork design from the Charles StarkDraper Lab (Fig 1). The design consistsof two tines connected to a junction barwhich resonate at certain amplitude.

When the tines rotate, Coriolis forcecauses a force perpendicular to the tinesof the fork. The force is then detected asbending of the tuning fork or a torsionalforce (Fig 2). These forces areproportional to the applied angular rate,from which the displacements can be

Figure 1 - The first working prototype ofthe Draper Lab comb drive tuning fork

measured in a capacitive fashion.

Electrostatic, electromagnetic, orpiezoelectric mechanisms can be used todetect the force. [6]

Figure 2: Tuning Fork Physics [6]

Since the development of theirfirst tuning fork gyroscope in 1993, theDraper Laboratory has made significantimprovements to the device. Their firstgyroscope was developed for theautomobile industry. The gyroscope had

command of 1 degree/hr drift, andpossessed 4000 deg/hr resolution. [4]These devices eventually functioned asthe yaw rate sensor for skid control in

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anti-lock braking applications. Tests runon these sensors involve the examiningthe change in bias and error of such overa number of variables. Proper data couldbe retrieved in 0.8 s and sent to thenecessary actuator to cause properbreaking in due time. These systemsneed to operate in a range oftemperatures, specifically from -40 to 80degrees Celsius. Over this range, boththe bias error and the scale factor errorare both quite stable. The bias error isapproximately 2200 deg/h. Scale factorerror was approximately 0.08%. Resultsfrom these tests are shown in Figure 3and 4. [4]

Figure 3: Bias vs. Temperature [4]

Figure 4: Scale Factor vs.Temperature [4]

Since this initial design, theperformance of the tuning forkgyroscope and gradually increased. In1994, a 500 deg/hr resolution wasachieved. The designs in 1997 resultedin resolutions of 100 deg/hr. Driftstability improved an order of magnitudeto 0.1 deg/hr. With these types ofresults, these gyroscopes can beimplemented with near exact datareplication and production. Along withthe increased resolution, the inputvoltage noise was lowered significantly,

leading to a stronger signal-to-noiseratio, providing sensors with the abilityto communicate better with theirdevices. [5]

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Piezoelectric PlateGyroscope

Introduction

While vibrating ring gyroscopesand tuning fork gyroscopes were the firstsuccessful MEMS gyroscopes and arestill the most widely produced, othersuccessful MEMS gyroscopes have sincebeen created. One of these gyroscopes isthe Piezoelectric Plate Gyroscope whichuses a PZT plate as its base. Thismethod, which in the past has been usedto try to build macro-scale gyroscopes, isactually ideal for micro devices. Atmicro levels, an entire plate can be madeof piezoelectric material. It hasadvantages over the common vibratinggyroscopes in that it requires a muchsmaller drive voltage to create readableoutputs.

Physical Description

The piezoelectric plate gyroscopeis very simple in its design. In fact, it ismuch simpler than the ring or forkgyroscopes. There is a piezoelectricplate, which has a length and widthmuch larger than its depth. The platehas electrical leads connected to all 6

sides and sits on top of a thin membraneof a cavity in a silicon wafer. The cavityallows more freedom for the PZT to

vibrate and deform. The leads providethe driving voltage and measure theoutput.

Figure 5: Cross Section of Gyroscope [8]

Fabrication

The following diagrams show abasic fabrication process that could beused to create the piezoelectricgyroscope. To save space not every step

is shown.

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Functional Description

Like other MEMS gyroscope thepiezoelectric plate gyroscope works onthe principle of a vibrating body. In thiscase, the vibrating body is apiezoelectric sheet. The sheet does notvibrate like a plate or fork. Instead thethickness vibrates which oscillates withtime. This requires an AC drivingvoltage applied vertically across theplate, which uses the electro-mechanical

properties of the PZT to create thevibration. Any piezoelectric materialcan be used, but PZT has highpiezoelectric constants, and can be addedat a precise thickness.

[8]Figure 6: Piezoelectric Plate with orthogonaldirections shown

When the vibrating plate isrotated about an axis perpendicular tothe drive voltage, a voltage is producedin the third perpendicular direction. Thisoutput voltage is proportional to theangular velocity. It can be proven thatthe relationship is:

[8]Here VA is the input voltage magnitude,. is the PZT density, . is the input

voltage frequency, t is time, a is the platelength perpendicular to the direction ofrotation, c is the plate thickness, d31 and

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d15 are piezoelectric constants, e11 is thepermittivity constant and O is theangular velocity.

Since the plate has x-y symmetryas shown above, it follows that a singleplate can measure rotation in twodirections. This is an added advantagewhen compared to traditionalgyroscopes, which only measure onedirection of rotation.

Extensive testing has beenconducted on piezoelectric plategyroscopes and the following data hasbeen determined. For a gyroscope withproperties:

The resulting attributes are as follows:

[8]Conclusion

The piezoelectric plate gyroscopeis a feasible alternative to traditionalMEMS gyroscopes. One of itsadvantages is a lower required drivevoltage. However, the sensitivity is onlyabout 38 microvolts, whereas thesensitivity of a ring gyroscope is around200 microvolts [10]. Also, when there isno rotation, traditional gyroscopes comemuch closer to the ideal zero voltsoutput than the piezoelectric plategyroscope, which still outputs up to 100

millivolts.

A major advantage and the onethat could prove most practical is theversatility of the piezoelectric plategyroscope. It can measure rotation intwo directions. In addition, if thedriving voltage direction is switched, thesame device can measure rotation in thethird direction, although with much lesssensitivity. Since this device is easilyincorporated into other IC chips, it couldbe controlled to do more things than a

ring or tuning fork gyroscope, whichrequire three gyroscopes to measurethree rotation directions.

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Laser Ring Gyroscopes

In order to discuss the difficultiesin creating a laser ring gyroscope in themicrometer scale, the theory behind themacroscopic gyroscope must be derived.Below is a picture of a simple lasergyroscope that happens to be in theshape of a triangle rather than a ring. Alaser source outputs two beams travelingin an opposite direction around the ringuntil they reach the detector. Thedetector counts the beat frequency of thecombined light wave. This beatfrequency is directly proportional to theangle of rotation of the gyroscope.

Figure 7: General Ring Laser Gyro

The following formula is derived for anyconstant laser ring gyroscope [1].

4A

(2) ..= O.p

A = area of ringP = perimeter of ring

There are two main sources oferror for laser ring gyroscopes. They arevarying offset bias and a dead band atvery small rotation rates. The offset biasis due to different indices of refraction

for the beam pairs. This is caused bysmall differences in the degrees ofsaturation in the original beams. [2]

Diddams, Atherton and Dielsexperimented with a light scattererplaced in the laser pulses at differentdistances from the detector whilekeeping the gyroscope at rest. Thisscatterer represented a reflection of lightparticles back with the beam travelingthe other direction. They found thatwhen the scatterer was more than 500

microns away from the detector, the beatfrequency was constant and stable. Thewidth of the dead band also showedgood consistency through many tests.When the scatterer was within 100microns, the beat frequency became non

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sinusoidal and therefore very hard tomeasure. When the scatterer was placedwithin 10-30 microns of the detector, thebeat frequency was erratic and noncontinuous.[2]

Figure 8: Beat Frequency vs. Scatter Position

The dead band region is anotherlimiting factor for this type of sensor.When you are at very small turningrates, the frequencies of the two lightwaves are very close to each other.When these frequencies are within acritical value, it creates a phenomenonwhere the frequencies converge towardeach other until they are the same. Thisgives you a false reading of a zeroturning speed when you are actuallymoving at a small angular velocity. [2]

Figure 9: Rotating Rate found by using Beat

Frequency

The following formula gives the deadband (flat part on Figure 9) for a laserring gyroscope.

r.c

(3) O =L 2Ar -backscattering amplitude for material

Micro-Laser Gyro

The miniaturization of a macro-laser ring gyroscope poses manyproblems. The largest problem is withscaling the device down to themicrometer level. The followingequation is the equation relating the beatfrequency to the angular velocity of thegyroscope. [2]

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(4)This formula scales in the followingway:

Beat Freq = (S)* Angular Velocity - 1/S

The scale in the example used aperimeter of 4.84 meters. This wouldhave to be lowered by a factor of 10-4 atleast to put it at 400 micrometers. Thiswould increase the size of theinterference due to backscattered light(1/S) by 104 . It would also provide lessangular velocity sensitivity per beatfrequency by a factor of 10-4 . Thiswould in turn affect the dead band asseen in equation 2.

Dead Band = 1/S^2

Using the same scaling as in theabove example, the resulting dead bandis 108 times bigger. Instead of getting

.25 deg/s drift, a .25*108 deg/s driftresults using the same wavelength oflight.

Now consider changing thewavelength of light. If the wavelengthof light is decreased to provide the samedead band as in the previous example, awavelength that is 10-14 meters, on therange of gamma rays, results. Thesegamma rays are very high energy andwould have to be shielded from any kindof human interaction. This would make

the device very complicated andexpensive for the same quality as amacroscopic laser gyro. This would notbe competitive with the other MEMSgyroscopes explained previously in priceor performance.

Another problem arises withtrying to change the frequency toaccount for a large dead band. The timevarying part of the equation would bemultiplied by 104 no matter thefrequency of light produced. This

creates a time dependant bias frequencythat is very difficult to account for inorder to get the correct beat frequency asshown in Figure 8 defined by the largepeak very close to the detector. In factthis is only the average beat frequencybecause the frequency is changingrapidly and never settles at a final value.

[2]


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Absolute Angle Measurementusing MEMS Gyroscope

Introduction

Measuring the angle using atypical MEMS gyroscope over a periodof time is not possible by integrating theangular rate, due to the presence of biaserrors which would cause a drift. Aninnovative design of a vibratinggyroscope is being developed whichwould directly measure both angle andangular rate. The design is based on theprinciple of measuring the angle of freevibration of a suspended mass withrespect to the casing of the gyroscope.

[11]Background workings of anangular rate MEMS gyroscope

A traditional vibrating mass

gyroscope consists of a mass suspendedby elastic members that allow it to travelin both x and y direction as shown infigure 10. The equations of motion forsuch a system once appropriatelycompensated can be approximated asshown below.

Fig. 10: Schematic drawing of asuspended mass vibratory gyroscope[12]

[12]When experiencing an external angular velocity the 2.x t(...) erm in the 2ndequation causes the y mode to vibrate atthe driven frequency with amplitude thatis proportional to the angular rate. Thevalue of the angular rate can then beobtained by demodulating the y outputsignal.

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Angle Measurement

The design for anglemeasurement is based on the principle ofmeasuring the angle of free vibration ofthe suspended mass with respect to thecasing of the gyroscope. The mass isgiven an initial condition so that itvibrates in a know direction. The angle,., in the global frame can be calculatedby keeping track of the direction ofvibration if the mass in the local frame,given by the angle a, as shown in Figure

11. When the gyroscope is rotated in theglobal frame the mass continues tovibrate in the same direction with respectto the global frame. [11]Fig. 11: mass motion with initial x-axisoscillation [11]

The method relies on the freevibration of the mass; therefore the

effects of damping forces must benegated as it would drive the motion ofthe mass to zero. Energy is suppliedusing actuators, which deliver small

forces to the x and y modes proportionalto the respective velocities. These forcescounteract the effect of damping in thesystem. Due to various difficulties afixed force cannot be selected for thispurpose. A control loop is used insteadto keep the total energy of the systemconstant. The forces counteracting the

damping of the system are continuouslyadjusted using the equations statedbelow:

where E is the energy set point andrepresents the instantaneous energy ofthe system and a is a constant positivegain:

E=

[11]

a steady state of energy function can beachieved close to the desired energy byselecting an appropriate positive valuefor a.

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Angular Rate Measurement

In order to measure the angularrate a sinusoidal excitation (.d) is addedto the steady state equation for the x-axisforce defined earlier, while the y-axisforce remains the same.[11]

When the system undergoes anangular rotation, the excitation term inthe x-axis equation causes vibrationsalong the y-axis at the driven frequencyof .d. The value of the angular rate canthen be obtained by demodulating the y-axis motion at the driving frequency.

In the above system, the x and ysignals obtained from the gyroscopeneed to go through a separate band passfilter at the natural frequency in order todetermine the angle value. Whenrunning the gyroscope at both its natural

frequency and the driving frequency therelative amplitude of the oscillation atthe two frequencies becomes important.Therefore it is necessary to endure thatthe driving frequency is at least an orderof magnitude different from the naturalfrequency.

Conclusion

Contrary to the popular designsof MEMS gyroscopes which can onlymeasure the angular rate and not the

angle due to presence of bias errors, theabove mentioned design can accuratelymeasure the angle of rotation. In orderto make a reliable and practical sensor acomposite nonlinear feedback controlsystem is used to compensate forimperfection induced in the designduring the manufacturing process. Thusthis gyroscope can accurately measureboth angle and angular rate for lowbandwidth applications. [11]

Applications

.Gyroscope-based sensorembedded in a shoe insole

A gyroscope based gait-phasedetection sensor (GPDS) is used inconjunction with a programmablefunctional electrical simulation (FES) tohelp people with a dropped-foot walking


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dysfunction. The GPDS is entirelyembedded in the shoe insole and detectsin real time the four phases during thegait cycle; stance, heel off, swing and

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heel strike. The gyroscope in the GPDSmeasures the angular velocity of the footand the three force sensitive resistorsmeasure the force load at 3 differentlocations. The gait-phase signal isprocessed in the embeddedmicrocontroller and then transmitted inreal time to the electrical stimulatorattached to the affected muscles. Theelectrical stimulations induce musclecontractions in the paralyzed musclesleading to a more physiological motionof the affected leg.

Previous versions of the gait-phase detectors had been insufficientlyreliable in everyday use as they wouldbe affected by non-walking activitieslike standing, shifting the weight fromone leg to another, sitting, etc. Thereforethose designs had to be turned on and offto avoid stimulations during non-walking activities. Also the gyroscope

in this device can be effectively used tomeasure the angle of the foot relative tothe ground and since there is a built inreset mechanism it avoids theaccumulation of drift errors in theintegrated system.

Tests conducted with the systemshow positive results. The GPDS worksrobustly on different types of terrains

with an accuracy level of over 96%,increasing comfort and confidence the

user has in the system. The GPDS hashelped users with dropped-foot walkingdysfunctional to effectively walk fasterwhile feeling safer and less tired at thesame time. Figure 13 shows byillustration the how the FES reduces theexcessive plantar flexion of the footduring the swing phase and provides abetter clearance. [13]

Fig 1 GPDS and the embeddedcomponents [13]

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Fig 13: Illustration of the foot positionduring a gait-cycle under variousconditions [13]

GPS Sensors

With the advancements made onthe Draper tuning fork gyroscope, itbecame obvious that this device could beused for more intricate devices such asguided military munitions and exactGlobal Positioning Devices. Not onlyare these devices considerably accurateat determining positioning and rates ofmotion, they are also low cost tomanufacture and due to their scale, easyto implement in many militaryoperations. Currently, the DraperLaboratory is working in part with theCompetent Munitions AdvancedTechnology Demonstration Programfrom the Office of Naval Research. The

object is to design a munition that isfully GPS aided and is able to flyinertially to prevent countermeasures orsignal jamming from either detonatingthe explosive early, or running it offcourse. A MEMS gyroscope isimplanted in the fuse assembly of thewarhead to sense direction. Joined withan accelerometer, the system is able tocontrol its flight with little adverseconditions. [7]

Fig 14: GPS guided munitions [7]

Inertial Measurement Unit

Honeywell has also used theDraper tuning fork gyroscope design fortheir technology. In 1999, Honeywellacquired the Draper lab technology inMEMS gyroscope design. One ofHoneywell.s major programs is thedevelopment of an Inertial Measurement

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Unit, a unit that can measure the rates ofmotion and displacements of an object inaction. At the time, they had been usingmacroscale gyroscopes, specifically, thering laser gyroscope. This gyroscopewas implemented in the HG1700 systemwhich could function properly andbeyond the original requirements forwhich it was planned. However, thisdevice was too costly, too large, and toohigh performance for the emergingsmaller, gun-launched systems. Byacquiring Draper.s tuning forkgyroscope, a new inertial measurementunit could be developed that was cheaperand smaller. Eventually, the HG1700system was integrated with MEMSgyroscopes from the Draper laboratory,replacing the ring laser gyroscopeclusters. These systems functionedsimilarly to their predecessors, with theexception that they could be madesmaller at an economical cost. Soon

after, the HG1910 was developed withthe use of Honeywell designedgyroscopes, utilizing similar techniquestaken from the Draper laboratories. Thisunit was designed to withstand the rigorsof an in-combat environment. The table

below shows the specifications of theHG1920 which is currently used incombat. [7] Figure 15 shows theexploded view of the HG1920.

HG1920 Specifications

Parameters Goals DeliveredPerformanceSize 10,000 G >10,000GGYRO CHANNELOperationalRange1440 deg/s 1440 deg/sBias, Turn-onerror stability=75 deg/hr 9 . 76 deg/hrBias, In-runError Stability

=50 deg/hr 6 -53 ged/hrAngleRandom Walk=0.5 deg/vhr 0.02 . 0.17deg/vhrScale FactorTurn-on Error=750 ppm 91 . 524 ppmScale FactorIn-Run


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Stability=1000 ppm 90 . 516 ppmG Sensitivity =10.0deg/hr/g=10.0 deg/hr/gMisalignment =1200 -rad 81 . 479 -rad

Figure 15: Exploded View of HG1920

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Conclusion

MEMS gyroscopes could be the next bigsuccess story after accelerometers.Multiple different techniques ofproducing gyroscopes were discussed inthis paper along with a few applications.There is still a lot of room forimprovement in current techniques,especially in reducing drift andincreasing sensitivity. We believe therewill be countless other applicationsdiscovered for MEMS gyroscopes in thecoming years due to their versatility andsize.


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Bibliography

[1] .Design of a Triangle Active Ring Laser 13 m on a Side. Robert W. Dunn AppliedOptics 20 September, 1998. Vol. 37, No. 27. 6405[2] .Frequency locking and unlocking in a femtosecond ring laser with application tointracavity phase measurements. S. Diddams, B. Atherton, J.-C. Diels. AppliedPhysics B: Lasers and Optics Vol. 63 1996. p. 473-480[3] Science and Technology Perspectives: Laser Gyroscopes . The Revolution inGuidance and Control William Siuru Jr.(http://www.airpower.maxwell.af.mil/airchronicles/aureview/1985/may-jun/siuru.html)[4]A. Kourepenis et al, .Performance of Small, Low-Cost Rate Sensors for Military andCommercial Applications,. Charles Stark Draper Laboratory release, (1997).[5]N. Barbour and G. Schmidt, .Inertial Sensor Technology Trends,. Proceedings of the1998 Workshop on Autonomous Underwater Vehicles, 20-21 August, (1998), 55-62.[6]N. Yazdi, F. Ayazi, and K Najafi, .Micromachined Inertial Sensors,. Proceedings ofthe IEEE, Vol. 86, No. 8, (1998) 1640-1659.[7]J. Hanse, .Honeywell MEMS Inertial Technology & Product Status,. Honeywell

Defense & Space Electronic Systems release, (2004).[8] .Design and Analysis of a Micro-gyroscope with Sol.gel Piezoelectric Plate.SmartMaterial Structures. 1999 Vol. 8. 212-217. He, Nguyen, Hui, Lee, Luong.[9] .Preperation of piezoelectric PZT microdiscs by sol-gel method.. IEE Japan Vol.121-E. No. 9. 1999.[10] .Micromachined Vibrating Gyroscopes: Design and Fabrication. Elliott, Gupta,Reed, Rodriguez. December 6th, 2002.[11] D Piyabongkarn and R Rajamani, .The development of a MEMS gyroscope forabsolute angle measurement.. American control conference, May 2002[12] D.A Koester, et. al., .Multi-user MEMS processes introduction and design ru

les,.rev 3, Oct. 1994[13] Ion P.I Pappas, T. Keller, S. Mangold, . A reliable gyroscope-based Gait-PhaseDetection sensor Embedded in a Shoe Insole.. IEEE sensors journal, vol 4 April 2004[14] History of Gyroscopes, Glen Turner. 2004 (http://www.gyroscopes.org/history.asp)19


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Biographical Sketches

Aaron Burg (6/30/1983) is amechanical engineering undergraduatestudent from Cleveland, Ohio. He is anactive participant in intramural ultimateFrisbee. In addition, he is an avid musicconnoisseur. Someday in the future hewill be known only as Dr. Burg and willbe a respected member of hiscommunity.

Azeem Meruani (11/29/1982) is amechanical engineering undergraduatestudent from Karachi, Pakistan. He is anentrepreneur, who seeks innovative waysof video game enjoyment. He plans oncontinuing his engineering education andsomeday taking over the world.

Bob Sandheinrich (3/31/1983) is amechanical engineering undergraduatestudent from St. Louis, Missouri. His

experience includes a long line of menialjobs. He plans include never finding ajob and being a bum on the streets ofEvanston. If you see him, please givehim a quarter.

Michael Wickmann (9/9/1982) is amechanical engineering major fromNorthfield, Minnesota. He is currentlythe oldest member of the group. He is aleading member of the university clubbaseball team and is a ferocious athletein many other sports. He will work for

Azeem someday.

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Gyroscope Notes and draft