Sensor and actuator considerations for precision, small machines: a review

Transcription

1 UCRL-JRNL Sensor and atuator onsiderations for preision, small mahines: a review S. T. Smith, R. M. Seugling April 1, 005 Preision Engineering

2 Dislaimer This doument was prepared as an aount of work sponsored by an ageny of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, epress or implied, or assumes any legal liability or responsibility for the auray, ompleteness, or usefulness of any information, apparatus, produt, or proess dislosed, or represents that its use would not infringe privately owned rights. Referene herein to any speifi ommerial produt, proess, or servie by trade name, trademark, manufaturer, or otherwise, does not neessarily onstitute or imply its endorsement, reommendation, or favoring by the United States Government or the University of California. The views and opinions of authors epressed herein do not neessarily state or reflet those of the United States Government or the University of California, and shall not be used for advertising or produt endorsement purposes.

3 Sensor and atuator onsiderations for preision, small mahines: a review Stuart T. Smith, Rihard M. Seugling Center for Preision Metrology, UNC Charlotte, Charlotte, NC 83 Lawrene Livermore National Laboratory, Livermore, CA Abstrat This artile reviews some design onsiderations for the saling down in size of instruments and mahines with a primary aim to identify tehnologies that may provide more optimal performane solutions than those, often established, tehnologies used at marosopi, or onventional, sales. Dimensional metrology within emerging appliations will be onsidered for meso- through miro- down to nanometer level systems with partiular emphasis on systems for whih preision is diretly related to funtion. In this paper, attention is limited to some of the more fundamental issues assoiated with saling. For eample, atuator work or power densities or the effet of noise on the sensor signals an be readily evaluated and provide some guidane in the seletion for any given size of devie. However, with redutions in sale these parameters and/or phenomena that limit performane may hange. Within this review, the authors have tried to assess these omple inter-relationships between performane and sale, again from a fundamental perspetive. In pratie, it is likely that the nuanes of implementation and integration of sensor, atuator and/or mehanism designs will determine funtionality and ommerial viability of any partiular system development. Corresponding author [email protected] This work was performed in part under the auspies of the U.S. Department of Energy by University of California, Lawrene Livermore National Laboratory under ontrat No. W-7405-Eng-48. 1

4 1.0 Introdution Although, small-sale mahine tools and instruments, suh as lathes, have been built for many years in the wath-making and other industries, a limited number of these systems have been inorporated into modern manufaturing. Most of the small sale mahine tools and instruments are merely a saled down version of a onventional mahine. Typially the auray or preision of these small mahines is no better, more often worse, than that of high-quality maro mahines/instruments. In an effort to identify areas of future researh, fundamental onsiderations are used to assess the fidelity of possible approahes to ommon design problems. At etremes of saling, it is obvious that some requirements of mahines and instruments suh as primary atuation methods or position sensing, for eample, may be best ahieved using different tehnologies. It is important that designers beome aware of both the available tehnologies as well as the relevant performane measures as a funtion of dimensional sale. With this in mind, it will then be possible to identify transitions in sale at whih different tehnologies will provide a more optimal solution to a design need. Key features ommon to the mehanial systems being onsidered in this review are the ability to provide work in a ontrolled manner and the use of sensors for feedbak of proess ondition, partiularly relative motions. Based on the fous of saling down, two major mahine requirements are disussed, these being; atuators to provide position and/or generate work and sensors for deteting surfaes and measuring relative motions. The dimensional sales of the systems lassifiations referred to in this tet are 1. Meso-systems, being intermediate between human sale devies and mirometer mehanisms, implies that major dimensions of suh a system will typially be measured in millimeters.. Miro-engineering is the intermediate region in whih mirometers are more sensibly used to speify funtional toleranes. This length sale is often onsidered to inorporate MEMS proessing.

5 3. Nano-engineering is onsidered to be any proess resulting in devies of defined struture or assembly in whih the nanometer is the most sensible unit for speifying dimensions or toleranes. Preision at marosopi sales is usually onsidered to start with range to auray, or range to resolution performane at around 1 part in 10 5 or better. A similar riterion applied to meso-systems immediately implies that, if preision is to be maintained, total errors should be below 10-8 m or so. In pratie, eonomis ditates that suh high preision only be maintained when absolutely neessary for the funtion of the devie. Currently, it is our eperiene that, when assembling small mahines using available small parts, tolerane stak-up often leads to unaeptable degradation of performane. In many proesses, to ontrol to the relevant preision will require development of metrology and atuation systems of onsiderably better performane than urrently available from marosopi devies. Consequently, these simple onsiderations indiate that dimensional metrology and mehanism design for small-sale mahines must ahieve reliable measurement and positional auray at, or approahing, nanometer levels. It is possible that, as the size of systems redue; major differenes are likely to inlude the following. 1. It may be viable to inorporate metrology systems within manufature and/or assembly.. There are likely to be more metrology systems, possibly one for every devie. 3. It must be possible to manufature these heaply and utilize automated assembly. 4. Power onsumption will be low while, for systems with inherent losses, effiieny will be diffiult to maintain or improve. 5. New, or onsiderably more ompat, methods of ommuniation and data handling will be required. Connetors and interfaes often aount for a major fration of the volume of a iruit. 3

6 6. It will be neessary to ahieve higher bandwidths and resolution than normally required of maro-sale metrology instruments. 7. Alignments of moving aes and subsequent errors will be partiularly diffiult to adjust and measure. 8. Measurement frames enompassing the whole instrument may not add signifiant ost and, being small, may be relatively insensitive to environmental variations. 9. Volumetri dimensions for measurement systems and fores imposed by the sensing devies should be low relative to the fores of the proess. A question that has not, in our view, reeived suffiient attention is the distintion between these different realms of tehnologial endeavor. In pratie, it is both logial and, probably, fair to say that we are onsidering a ontinuum of omponent sales inorporated into any modern mahine. Currently, it is ommon to distinguish different sales by the proesses used in manufature. As manufaturing and assembly proesses develop and adapt, it is likely that these distintions will be less lear and designers will be required to inorporate tehnologies overing all dimensional sales as a matter of ourse. However, there are important features to be onsidered as dimensional sales redue. Primary among these are 1. There is a ertain ut-off after whih the use of manual assembly, that has been spetaularly useful and essential in the development of tehnologies so far, is no longer viable.. Phenomena within mehanisms that produe signifiant mehanial fores may hange (i.e. ontat fores, adhesion fores, menisus effets, eletri dipoles, van der Waals and Casimir fores) thereby requiring additional onsideration in the alulation of two-body surfae interations. 3. Saling an hange the relative dynamis of phenomena. For eample heat transfer is often onsiderably slower than mehanial motion at maro-sales 4

7 while thermal agitation might be the fastest means of providing motile fores at moleular levels. From another perspetive, thermal epansion, whih is a major limiting influene on possible preision in a large mahine, may be insignifiant at smaller dimensions. 4. As the net removal or deposition volumes redue, other manufaturing proesses, redutive or additive, previously onsidered too slow, may provide eonomi prodution rates. Suh onsiderations may provide a guide to favorable saling in the seletion of proesses and omponents. Consider a mahine or instrument arriving in a bo weighing approimately 50 kg or less, able to fit sparingly on a desktop and apable of produing or measuring parts with a preision of 1 part in 10 6 given a work volume of several m 3. As already mentioned, given the preision stated, the resolution of the mahine or instrument would have to be on the order of tens of nanometers over entimeter ranges. The onept seems very straight forward given the advaned tehnology of today. However, why don t these types of mahines show-up in manufaturing plants around the world? Simply saling down urrent tehnologies used in modern omputer ontrolled mahine tools or instruments would initially give the impression of providing for urrent manufaturing needs. However, this may not be viable beause the omple nature of the interrelated physial and hemial interations at different sales often urtails the designer s ability to shrink a omple mahine/instrument without areful onsideration of how the redution-to-pratie of suh a system would perform under real operating onditions. Suh issues are beyond the sope of this review. However, to ahieve preision, small atuator and sensor systems are neessary enabling tehnologies of meso- and smaller sale systems. Fortunately, there are limited numbers of possibilities for these and an assessment of the relative merits of available options in terms of the effets of saling is presented in this review. Atuator methods urrently onsidered inlude; piezoeletri, eletrostati, eletromagneti, magneto-stritive, hydrauli/pneumati, thermal and shape memory. 5

8 One partiular measure of the fidelity of these atuators is the theoretial maimum amount of work and/or power that an be produe per unit volume oupied by the atuator (alled the work density or, when saled by the dynami bandwidth, power density). Considering speifi implementations it is found that some of these methods maintain performane (piezo-eletri, hydrauli, eletrostati) as sales redue while eletromagneti atuators tend to ehibit redued work density and thermal-based atuators appear to improve. Identifiation of the sales at whih different tehniques dominate will help the designer to selet the appropriate tehnology for a given appliation. Suh analysis also provides information about other parametri saling fators suh as drive voltage amplitudes, fores et. A number of implementation issues will also be onsidered. A similar approah has been applied to sensors for small-sale systems suh as optial (line sale, interferometri, diffrative, position sensitive detetors) and eletromagneti. In this later ategory it is neessary to split the ategories into transduers and displaement sensor systems. In our study we have attempted to identify the relevant saling parameters and assess their relative influene as sale redues..0 Displaement sensors.1 General onsiderations Displaement sensors may be onsidered any transdution method that results in a deterministi variation in output for a hange in relative position between two objets. Outside of ost, in terms of performane measures signal to noise, repeatability and stability tend to be the most important parameters for the assessment of potential preision. In many ases a smooth and ontinuous variation of output with displaement will provide adequate means for the determination of relative displaements. Periodi rulings an be used with most of the onsidered sensing methods to enable an inrease in preision by effetively repeating the short-range performane while inreasing total range in proportion to the number of periods. However, in this ase, auray also depends upon the auray of the periodi ruling. For eample, in optis it is possible to 6

9 eploit near field probes to read a grating of sub-wavelength pith, while using apaitane it is possible to use an almost arbitrarily small tip [1, ] and again read from a periodi struture. Magneti sensing from a periodi magneti struture is ommonplae in the magneti data storage industry and it is possible to disriminate sub-mirometer magneti features in some ases. It is not always neessary that the rule have eat periodiity and in some ases it is possible to read displaements from a random pattern of known harateristi leading to a pseudo-absolute sale. However, ommon to most of these methods is the requirement for the sensing element to be in near proimity to the sale and usually with a separation omparable to the finest features on the sale (diffrative sensors that effetively average over many lines of a grating represent an eeption). Often times these are referred to as near-field probes and represent a generalized approah to small-sale (often highly loalized), long-range position sensors. In this ase, there will be onstraints on the neessary preision of aligning the sale with that of the moving platform to provide suffiient signal ontrast during traverse. It is also ommon to utilize multiple measurements of the periodi grating with a lateral phase separation to enable amplitude independent, diretionally sensitive measurement of displaement. Again, the preision of suh tehniques are predominantly limited by signal ontrast. Other near-field phenomena are adequately represented by the sensing elements ommonly used in sanned probe mirosopy utilizing ontat based or near-surfae interations suh as eletrostati, tunneling, van der Waal, menisus, Casimir, magneti resonane, optial, ion ondutane, thermal, squeeze-film and piezoeletri. Of eah of these phenomenologial interations there are a large variety of methods for onditioning the signals to derive different surfae interation information. In many ases, ombinations of these interations are either eploited or impinge upon the interpretation of the measured signals.. Optial A omprehensive study of the methods and tehniques for optial measurement of displaement ould fill libraries. In this setion we will restrit our attention to only those fators affeted by saling to small size. In partiular, as the mehanisms redue from 7

10 meso- to miro- sale, the size of omponents will typially be omparable to the wavelength of visible light. Whether or not this imposes pratial limitations on optial position measurement methods will be seen in the future...1 Laser interferometry Ignoring tehnial error soures, the fundamental limits to interferometer resolution are determined by noise in the laser soure and the detetors [3, 4]. Mathing both noise soures to produe an equal ontribution, the bandwidth, B, limited resolution in displaement d an be shown to be h B d, (1) πηnep where h is Plank s onstant, is the veloity of light in a vauum, η is the quantum effiieny of the detetor and NEP is the noise equivalent power of the detetor. Using ommerially available detetors a noise level of pm over bandwidths of many khz are theoretially possible. In pratie, there are a large number of other fators that limit auray and resolution in the implementation of a partiular interferometer method. For eample, most ommerial interferometers utilize frequeny splitting with eah frequeny traversing the two paths within the interferometer. These are reombined and the Doppler shifted beat frequeny used as a measure of displaement. The use of polarizing optis and imperfetions in the assembly or optial omponents often lead to errors that are onsiderably larger than those due to detetion and laser noise [5]. At meso- and miro-sales, interferometer pakages will require small optis to ompatly integrate within a system. As well as the usual environmental effets suh as orretions in air for pressure, humidity and temperature, there is also aperture orretion given by [6] R s s f Δ =, () where R is the radius of the soure (aperture stop or ore of fiber-opti light guide), s is the measured length hange of the optial path based on laser frequeny and f the 8

11 ollimator foal length. Typially, for a meso- system with laser soure oming from a fiber feed, R 10 5 m, ollimated at f 10 3 m, it is possible that this partiular error term may introdue a limit on preision of the order one part in 10 5 or worse. Other orretion fators depend on the path length in air. Fortunately, while the effets are often more signifiant for interferometers with large ranges, produing path length variations of the order of parts in 10 7, this represents typial unertainties of nanometers for ranges of less than 10 mm. Another problem is the size of the laser soure. Conventional HeNe an provide stabilities of better than 1 part in 10 7 at reasonable ost and with small line width (long oherene length) but the laser tubes are of the order of tens of entimeters in length. Laser diodes with grating stabilization might realize stabilities of the order of parts in 10 7 but are limited in their oherent lengths [7]. Eletrial urrent (or parameter) stabilized diode interferometers with stabilities of the order parts in 10 5 to 10 6 are likely to beome available in the near future [8]. Currently, ranges of greater than 100 μm with measurement unertainties of better than 10 nm are being laimed. In priniple, it is possible to enhane oherene (redue line-width) by filtering through a Fabry-Perot avity. However, it is not lear whether this an be ahieved without resulting in a bulky soure. Interferometers using small optis have been developed by Renishaw, PTB with the frequeny stabilized laser diode, the Tropel small bore interferometer [9], Dunn et al., 00, Swiss-based small optis manufaturers Fisba [10]. Like some of the larger optial interferometers, to keep the bulky laser head out of the mahine and away from harsh environmental effets, the laser beams are fed to the optial system through an optial fiber. In some systems the fiber itself forms an intrinsi omponent of the interferometer, thereby further reduing the size and number of optial omponents. Suh systems are often alled fiber interferometers [11]. White light probes have been developed to measure loal heights on surfaes. In many ways suh systems ontain similar elements to a Mihelson interferometer. In this ase the white light is split between a stationary referene and the seond is foused onto an area of the surfae to be measured. When the two beams are reombined, there 9

12 will be interferene with the intensity depending on the path lengths of the two beams and wavelength that will generally average out to a mean intensity. In the ase where both beams have the same optial path length, all frequenies will onstrutively interfere with similar phase shifts resulting in an inrease in intensity signal. Hene, it is possible, by hanging the path lengths to reord the orresponding hange in intensity at any point and use this information to reonstrut the three dimensional topography of the surfae refletions. However, in suh a system, loal surfae height is transferred to a displaement of the stationary mirror, or referene surfae, relative to the speimen surfae. The point at whih this measurement is triggered is ompliated by the surfae refletive properties of the speimen being measured and the spetral ontent of the illumination. Given these limitations, it is possible to monitor surfae height variations at nanometer levels while sanning surfae heights measured in millimeters. Other advanes in data proessing and system design have enabled dynami sanning of relatively large areas with movie apabilities providing visualization of motions and distortions in mirometer sized mehanisms (MEMS). An alternative white light tehnique is to fous the light to a point on the surfae and monitor wavelength maima upon reombination with a referene. Variants on this inlude onfoal imaging in whih the white light is foused through a lens to reate a wavelength-dependent foal spot. Again monitoring the wavelength on refletion or hasing the foal point refleted bak through a lens enables a measure of the surfae height from a referene. This enables fast measurement of surfae displaements with nanometer resolution over measurement ranges of hundreds of mirometers (range-toresolution of better than 10 5 ) and requiring spot sizes typially less than a millimeter [1]... Linesale interferometry There are a number of suppliers of linesales for the measurement of both linear and angular motion [13]. Generally, sales are supplied in the form of a bolt-on linear sale or in tape form with self adhesive for ease of installation with a separate read head. In general, high-preision linesale interferometers utilize hange in intensities of the various orders of refletion from a finely sribed diffration grating. With any grating, one of the limitations is the size of the illumination spot relative to the spaing of the 10

13 grating,, whih are, in turn limited by the diffration angle, φ n, of orders n governed by the relation nλ sin φ =, (3) where λ is the wavelength of illumination on the grating by the inident beam. Clearly this funtion must be less than 1, thereby setting a limit on the spaing of the grating for a given wavelength and thereby imposing a limit on saling. For eample a grating of 1 μm illuminated with a wavelength of 0.78 μm will have first order diffration peaks at angles of ± 51. Similar limitations apply to transmission gratings. Reent designs have enabled the use of integrated optis for ompat optial sensor systems of major linear dimensions of less than 10 mm. An eample of this is the ommerially available sales of Sony that use 100 nm grating pith with quadrature detetion yielding a signal pith of 400 nm [14]. With suitable phase measurements, resolutions of better than 10 nm are possible. For a suitable geometry of linesale and analyzer gratings at the sensor [15], the phase, Ω, of any individual order of diffration as a funtion the relative position of the grating,, is given by nπ Ω =. (4) The output intensity at the sensor, I o, is proportional to ( 1+ os(ω) ) I. (5) o This orresponds to a periodi variation in intensity at twie that of the grating period,. Other designs may inrease this further to 4 or more variations per period. By monitoring the symmetri orders it is possible to derive a diretionally sensitive measurement of motion of the grating relative to the optial probe. At redued sales, the effet of the relative spot size is to influene the disrimination of different orders. For a spot size oupying N grating periods, the 11

14 intensity of refletion at an angle θ from the point of inidene an be approimated from [16] Nkθ kθ sin sin 4 I f, (6) kθ kθ sin 4 where N is the number of lines in the field of the inident beam and k is the wave number (= π / λ ). It an be seen by plotting the above equation that the disrimination of eah diffration order will diminish with the relative spot size. In general, mainly beause of problems with alignment errors, alibration of sales and fringe interpolation, linesales typially provide 5 nm 10 nm resolution with some etending down to sub-nanometer. At the etremes of performane, it has been shown that linesales an provide displaement repeatability at better than 0.5 nm [17] and alibration failities at PTB in Germany and Mitutoyo in Japan have demonstrated unertainties of better than 30 nm in the alibration of sales longer than 500 mm [18]. Currently, there is a lot of ativity in the field of small-sale optial form and displaement measuring devies. Reent developments inlude pattern reognition of 3-D interferograms, diode laser interferometry [19] and many variants of near-field sanning optial mirosopy and related probing tehniques [0, 1]. It is lear that efforts are being made to derease the size of these measurement systems, while maintaining or inreasing their resolution apabilities...3 X-ray interferometry X-ray interferometry is often referred to, with some voifierous opponents to this, as the -ray equivalent of the Mah-Zehnder interferometer. Being based on the lattie spaing of a rystal, it is intrinsially aurate to better than parts in 10 7, is portable and an be alibrated to two orders of magnitude better than this. Additionally it an operate in air with little influene of refrative inde beause of the low unit derement (i.e. near unity refrative inde) of materials at -ray wavelengths. 1

15 In priniple, it is possible to shrink -ray interferometers to produe a linesale in whih the splitter and mirror need be only large enough to diffrat the -ray beam whih, in turn an be miro-foused to sub-millimeter ross setion. The analyzer would then be limited only by the length of the available rystal. Currently, rystals of near thermodynami perfetion an be obtained in lengths of up to 1.0 m. In pratie, there are onsiderable tehnologial barriers in implementing this interferometer. Most demanding is alignment with angular deviations of better than a few tens of nano-radians and mirometer separation toleranes between the three rystals being neessary. Another onstraint is the speed of the interferometer that is limited by the intensity of available soures and detetor quantum effiieny. The epense, size and safety onsiderations assoiated with high intensity -rays has limited this measurement tehnique to a few researh labs sattered around the world..3 Capaitane Capaitane is ommonly utilized for preision measurement of relative displaement. Like any single degree of freedom system the voltage noise will be fundamentally limited by Brownian motion [] of harge suh that 1 CV 1 q 1 = = kt, (7) C where C is the apaitane, V is the applied voltage, q is the stored harge, k is Boltzmann s onstant ( J K -1 ) and T is the absolute temperature. In pratie, suh a noise flaw ould only be realized if a perfet signal onditioning iruit was to eist. In pratie, apaitane is measured by providing an osillating voltage (or urrent) aross (through) the apaitor and measuring the reatane of the apaitive element. Noise soures in suh a measurement inlude 1. Osillator noise. This is a funtion of the osillators hosen and will manifest as ombinations of amplitude and phase omponents. Typially it is the amplitude that is most diffiult to ontrol. However, this situation is hanging with digital 13

16 osillators. This will be onsidered an inetriable noise present in the arrier signal and having both 1/f and white omponents.. Amplifier noise. It is assumed that the output from a Wheatstone bridge is monitored by an instrumentation amplifier, the input being a single harmoni arrier frequeny. In suh a iruit the amplitude depends on the imbalane of the bridge. Stray apaitane effets will not be inluded in this analysis. The output noise per root frequeny, e s, from the amplifier of voltage gain zero impedane from the soure is given by e = e G, (8) s n V G V with where e n is the input noise typially of the order 1 nv Hz -1/ for a preision instrumentation amplifier at frequenies above 1 khz. Beause we will be using arrier frequenies of 1 khz or greater the 1/f noise omponent is onsidered negligible. Adding a soure impedane s [ e + ktz + ( i Z ) e ] BG n Z s the amplifier output noise is given by e = +, (9) 4 s n s o V where i n is the input noise figure (often less than 1 pa Hz -1/ at frequenies higher than 1 khz), B is the bandwidth, and e o is the osillator noise per root Hertz (assumed to be zero for the present purposes). The above values have been used to derive Figures 1 and and represent the theoretial noise limits as a funtion of geometry. As an eample, onsider a soure of the form of a transformer ratio on one arm and mathed apaitanes making up the other [3]. This an reasonably be modeled a half bridge input to one terminal and a zero soure impedane on the other. The soure impedane is Z Z Z 1/ ω C C 1 o s = =. (10) Z1 + Z 1/ jω C + 1/ jω Co Coω 1 14

17 Noise (pm/hz 1/ ) pf 0 pf 30 pf 40 pf 50 pf Nominal displaement (μm) Figure 1: Noise as a funtion of gap for a number of apaitane values. Eletrode Radius (mm) Range Nominal displaement (μm) 50 pf 40 pf 30 pf 0 pf 10 pf Sensor Range ( m) Figure : Combined plot of the eletrode radius and sensor range as a funtion of nominal displaement. Illustrates some important performane parameters of typial parallel plate apaitane gages. For high preision measurements it is most ommon to utilize the more sensitive variable gap onfiguration onsidered below over the variable area. Typially, for a apaitane gage we seek to utilize a range inorporating apaitane in the ratio 1::3. 15

18 This gives rise to the important relationship that the range of the apaitane gage is 4/3 times the nominal value defined at the enter value of apaitane. In general, the apaitane ratio from a nominal value an be epressed by k1 Co Co : k : C. (11) o The apaitane range is given by the differene between the maimum and minimum displaement given by k o 1 k o = o 1 k1 1 k. (1) It an be readily verified that the 1::3 (k values of 1/ and 3/ respetively) rule provides a apaitane range of 4/3 of the nominal eletrode separation. Consequently, at the maimum eletrode separation the apaitane will be redued to a value of 1/ of the referene. This will inrease the soure resistane by 17% (1/6). Substituting (10) into (9) for the maimum soure resistane yields s [ e + kt / 3C + (i / 3C ) e ] BG e = ω ω +. (13) n 4 o n o o V In pratie, this appears to be dominated by the amplifier urrent noise followed by thermal noise. It an readily be shown that the output voltage from the transformer ratio bridge for small hanges in one apaitane is given by VbsGV Vout = = S 4 o d. (14) Additionally the nominal separation is related to this nominal apaitane by o εa =, (15) C o 16

19 where is the displaement of the apaitane eletrode, V bs is the bridge supply voltage and S d is the sensitivity of the bridge iruit in units of volts per meter. This an be epressed in alternative forms given by S d VbsG = 4o V VbsGV C = 4εA o. (16) From equations (13), (14) and (15), the displaement noise is given by e B = [ e + 4kT / 3C ω + (i / 3C ω ) + e ] n 16 = V bs o 1 S d [ e + 4kT / 3C ω + (i / 3C ω ) + e ], n o o n o n o o G V o, (17) in units of [m Hz -1 ]. In general, the amplitude (with sign hange aross bridge balane) of arrier frequeny is provided by the synhronous demodulator. Taking the square root of equation (17) gives the displaement noise of the iruit e B 4o = en + 4kT / 3C ω V bs oω + (in / 3C o ) + eo. (18) In the design of a apaitane gage, there are three onsiderations; range, eletrode geometry and noise floor. Basially it is required that the noise floor of the apaitane gage is less than a design goal. Typially this would be the desired resolution of the measurement system at an aeptable bandwidth. In pratie, this ould always be ahieved with a suffiiently large eletrode area. However, this is impratial for reason of eletrode alignment requirements (aeptable parallelism) and volume oupied. A omparison of these trade-offs an be seen from the design harts of Figures 1 and. From this it is lear that there are limits on size being fundamental and dependent upon the preision of the measurement eletronis. 17

20 Comparison of these figures with urrently state of the art sensors is only possible if the harateristis of the first amplifiation stage and ratio k are known. Ignoring this and noting that the following two graphs are based on rather onservative estimates for amplifier noise figures, it is found the noise data from ommerial suppliers, although lose, often surpasses that shown in these plots. Typially, the differene from these plots and available sensors is within fator of and therefore gives a reasonable estimate of ahievable preision in term of seleting and appropriate ADC (i.e. hose an ADC of preision better than 1 bit that predited for the sensor). However, ahieved noise levels will depend upon implementation and we onsider that these graphs are representative of what might urrently be realisti for many appliations..4 Indutane The so-alled linear variable differential indutor (LVDI) has been used as the sensing element in the Talystep stylus profilometer for upwards of fifty years and still represents one of the best methods for measurement of nanometer sized step heights for alibration of film thikness monitors in thin film deposition units. Again, it is ommon to measure variations in reatane using an AC driven Wheatstone bridge. Assuming equal indutors on eah arm of the bridge of nominal value, L o, the output voltage, v o, for a hange in indutane, one arm is ± ΔL, of the indutors on v o ΔL = vs. (19) L To assess the performane of a simple indutive probe, onsider a magnetially permeable ore of length l and permeability μ having a oil of N turns surrounding it. If this ore terminates from forming a loop so that there is an air gap of length nearby permeable target that forms a further part of the ore, see Figure 3. Upon a with a eitation of the oil with a urrent I there will be an indued magneti flu Φ given by 18

21 19 a a a A l A NI NI μ μ + = Φ =. (0) where A μ and A A represent the permeability and effetive area of the gap respetively. Figure 3: Shemati diagram of an indutive sensor utilizing a permeable target. The indutane L of the sensor an be approimated from = + = Φ = a a a a a a o a a a o a a a l A A l A A L l A A L l A A N l A I N L μ μ μ μ μ μ μ μ μ (1) For very small air gaps, so that only the seond term in parentheses is signifiant, a small hange in displaement will produe a orresponding hange in indutane suh that Δ + + Δ a a a o l A A L L L μ μ 1, () Effetive ore length and area, A l, Coil of N turns i,ω a Core, Target Air gap

22 N μ A ΔL a A μ a l Δ. (3) As with apaitane, the noise limit of suh a sensor an be determined from the amplifier performane and the output impedane of the bridge. With an ideal referene arm of the bridge, the output impedane is Z 0 jωl =. (4) Using the same proedures as stated previously, the noise power of this sensor is s [ e + L kt + ( i L / ) e ] BG e = ω ω +. (5) n n o V In this ase it an be seen that the noise will inrease with the arrier frequeny. A variant on the differential indutor is the linear variable differential transformer (LVDT). LVDT s an onsume low power and operate in high vauum, as a non-ontat position sensor that has nanometer resolution and entimeter range [4]. In terms of saling, for either a transformer or differential indutor it is neessary to inorporate at least two separate loops of ondutor with eah having as many turns as possible to inrease indued voltage. A permeable material must also be introdued into these loops and will eperiene an indued magneti flu, the density of whih is inversely proportional to area of ross setion through whih the flu passes. Currently, as far as the authors are aware, suh transduers are manufatured and assembled using onventional wires as ondutors and ferrite materials to reate the permeable paths. Typially, these are of marosopi sale with most manufaturers providing miniature sensors of the order 6 mm - 8 mm diameter and 10 mm 0 mm long. Some LVDI s have been manufatured with total dimensions of around 5 mm 5 mm 5 mm and able to sense displaements of up to 00 μm and with signal to noise ratio of approimately 1 part in 10,000. By inreasing amplifier gains, resolutions of better than 50 pm have been observed with a range of around nm [5]. At smaller sales, it is diffiult to manufature multi-turn oils having sub-millimeter dimensions and inorporate 0

23 permeable materials. While it might be possible to manufature these omponents using MEMS or similar proesses, it is not lear that oils of adequate performane an be readily produed..5 Resistane To the author s knowledge, diret methods for using resistane as a measure of displaement have not found widespread appliation for preision measurement. For limited rotations potentiometers have been used as a method of feedbak for spindle rotation. For eample, in the auto industry these are sometimes used for throttle position, steering angles et. However, these have been almost universally supereded by optial or magneti enoders for more preise sensor appliations. For limited range motions, piezo-resistive strain gages have been used for many deades to detet strain of piezoeletri atuators either by attahing the gage diretly to the atuator element or indiretly by monitoring strain of the fleure in whih the atuator is onstrained. Having upwards of 50 times the sensitivity of onventional metal strain gages, relatively high preision measurements are possible. For eample, typial ommerial atuators having a range of 0 μm will laim resolutions of better than 5 nm with bandwidths of around 1 khz. Typially, metalli resistors have gage fators of around and maimum elasti strains of the order 0.4 % while voltage noise is often measured in mirovolts over bandwidths of around 1 khz [6]. A simplisti alulation indiates signal to noise ratios of the order , a figure omparable to those quoted for ommerial devies Proimity probes are also produed using this sensing method and, suitably designed; demonstrate sub-atomi resolution, although at the epense of limited range..6 Magneti There are a number of different sensors that an be used to measure magneti fields. Partiular sensors, suh as SQUID s (super-onduting quantum interferene detetors) or flugate sensors an ehibit very high sensitivities but are urrently limited in terms of a relatively large power onsumption and size. Promising sensors for the detetion of magneti fields are those based on spin-dependent ondution suh as giant magneto- 1

24 resistane, (GMR) [7] and spin dependent tunneling (SDT) sensors as well as anisotropi magneto-restritive (AMR), or Hall and 3-D Hall sensors [8] all of whih an be ompat, are sensitive to small fields or an be onfigured as gradiometer sensors. These types of onfigurations, in general, require low power, operate over a very broad range of frequenies and an be readily manufatured and miniaturized using miroeletroni proesses. In fat, it is possible to use GMR sensors of similar type to those used in magneti dis data storage read heads to obtain positional information with resolution in the region of a few tens of nanometers [9, 30]. In priniple, there is no reason why this annot be used for position measurement if inorporated for the detetion of urrents in a wire patterned for a speifi measurement (i.e. radial lines or a periodi meander for rotational or linear measurements). Alternatively, it might be possible to use the read head diretly to detet patterned magneti domains on a referene. The simplest referene would be a periodi grid that ould, for eample, be written onto a magneti tape and then adhered to a surfae. However, the ease of manufaturing arrays of suh sensors readily enables absolute or inremental enoder onfigurations [31] for graysale or quadrature type displaement measurements..7 Eddy urrent A simple eddy urrent probe for monitoring displaement between a surfae and a irular oil at a distane z above the surfae is given by [3] π μn r L = l t 0 I 1 l + e α ( r, r ) α 5 αl 1 + α α + 1 ( ) ( ) α α αl l+ z αz α l+ z 1 [ e + e e ] dα, (6) where I ( r r ) = J ( ) 1, αr α r1 1 d, (7)

25 1 1 ( α + jωμσ ) α =, (8) t is the differene between the inner and outer radius, r, r 1, of the eitation oil, l is the length of the oil, μ is the permeability of the speimen surfae material, σ is the eletrial ondutivity of the speimen surfae material, ω is the frequeny of eitation and α and are dummy variables of integration. Correspondingly, there will be a repulsive fore between the surfae and oil of value F z i = i = L z π μn r l t I ( r1, r ) 5 α αz αl αl α α 1 ( e ( e e + 1) ) dα. α + α 0 1 (9) These equations an be solved numerially to show the dependene of indutane and fore with separation. For a flat oil of 40 turns, an inside diameter of 8.0 mm, an outside diameter of 1.0 mm and a wire diameter of 0. mm being driven at a frequeny of 0 KHz, 0.35 V at a urrent of 0.70 A, is shown in Figure 4. In most instanes, as with apaitane sensors, the fores might be onsidered insignifiant when ompared to the size of the sensor. In pratie, the referene surfae should be relatively flat, larger than the oil and etend to a depth onsiderably greater than the skin depth, δ, given by 1/ ( ) δ = ωμσ. (30) A disadvantage is that the sensitivity is dependent upon the materials type and it is possible that the eddy urrents an ause loal heating of the target surfae, whih must also be an eletrial ondutor. Suh eddy urrent based indutive probes an have high resolution and bandwidth and have the additional advantage that eletrial onnetion to the target surfae is not neessary. Typial ommerial probes will resolve to within tens of nanometers over millimeter ranges. The limit on range is set by the size of the oil or diameter at whih the magneti field is being generated. For eample, if a irular oil is used to generate the osillating fields, it is found that, as a rule of thumb, the field generated by the oil is 3

26 substantially attenuated at a distane approimately equal to its mean radius. Consequently, this type of sensor might be onsidered as a probe with a measurement zone etending a maimum of the oil radius while also requiring a speimen surfae of irular dimension twie that of the oil outer diameter. Fore (mn) Voltage = 0.35 V Current = 0.7 A Frequeny = 0K Wire dia. = 0. mm Inner dia. = 8 mm Outer dia. = 1 mm indutane measured theory Indutane theory Indutane meas Liftoff (mm) Indutane (mh) Figure 4: Dependene of indutane and fore on separation. Theoretial and measured values are shown. Alternatives, to indutive oils an be found in the use of sensing elements to detet the magneti fields produed by the eddy urrents. In priniple suh probes an be made with the sensors suitably plaed and biased to measure only the field of the eddy urrents independent of the eitation field [33]. Suh probes an also be miniaturized to produe loalized measurement of surfaes for pattern reognition and, possibly, lateral position measurement [34]..8 Proimity probes A proimity probe is onsidered to be any sensing method that provides a measurable signal as it is brought into lose proimity to a surfae. Often proimity probes are used as a means of ommuniating a translation from a relatively small area on a surfae; in a oordinate measuring mahine (CMM), stylus profilometer or sanned probe mirosope 4

27 (SPM) this is the probe. This is then ommuniated to an atuator that an move the probe and reord subsequent displaements. In suh systems, it is also apparent that there is still the requirement for a displaement measuring system. One area in whih the saling of proimity sensors has seen etensive development is the in the field of SPM sensors. Sensing methods inlude tunneling, strain gage, near field optial, thermal, ion ondutane or apaitane. The relative merits and limitations of these proimity sensors are 1. Small probes an measure surfae heights in a small and loalized area (sometimes with resolution of better than one atom for the smallest of probe tips).. When ontrolling the probes to maintain a null signal level, as long as the sensing harateristi as a funtion of tip/sample interation is stable and repeatable, the auray is little influened by non-linearity. 3. Etremely high resolution and bandwidth measurement of variations in the probe to surfae interation are possible. 4. Most probes provide only proimity information and do not have the intrinsi apability for the measurement of displaement. This is usually transferred to another displaement measurement transduer of the types outlined above. 5. In priniple, any of these probes ould be used to detet variations of, and therefore represent a sensing method for, a periodi sale. In the initial sanned probe mirosope designs of Young, et al. [35, 36], the proimity sensing method was Fowler-Nordheim field emission from a sharp eletrode tip and later efforts were attempted to utilized eletron tunneling at tip-speimen spaing of less than nm and lower applied voltage levels. Problems with relative vibrations between probe tip and surfae prevented sanning until a deade later, Binnig, et al. [37, 38], were able to redue the mehanial noise and ahieve atomi sale images on silion, for a brief review see [39]. 5

28 A tunneling probe onsists of an eletrially ondutive sharp tip that is brought into lose proimity to an eletrially ondutive surfae. With applied voltage differenes of a few tenths of a volt, there will be an eponential inrease in urrent as the separation redues. Typially this will range from pioamps to miroamps with separation hanges of around one nanometer. Using a logarithmi amplifier it is possible to obtain a sensitivity of many gigavolts per meter over, of ourse, a very limited range. In pratie, suh a probe is sensitive to the separation of the outermost asperity of its tip and is therefore etremely loalized and, for measuring surfaes that are smoother than the tip geometry, may be onsidered to measure the proimity at a point on the surfae. However, a drawbak with tunneling is that it requires eletrially ondutive surfaes, must maintain nanometer level separations and is suseptible to surfae ontamination. For these reasons, tunneling probes are not widely used in meso and miro sale appliations. While tunneling probes may not be partiularly popular today, beause of their spetaular ability to disriminate individual atoms, whih in turn, fueled the imaginations of nanotehnology visionaries aross a broad range of sientifi and ommerial disiplines, they were predominantly responsible for the eplosive emergene of the sanned probe mirosope industry. Among the many proimitysensing methods that have been developed, by far the most ommon is the so-alled atomi fore probe [40]. This also omprises a sharp tip that is brought into lose proimity or ontat with a point on the surfae. However, it is the interation fore that is transformed to a displaement (or, equivalently, strain) and it is this displaement that is then measured to determine proimity. In pratie, given suffiient sensitivity it is possible to monitor both non-ontat (eletri dipole, van der Waals/Casimir, gas squeeze film) and ontat (menisus, elasti) fores with this form of sensor [41]. While, tunneling probes, optial levers, apaitane and (piezo-resistive) strain gaging have been used to determine the fore of interation, in general it is neessary to use a larger surfae or volumetri sensing area to determine a measure of the fore thereby inreasing the footprint of this probe. However, all of these an be readily produed using maro to MEMS and, reently, nano manufaturing proesses and therefore suh probes an be readily saled. 6

29 3.0 Atuators There are an almost limitless number of atuator designs that an be employed in a given system using any number of mehanisms. In general, the major figures of merit quantifying the performane of different atuator methods as they apply to a speifi mahine appliation inlude 1. Mahine volume/atuator volume.. Range/resolution, or preision, requirements. 3. Effiieny, measured as a ratio of power delivered to a proess to that supplied to the atuator. 4. Type of oupling between atuator and objet to whih fore is to be applied. Generally this an be lassified as either ontat or non-ontat. 5. Bandwidth, generally measured by available power-density. Also at issue is the onnetion to the motion ontrol system. In partiular, there is a onern in design with the removal or redution of parasiti motion of the driver. There are relatively few atuators that an be applied to mahines at smaller sales. This is rather surprising in view of the sale of biologial proesses. However, in engineering systems, we are restrited in the seletion of power soures and it is onsiderably more effiient to generate power using marosopi systems and hannel this into the meso-sale mahine. Novel power soures inlude 1. Solar.. Eletro-rheologial fluids [4]. 3. RF absorption. 4. Miniature ombustion [43, 44]. 5. Fuel ells. 6. Biologial systems, ellular or life-based. 7

30 While interesting, a disussion of these is outside of the sope of this paper and epertise of the authors. However, these are, for the most part, alternative ways of produing eletriity that will then be onverted bak to work through some atuation mehanism. It is these primary atuator mehanisms that form the basis of the disussions in this setion. Assuming that energy soures are available, the main lasses of atuator likely to find appliation in meso- and miro-systems in preision mahine design inlude 1. Piezoeletri. Eletromagneti 3. Eletrostati 4. Pneumati 5. Hydrauli 6. Thermal 7. Shape memory Thermodynamially, it an be demonstrated that all atuators, in the proess of doing work on a system will generate heat. In pratie this an severely limit performane of instrument and mahine mehanisms. Therefore, atuators suh as voie oils and purely eletromagneti or eletrostati atuators an provide highly effiient eletromehanial oupling and, therefore, dissipate minimal amounts of heat at the drive. In other ases it may be desirable to loate the atuator remote from the mehanism. In this ase it is then neessary to transfer the work mehanially to the mahine. This an be very effiiently ahieved using push-rods or, possibly, pulleys. In this ase, the desirable saling of the atuator mehanism might also help determine the nature of the work transfer mehanism. For eample, beause eletromagneti atuators favorably sale to large devies, it might be desirable to use one large motor and use this to drive multiple smallsale mahines, just like the power soures in fatories in the late nineteenth and early twentieth entury! 8

31 3.1 Work and power density The limits on work and power that an be ahievable for an atuator onstrained within a speifi volume (referred to as the work density and power density), will be onsidered in terms of what is possible in an ideal system, initially ignoring the issues of implementation. In some ases, partiularly aerospae based, the power or work per unit mass may be of interest to the designer. For some of the atuators it will be obvious that other omponents required for implementation must share the spae of the atuator mehanism for it to be eploited, thereby reduing the theoretially ahievable densities. Generally the work and power density will be defined as 1. Work density is the maimum amount of work that an be done per unit volume oupied by the atuator.. Power density is the produt of maimum work density and bandwidth response. A very important onsideration in the following disussions is that maimization of the atuator work and power density will be a matter of implementation and, beause simply saling down from marosopi or up from mirosopi might not be feasible, new approahes may be required. These issues will also be disussed throughout this setion with a ompilation of work densities for various atuators ontained in Table 1. Table 1: Indiating approimate power densities for a range of atuator types Atuator type U 10 6 V Eqn. Comments Hydrauli 10 Ρ Pressure SMA 6 σε Cyli binary Solid-liquid phase hange 1 ΔV 5 k 3 V Water-8% aetimide Some other researher s may refer to this as the energy density of an atuator. 9

32 Gas epansion (thermal & press.) 1 Ρ Pressure Thermal epansion 0.5 E( ΔT ) / 4 α 00 K temp. hange Eletromagneti See tet Variable relutane motor 0.5 mm 3 Eletrostati See tet Ideal to MEMS omb-drive estimates. 33 ma E Piezoeletri ( d E ) / PZN Musle 0.0 NA 350 kpa at 10% 3. Piezoeletri At marosopi sales piezoeletri atuators [45, 46] are often used in the form of staks [47] (to redue the neessary drive voltage) or with lever mehanisms to inrease the range of motion [48, 49]. Single element eramis have limited range, but losses due to hysteresis an be substantially smaller than staked orientations. Single element piezoeletri materials have most notably been used in sanned fore mirosopy [50, 51]. Lever mehanisms an take the form of bimorph type atuators [5] or mehanial linkages. Ignoring suh issues for the time being, onsider two different atuator implementations; in the first, it will be assumed that the atuator is inorporated into a fleure type mehanism that provides a resistane fore proportional to the atuator displaement. In this ase, the bandwidth response is going to be limited by the amount of work that an be done by the atuator on the fleure system. Ignoring any preload, it is possible to model the system as an atuator, of stiffness a fleure of stiffness k p = EA/ L, that pushes against k f. In pratie, the stiffness of the fleure will redue the range of motion of the atuator when in its free or lightly preloaded state. Denoting the free 30

33 motion range of the atuator, i and the output motion in the presene of the opposing stiffness o it is relatively simple to show that they are related by the equation o i k p =. (31) k + k f p Work done, U, in a linear translation of the fleure system is U 1 1 k f k p = k f o = i. (3) ( k + k ) f p It an be shown that this is a maimum when the two stiffness values are the same, hene 1 k p EA U ma = k f o = i = i. (33) 8 8L The maimum free strain of the atuator is a produt of the maimum eletri field, E ma applied to the material and the oupling onstant in the diretion of the eletrodes usually denoted by the symbol d 33 in units of [m V -1 ]. Multiplying strain by the length of the atuator, the maimum free translation of the atuator is given by l = d L. (34) E 33 ma Substituting (34) into (33) and dividing by the volume of the atuator ( V = AL), the maimum work density for a fleure driven system is ( d E ) U E = 33 ma. (35) V 8 Considering this struture as a positioning stage, effetively doing no work on the outside world, the major performane measure is likely to be response time. In many appliations it might be desired to use the atuator for ontrolled work on a speimen for mahining or ontrolled distortions. In this ase the atuator will be driving against a nominally onstant load. Under these irumstanes the eternal work done on 31

34 the speimen will be the produt of fore and etension and these will in turn be limited by the maimum pressure loads, σ ma, that an be sustained while maintaining a finite strain oeffiient. For eample, the PMN-PT eletrostritive erami an reliably ahieve strains of up to 0.1% with pressure loads up to 100 MPa and applied fields of MV m -1. At this load, the ahievable free strain has redued by around 30 %, while the elasti modulus is a little over 100 GPa. Using similar analysis, it an be shown that the work done per unit atuator volume is given by U V Ed33Ema = σ mad 33Ema. (36) 1000 It should be mentioned in passing that larger strains ould be obtained using an eletrode pattern orresponding to an eitation field perpendiular to the polarization ais that results in a shear mode deformation. The drawbak with this is the additional ost assoiated with poling of the eramis. To develop long-range systems with a power density on the order of the piezoeletri stak, aumulation type atuators have been onstruted [53, 54]. Common forms of this type of system an be found in Piomotors and Inhworm drives where a erami atuator is used as a means of stepping or walking along a guide rail. Other useful appliations for piezoeletri atuation inlude multiple degree-of-freedom strutures [55, 56] and losed-loop ontrolled error ompensation systems [57, 58]. 3.3 Eletromagneti Eletromagneti atuators are a little more diffiult to quantify [59] in terms of power density. In general, there are two designs for fore atuation involving the magnetization of ferromagneti materials. The first uses eletrial urrents to produe attrative fores between two solids and the seond uses permanent magnets to produe a magneti flu through urrent arrying wires. Magneti field driven atuators an be lassified as eletromagneti, eletrodynami, magnetostritive and magnetorheologial as disussed in more detail by Janoha [60]. In general, the fore, F, on the moving harge of strength q moving with a veloity, v, an be obtained from the Lorentz equation 3

35 ( E + B v) F = q, (37) where E is the eletri field and B is the magneti field. For most systems this equation must be integrated over all interations to determine the fore available to do work. One of the most ommon methods for deriving known fores is to arrange for the urrents to pass through wires in a fied magneti field often reated by a permanent magnet. Suh devies are often lumped into the generalized ategory known as voie oils. In suh systems, in whih the harge distribution and veloity is ommon throughout the length of the wire in the field, the integral over all harges an be epressed in the salar form F = Blisin(θ ). (38) In equation (38) the produt Bl represents the integral of the field values over the length of the wire of the voie oil and i is the applied urrent. This fore is learly maimized when the permanent field and the urrents are perpendiular. In priniple, the fore ould be epressed as the flu from the permanent magnet multiplied by the maimum urrent density, j ma transmitted through a given area over a given length. Considering that it is possible to derive suffiient urrents, it should be possible to utilize the maimum energy stored within a given magnet material. In general this is given by the maimum produt of flu density and applied magneti field whih is a diret measure of the energy storage per unit volume given by ( BH ) U = ma. (39) V Unfortunately, a method for implementation of suh a devie is not readily apparent and in pratie it is desired to reate fores using a urrent arrying wire oupying a gap of part of a magneti iruit. Again, an ideal system may be envisaged in whih the gap flu, B g is related to the energy density of the permanent magnet by the relationship ( BH ) g 1/ ma m B g =. (40) V V 33

36 The volumes in this equation represent the magnet and gap respetively. Generally, this gap flu ould be used to provide the magneti fore on a urrent arrying wire. From (38), the fore on a wire entirely immersed in the field an be approimated by F ( BH ) V 1/ ma m = Bgli = BglAg jma = lag j ma (41) Vg Dividing this epression by the total volume ( V = V g + V ) yields the maimum fore m F V ma ( BH ) 1/ ( BH ) ( 1+ k) ma VmV g ma k = j ma = j ma ( Vg Vm ), (4) + 1/ where V V m k =. (43) g Noting that this is a maimum when k = 1 and assuming that the fore on the wire will redue linearly as it moves out of the volume at a displaement l, the work done per unit volume may be epressed in the form (( BH ) ) 1/ U ma jma ma = l. (44) V 4 This rather over simplified view of a voie oil drive ignores a number of ompliating issues suh as reoil permeability, temperature and field interations among many others. In many voie oil atuator designs, the flu is often onentrated using soft iron ores. While this will inrease fore, it will orrespondingly limit the range and, ultimately, the two effets tend to anel in the work density piture. However, the key feature of this equation is the linear saling of work density with dimension. This is illustrated by the graph in Figure 5, in whih the work (produt of fore and stroke) that an be obtained from ommerial voie oil atuators divided by their volume is plotted as a funtion of the atuator length in this ase onsidered to indiate size of atuator. 34

37 Voie oil atuators have been suessfully designed and utilized in a number of Work density (arb) Length (mm) Figure 5: Work density plotted against length of ommerial voie oil atuators (details available on request) preision appliations inluding mahine tools [61] and displaement instruments [6]. The solenoid atuator design is not dissimilar to the voie oil already onsidered (in fat most voie oil atuators ombine permanent magnets and soft magnet materials to guide and onentrate the flu). In this system, the field is generated by the oil and flows along the permeable path of a ore material with the moving omponent hanging the relutane,, of the loop of magneti flu. In general, a solenoid of length, l s provides the field resulting in a flu loop passing through a total of K omponents of the magneti iruit and having a magnitude given by Φ = NI k k = K k k = 1 μ k Ak NI l. (45) By definition, the indutane is the flu passing through the N turns divided by the urrent required for its generation i.e. 35

38 36 = Φ = k k k k A l N I N L μ, (46) where l k, A k and μ k orrespond respetively to the effetive length, effetive area and permeability of the k th omponent in the flu loop. Again, a simple system will be onsidered onsisting of a permeable ore denoted using a subsript (usually E shaped) with a moving omponent onstruted of the same material. These two omponents are onsidered to be separated by an air gap where the magneti and geometri properties of whih are given a subsript a. In general the magneti potential, U, of this system is given by ), ( ), ( ), ( ), ( i y A y l y A y l A l N i L U g a g m m E E + + = = μ μ μ, (47) where the subsripts E, m and g represent the stationary ore, moving omponent and gap between them, respetively. Being a general epression for the potential of the systems, the vetor omponents of fore in the y plane an be obtained from + = = j i F y U U (U ) grad. (48) Usually, by design, it is arranged for the moving omponent of the atuator to operate with a hanging separation at onstant area, motion, or vise versa for y motion. Substituting (47) into (48), eah of these atuators produes a fore given by i A l A l A l A N l U U F g a g m m E E g a g + + = = μ μ μ μ, (49)

39 F y U = y U b A g = le μ a μ A E bn l g lm + μ A m l + μ A g a g i. (50) Again, onsiderable liense with assumption of the parameters has been used to derive these epressions and there are other more preise modeling approahes that may be applied for speifi appliations and materials. However, a few general points beome lear from these equations. Being proportional to the square of the urrent, the fore between the two bodies is always attrative independent of the urrent polarity. Also the fore varies approimately with the inverse square of the motion. To assess the effet of saling, onsider equation (49) where the geometry of the atuator is fied with a reasonably large gap and in the ase when the permeability of the ore is onsiderably higher than that of air while the geometri fators are of omparable value. Under these irumstanes equation (49) redues to F ( Ni) U U μ a Ag = =. (51) l l g g Again, using similar arguments as before, the produt of turns and urrent represents urrent density. This will sale with area of the winding. Additionally, it has rashly been assumed that the permeability is a onstant independent of the field. In pratie, this will be limited by the saturation field that has, in turn, been shown to have a maimum potential orresponding to a high ( BH on the B-H urve for many of the ore ) ma materials ommonly seleted for solenoid appliations [63]. Simple dimensional analysis on equation (51) produes a work density saling of the form U V ma a g lg ( Ni) A l ( ) ( jmal ) 1 jma = μ BH ma ( BH ) ma l. (5) V l Comparing equation (44) with the work density proportional to the square of the dimensions of a devie, it is suggested that suh systems sale even less desirably than voie oil designs. 37

40 In both of the above approahes, it is apparent that, based on the simplified model, the fore sales with maimum urrent density. In pratie, it is resistive heating and the subsequent heat dissipation (usually being transferred by ondution from the surfae of the outside of the oil) within the atuator that imposes a limit on the urrent density and, therefore, the work available to the system. In general, beause the ratio of surfae area to volume inreases with redued size, it is possible that the limiting urrent density will be inreased with redued size, thereby offsetting, to some etent, the unfavorable saling indiated by the above analyses. In general, based on the above onsiderations, it is not surprising that eletromagneti atuators have found few appliations in meso and miro-sale devies. However, this is not to say that appliations do not eist [64, 65]. One has only to disassemble digital wathes with mehanial hands to find meso-sale eamples of both types of atuators. 3.4 Eletrostati Eletrostati atuators have been used etensively for providing fores in MEMS systems [66,67]. This, in part, provides a lue as to the favorable, or, at least, ompetitive, saling of suh a mehanism. One partiular advantage of eletrostati over piezoeletri atuators is that eletrostati fores an be non-ontat, utilizing air or fluids as the dieletri material. When they are apable of providing suffiient fore to produe the desirable displaements, this makes them favorable for ontinuous motion systems and, for positioning systems. In general, the fore is derived from the gradients of eletrostati potential between two or more eletrodes. Taking the simplest instane of two parallel plate eletrodes of square shape of length L and separation distane, the potential energy, U, as a funtion of applied voltage V is approimately given by U = 1 CV 1 = L y L ε ( )( ) z V, (53) where, y and z represent the possible linear translations of one of the eletrodes. Considering the ase of variable separation (i.e. y = z = 0), the fore on the eletrodes in the diretion normal to the plane of the eletrodes is 38

41 F U εl V = =. (54) The maimum fore is learly a funtion of the maimum voltage that an be applied to the eletrodes and this will, in turn, be limited by the maimum eletri field, E ma that an be sustained by the dieletri. Consequently, the maimum voltage that an be utilized will vary with aording to V ma = E. (55) ma Assuming that the atuator operates at this voltage, the maimum work that an be provided by this atuator is given by ma ma L Vma U ma = Fd = ε d. (56) min min In the above equation, it is assumed that the dieletri onstant and field strength are both onstant. However, it is known that the dieletri strength an inrease at redued separation. For eample, in air the field strength is known to inrease dramatially as separation between eletrodes redues to below a few mirometers (a plot of field strength as a funtion of the separation is sometimes referred to as the Pashen urve). Substituting (55) into (56) and rearranging, the maimum work is given by U ma εl E = ma ( ) min ma. (57) The maimum volume of the atuator is V = L ma, (58) from whih the maimum work density is given by U ma V εe 1 = ma min ma. (59) 39

42 Clearly, the work density is limited by the translation range whih will, in pratie, be limited at one end by the maimum voltages that an be generated and at the other by the ability to measure and ontrol small separations and/or atuator geometry. There is another limitation imposed on the minimal separation that ours in many appliations due to the non-linear stiffness of the atuator at a given applied voltage. In some ases, the atuator will be used to drive a fleible mehanism that itself will have a finite and, generally, linear stiffness atuator will be a funtion of the separation,, given by k f. However, the stiffness of the eletrostati k E F εl V = =. (60) 3 Subtrating the work done by the atuator from the work done on the fleure mehanism gives the work available to drive eternal proesses i.e. U et = U U = k ( ) k. (61) f E f o E Differentiating (61) yields F et U = ( k k ) = k εl V = et f E f 3. (6) Notieably, there will be a point in after whih the fore term of equation (6) hanges sign. At this point, any small perturbation in the separation is likely to result in an unstable, and sometimes atastrophi motion of the eletrodes towards eah other. In the absene of mehanial stops, this motion will ontinue unabated until the eletrodes ome into ontat. This is often referred to as the jump-to-ontat ondition at a separation, representing a theoretial minimum separation, given by jump ε = k L V f 1/ 3. (63) If there is no feedbak to determine the maimum possible voltages that an be applied, assuming that this is greater than the jump-to-ontat ondition, it is ommon to use a 40

43 maimum supply voltage that an be tolerated at the minimum mehanial separations enountered in pratie. Under this ondition the maimum applied voltage is fied and the work done by the atuator is given by U ma ma ma 1 εl Vma 1 1 = Fd = ε L Vma d =. (64) ma min min min Assuming that the minimum separation (or maimum voltage) is field strength limited, we may assume ma = onst =, (65) min where V ma min = (66) Ema Substituting equations (65 and 66) into (64), dividing by the maimum atuator volume and rearranging gives U ma εl Vma 1 = 1 V. (67) min The maimum of (67) is given when =. (68) After whih the work density an be epressed by the equation U V ε = 8 ma E ma. (69) This is also independent of saling. Consider now the alternative mode of operation in whih the eletrode is onstrained to move in a diretion parallel to the plane of the eletrodes. In this ase, only translations 41

44 in the y diretion will be onsidered (i.e. z = 0) so that is a onstant, given as o. An interesting onsideration with suh an approah is that, in theory, it should be possible to overome the jump to ontat by using a omb of eletrodes. In this the fores and suessive derivatives, in the diretion perpendiular to the plane will ompensate, thereby eliminating the problem of jump to ontat. In pratie this problem will still eist in the presene of small perturbations and/or asymmetries due to manufaturing toleranes and other soures. However, beause the eletrodes are onstrained in this diretion by design, the fleure stiffness is likely to be onsiderably higher, thereby reduing the possible separations for a given applied voltage. In this mode of operation, the fore on the eletrodes is given by F y U y ε L = = V. (70) o Again substituting for the maimum voltage as determined from the field strength of the dieletri gives F U =. (71) y y = ε LE ma o It is readily apparent that this is independent of displaement and therefore suh an atuation mode ontributes zero stiffness in the drive diretion. Suh a simplisti model enables the fore to be applied over a omplete traverse of the eletrode over a distane L. Hene, ignoring edge effets and other ompliations, the work density is given by U ε L E ma ma o = = V L o ε E ma. (7) In this ase it is apparent that the work density is, yet again, independent of saling. Reently, there has been a growing interest in the prodution of polymeri layered eletrostati atuators that an have enhaned dieletri oeffiients and therefore inrease the ahievable work density. The relatively large strains that are possible with these atuators have lead to onsiderable researh towards the manufature of artifiial musle and these integrated fore arrays produe omparable strains of approimately 4

45 1/10 th of the work density of human musle [68]. More reently, some ioni polymermetal omposites have demonstrated work densities omparable to human musle [69]. 3.5 Eletrostritive Eletrostrition is a phenomena, similar to the piezoeletri effet, whih gives rise to a strain proportional to the square of the applied eletri field [70] as seen in lead magnesium niobate (PMN)-based relaer ferroeletri materials [71]. A omparison of piezoeletri, eletrostritive and phase-hange materials has been given by Uhino [7] and Cross [73]. Eletrostrition polymers [74] have been shown to produe atuation with strains near 4.0%. These atuators tend to be highly non-linear due to their dependene on the square of the applied voltage, but may be less hystereti at a given temperature than the more ommon lead-zironate-nitrate PZT materials. Eletrostritive materials also tend to have 3 to 4 times the apaitane of piezoeletri materials, whih may redue their effetiveness for dynami appliations. 3.6 Magnetostritive Magnetostritive atuators found a resurgene with the disovery of Terbium-Iron- Dysprosium alloys ommonly alled terfenol that ehibit a relatively large magnetostritive effet. For this material, appliation of a magneti field auses the internal magneti domains to rotate resulting in an epansion strain that an be up to around 0.1% at magneti fields of around 40,000 amp turns per meter. This strain is signifiantly affeted by mehanial pre-stresses that tend to align the internal magneti domains along the rystal. Maimum energy densities of around 5 kj m 3 are possible with this material and this appears to remain approimately onstant with sale. In pratie atuators typially omprise a plate or rod of the metalli rystal surrounded by a solenoidal oil. Beause of the similar strains produed by this atuator, marosopi devies tend to have a performane and footprint omparable to piezoeletri atuators. Saling of these atuators is diffiult to assess. One lue to this an be obtained by eamining ommerially available systems [75]. In these, the winding tends to oupy a onsiderable proportion of the atuator volume. In priniple this should lead to a onstant 43

46 work density. In pratie, as oils get progressively smaller, there are substantial problems assoiated with the volume oupied by insulation and air gaps (referred to as the paking fator of a oil) and this will ultimately limit the fields that an be generated as sale redues. Suh onsiderations also apply to eletromagneti atuators. 3.7 Hydrauli This and the following ategory, represent a form of fluid power. One key attribute of hydrauli systems is that the work an be arbitrarily distributed through a system given appropriate piping and ontrol valves. This appears to be the major obstale. In the absene of suh onerns, the maimum work density an be onsidered to be that provided by filling a fied volume with a fluid of pressure P. From basi thermodynami onsiderations, the maimum work density is U V PdV = V = P. (73) One of the problems assoiated with suh a simplisti model for possible power density is that of ontrolling the work delivered by the hydrauli atuator. In marosopi systems, this is ahieved via disrete valves that are used to diret the pressurized fluid to either side of a hydrauli piston. Typially, spool valves are used and these rely on preision manufature to provide the sealing ation often with auraies of the order of tens of mirometers or better. In turn, the spools of these valves are atuated either by solenoids or the moving omponents of the hydrauli atuators themselves. Normally, the rate of etension or retration of the piston is ontrolled by a restritor at the outlet port of the atuator. When the piston is reversed the role of the ports either side of the piston are swithed and a non-return valve is neessary to enable free flow of high-pressure fluid bypassing the restritor. Although possible, it is unlikely that manufaturing proesses will be developed to sale these systems to mesosopi dimensions and it might beome ineffiient to use solenoids as the main atuator. In all ases, the omponents for ontrol of hydrauli systems an be thought of as providing the funtions of restrition or flow rediretion. In essene a restritor is a twoport devie while a rediretion devie requires and minimum of three and more typially 44

47 four ports (one for the drive (inlet), one for the ehaust (outlet) and one (two) to whih the flow is to be direted). In many ases the outlet port represents a return pipe to the fluid reservoir. All of these funtions an be ahieved through suitably ontrolled arrays of restritor mehanisms apable of ontinuous operation from full flow to omplete restrition. While marosopi systems have been evolving for over a hundred years and have been inorporated for preision appliations [76], it is diffiult to predit what devies will be best suited for flow ontrol as dimensional sales redue. At meso-sales, it is still likely that the fluid power will be supplied from some entral soure where elaborate plumbing systems will be used to route the fluid to a speifi loation, not unlike biologial organisms. A brief mention regarding mirofluidi devies; mirofluidi systems have been developed for use as pumps, valves and flow sensors [77]. At this time, it appears that the majority of these devies are being applied in hemistry and miro-biology studies as illustrated by Lab-on-Chip (LOC) devies. There have been two major fous areas of mirofluidi design as mentioned by Andersson and van den Berg [78]. The first looks at applying fluidi omponents (pumps, valve, et.) into fluid based systems, while the seond looks at miniaturizing analytial hemial methods, suh as the ability to sort and manipulate single ells. Pumps and valves are urrently being used to mi fluids, pump fluids and sort different miro-strutures [79, 80] at the mirosopi sale. The funtionality of these types of systems at the ellular level has and will ontinue to promote single ell manipulation and treatments. It is lear that these kinds of appliations will ontinue as miro- and/or nanotehnology appliations beome more prevalent. 3.8 Pneumati Pneumati based atuators have the advantage of a readily available soure (air) and the ehaust an be freely vented. In many aspets the relative advantages mirror those of hydrauli based atuators with only one major eeption being that the pressures attainable with gases are typially less than those ahievable with a fluid. Another 45

48 limitation is the ompressibility that leads to thermal hanges, and therefore losses, upon ompression.this is ommonly used to eplain the Carnot yle in introdutory thermodynamis, although, in pratie all atuators an be modeled by the Carnot yle [81]. Typially atuators might be in the form of a piston, diaphragm or bellows type of mehanism. In all ases, the method of onstraining the gas and enabling its epansion with pressure will oupy spae thereby reduing the work density of the atuator. One of the major problems is that of redireting the flows of pressurize air. To do this requires valves and restritors for full motion ontrol. At the meso-sale, it has been possible to use fluidi devies to ontrol airflow at moderate pressure differenes (around 0.5 bar). These use the boundary layer effet to guide air flows along different paths within a valve enabling ommon logi operations suh as and, or and flip-flop ontrol of pressure signals. As the sale redues it is neessary to orrespondingly redue the sale of the valves and flow ontrol devie. There has been onsiderable researh and development of thermo-pneumatially ontrolled valves [8, 83], whih may be used at the meso-, mirosales sine thermal time onstants sale favorably thus inreasing operational bandwidths at small-sales. Typially, the valve is opened or losed by defleting a diaphragm against an orifie using the thermo-pneumati atuator. This atuator onsists of a fluid (Fourinert) that is ontained in an enlosure with one of its walls being a fleible diaphragm. Also within this enlosure is a heating element that is used to heat and therefore epand the fluid. Movement of this diaphragm an then be used to open and lose a valve or an be used to operate a peristalti type pump, in the referene ited to generate pressures of up to 30,000 N m -, for eamples see [84, 85]. 3.9 Thermal At marosopi sales, thermal atuators tend to be too slow and of limited displaement range for most appliations. However, when bandwidth is not important, suh atuators an provide a smooth and ontinuous ation that has been used for sanning mirrors in 46

49 optial interferometers and other fine motion appliations. Typially, ignoring the thermo-pneumati atuators mentioned above, the atuator omprises a simple monolithi element heated either by surrounding it with a heating wire, indution oil or, if it onduts eletriity, diretly by passing a urrent through it. While other soures of heat are possible (inluding hemial potential from interations or burning of fuels) eletrial heating provides more ontrolled power. One of the main advantages of a thermal atuator is its simpliity sometimes requiring little more than a pair of eletrial onnetions. In its simplest form, a thermal atuator an be made from a ube of material of length L. While the ube will typially epand linearly with an inrease in temperature, it will generally be used to provide a linear motion in a defined diretion. For relatively small hanges in temperature, it may be assumed that the volume epansivity is onstant resulting in a dimensional hange δ = αlδt, (74) where α is the oeffiient of thermal epansion and ΔT is the hange in temperature (usually taken from a nominal 0 C). An estimate of work that an be obtained from a thermal atuator is ompliated by a orresponding variation in the elasti modulus with temperature as well as variation in the epansion oeffiient with temperature [86]. The hange in energy of the atuator system an be epressed by du = mc ΔT pdv, (75) p V where m is the mass, C p is the speifi heat, p is the pressure and V is the volume. More generally, the first term in this equation represents the entropy while the seond term represents work done by the atuator. Again, for small temperature hanges it is reasonable to assume that the atuator will operate at a nominal elasti modulus and thermal epansion oeffiient given by the average between the start and finish value. Again, assuming that the atuator drives a stiff load, the strain energy stored is given by 1 1 EA ( ) EAL U = k L T ( T ) f = α Δ = αδ. (76) L 4 47

50 Hene the energy density is given as U V 1 EA ( ) E = α ΔT = ( αδt ). (77) 4 L 4 The speed of response of the thermal atuator an be represented by the diffusivity. In general, the time onstant, τ, of a thermal system is given by k =, (78) L ρ τ C P where k is the ondutivity and ρ is the density. Clearly, this inreases with the reiproal square of the linear dimension, thereby indiating a very favorable dynami benefit for small systems Shape memory In pratie, shape memory atuators are really a subset of thermal atuators. Shape memory alloys (SMA) were first developed in the early 1950s and have been used for a myriad of mehanial devies, suh as ouplings, sensors, springs and atuators [87]. Beause of the vast array of proessing tehniques available, SMA atuators an take on any number of forms. Researh has been done using SMAs as biomimetis [88] and in medial devies [89] where fluid environments inrease heat transfer rates due to onvetion and stimulate atuation. They have also been used as atuation mehanisms in robotis [90] and been ombined with other materials suh as elastomers [91] to inrease response time and ontrollability. Thin film atuators for MEMS type appliations provide high work to volume ratios and an have bandwidths up to 100 Hz [9] given that the rate of heat transfer is inreased due to the large surfae area to volume ratio. SMA materials an also be utilized for damping in strutures beause of relatively high internal frition. There are a number of parameters that ould affet the SMAs damping apaity. These inlude material type, grain size, martensite density and defet struture. SMA materials suh as Cu-based alloys and Ni-Ti have been shown to have damping apaities an order of magnitude larger than ommon steels, whih may prove to be ritial is some preision appliations [93]. 48

51 The shape memory effet (SME) is a property of ertain materials whereby deformations attained at low temperatures an be removed by heating the material. For some materials strains of up to nearly 10% an be ompletely removed upon heating above the transformation temperature. This type of transition is alled one-way shape memory effet. Two-way shape memory effet allows the SMA to return to a preset shape upon heating and then return bak to its original shape upon ooling. The SME proess is fundamentally related to phase transformation of the material, for most shape memory alloys, from austenite to martensite and vise versa. These materials also have another interesting and potentially useful property of superelastiity. Superelasti SMAs an sustain strains of 8-10 % at a reasonably onstant stress. This makes SMAs useful as onstant fore springs, for appliations suh as preload mehanisms for preision atuators [94], provided that the strain levels stay within the superelasti limit. There are three primary variables that affet the stress behavior of the SMA, ξ the fration of martensite, T the operating temperature and ε the strain, whih give σ σ ( ε,t, ξ ) =, where σ is the Piola-Kirhoff stress and ε is the Green strain. A ommon form of the onstitutive equation is given by the following; & σ = D & ε + θt& + Ω & ξ. (79) Taking the integral of equation (79) with respet to time, yield the following relation; o ( ε ε ) + θ ( T T ) + Ω( ξ ξ ) σ σ = D, (80) o o o where D is Young s modulus, θ is the thermoelasti tensor and Ω is the transformation tensor as given by Liang and Rogers [95]. A more omplete desription of the details of shape memory effets (SMEs) and superelastiity are presented by Otsuka and Wayman [96] and Srinivasan and MFarland [97]. To develop the amount of work available per unit volume of SMA atuator, the strain energy of the system an be alulated using the straightforward relationship; U = σdε, (81) 49

52 in units of [J/m 3 ]. Considering a stress of 300 MPa and a.0% strain operating in the supereleasti region where the stress is nearly onstant over the strain range, the work density of a SMA atuator is on the order of J m -3. This simplified representation of the work density is a useful tool for desribing the material behavior and possible appliation of suh a material as an atuation mehanism. Conluding remarks The atuator and sensor methods outlined above represent a large number of design options. It is hoped that by highlighting the relative merits and limitations of these devies, future designers might be able to narrow their hoies more rapidly. As funtional toleranes and overall dimensions beome smaller and more attainable, sientists and engineers will undoubtedly be epanding and reinventing some, if not all, of the topis disussed throughout this paper. It is the wish of the authors that this somewhat limited review provides a starting point for the plethora of researh and development required before fundamental physial limits are reahed for a large number of systems. Clearly, as we enter into the design of ever shrinking mehanial systems it will be the job of the designer to make hoies based on performane speifiations and their sale dependene. It is hoped that suh data will be olleted in a systemati and unified format, and any gaps in knowledge filled in by future researhers. As stated earlier, we believe that it will be the implementation of these tehnologies that will determine their relative suess in the marketplae. We are also aware that there an be other signifiant fators, partiularly eonomi, that might drive the widespread use of one tehnology over another. As smaller sale systems are developed so too will manufaturing proesses. Subsequently, with growing markets there will be aompanying eonomies of sale. For this reason, our attention is limited to the physis of the devies rather than tehnology barriers that also have an influene on implementation. Sensors are ontinuously shrinking with the development of new manufaturing proesses. While there are no lear winners, the highest preisions are more often than not ahieved with periodi sales having some form of quadrature detetion. 50

53 One pattern beoming apparent is the relative footprint of atuators in omparison to the proesses they drive. This is readily seen with the eletromagneti motors of mesosale lathes being omparable to that of the lathe itself and the eletrostati omb drives of MEMS devies typially around 1- or more times the size of the miromirrors and gears that they drive. Solution of these types of problems might drive new paradigms in system design. One possibility, for eample, would be to selet aross these sales and use a maro-sale motor to drive many mesosale mahines, muh like the old 19 th entury fatories. Perhaps this, and other, broader views may help identify patterns of hange in sale. From this, optimal system designs will emerge and hange as sales are further redued, ultimately to the fundamental physial limits imposed at atomi sales. Aknowledgements The authors would like to thank Dr s. Lowell Howard and Jon Pratt for their interest and thought-provoking onversation regarding the topis epressed in this paper. Thanks are also due to Dr. Steve Ludwik for his insightful omments. This work was performed under the auspies of the U.S. Department of Energy by University of California, Lawrene Livermore National Laboratory under ontrat No. W-7405-Eng

54 5

55 Referenes [1] Matey J.R. and Blan J., 1985, Sanning apaitane mirosopy, J. Appl. Phys., 57(5), [] Bugg C.J and King P.J., 1988, Sanning apaitane mirosopy, J. Phys. E: Si. Instrum., 1, [3] Lawall J. and Kessler E., 000, Mihelson interferometry with 10 pm auray, Rev. Si. Instrum., 71(7), [4] Badami V.K. and Patterson S.K., 00, A frequeny domain method for the measurement of non-linearity in heterodyne interferometry, Preision Engineering, 4(1), [5] Bobroff N., 1993, Reent advanes in displaement measuring interferometry, Meas. Si Tehnol., 4, [6] Shott, Walter and Jager, Gerd, 00, Miniature interferometers for preise distane measurements, Pro. ASPE, 7, [7] [8]Abou-Zeid A. and Wiese P., 1998, Interferometer with a wavelength tuned diode laser for surfae profilometry, Meas. Si. Tehnol., 9, [9] Dunn T.J., Mihaels R., Lee S., Tronolone M. and Kulawie A, 00, Fast optial form measurements of rough ylindrial and onial surfaes in diesel fuel injetion omponents, Pro. ASPE, 7, [10] 53

56 [11] Young, M., 000, Optis and lasers, Inluding Fibers and Optial Wavegides, Springer-Verlag, New York. [1] See for eample [13] See for eample [14] Kuroda A., Optial displaement measurement system for deteting the relative movement of a mahine part, US Patent # 6,166,817 and referenes therein. [15] Teimel A., 1991, Tehnology and appliation of grating interferometers in highpreision measurement, in Progress in Preision Engineering, eds. Seyfried P. et al., Springer-Verlag, Berlin, ISBN , [16] Born M. and Wolf E., 1980, Priniples of Optis, 6 th edition, hapter VIII, Cambridge University Press, the equation presented in this tet is an approimation to the more omplete analysis presented in this book. [17] Yaoot A. and Cross N., 003, Measurement of piometer non-linearity in an optial grating enoder using -ray interferometry, Meas. Si. Tehnol., 14, [18] Sawabe M., Maeda F., Yamaryo Y., Shimomura T., Saruki Y., Sakai H. and Aoyagi S., 00, Development of the vauum interferometri omparator for alibrating the fine linear enoders and sales, presented at the 7 th International Symposium on Laser Metrology, IMEKO, September 10 th. [19] Howard, L., Stone, J. and Fu, J., 001, Real-time displaement measurements with a Fabry-Perot avity and a diode laser, Preision Engineering, 5 (4), pg

57 [0] Froehlih, F. F. and Milster, T. D., 1994, Minimum detetable displaement in nearfield sanning optial mirosopy, Applied Physis Letters, 65 (18), pg [1] Paesler M.A. and Moyer P.J., 1996, Near-field optis: Theory, instrumentation, and appliations, J. Wiley and sons, NY, ISBN [] Bowling-Barnes R. and Silverman S., 1934, Brownian motion as a natural limit to all measuring proesses, Rev. Mod. Phys., 6, [3] Jones R.V. and Rihards J.C.S., 1973, The design and some appliations of sensitive apaitane mirometers, J. Phys. E., 6, [4] Tariq, H., et al., 00, The linear variable differential transformer (LVDT) position sensor for gravitational wave interferometer low-frequeny ontrols, Nulear Instruments and Methods in Physis Researh, Setion A: Aelerators, Spetrometers, Detetors and Assoiated Equipment, 489 (1-3), pg [5] Bowen D.K., Chetwynd D.G. and Shwartzenberger D.R., 1990, Sub-nanometer displaement alibration using -ray interferometry, Meas. Si. Tehnol., 1(), [6] Bekwith T.G., Buk N.L. and Marangoni R.D., 198, Mehanial measurements, 3 rd ed., AddisonWesley, Ma, hapter 1. [7] Miller, M. M., et. al., 1997, Development of a high preision absolute linear displaement sensor utilizing GMR spin-valves, IEEE Transations on Magnetis, 33 (5), pg [8] Popovi R.S., Flanagan J.A. and Besse P.A., 1996, The future of magneti sensors, Sensors and Atuators A, 56,

58 [9] Tsang C., 1984, Magnetis of small magnetoresistive sensors, J. Appl. Phys., 55(6), [30] Srag B.D. and Xiao G, 003, Submiron eletrial urrent density imaging of embedded mirostrutures, Appl. Phys. Letts., 8(19), [31] Smith C.H., Shneider R.W., Dogaru T., and Smith S.T., 00, GMR magneti sensor arrays for NDE eddy urrent sensing, Rev. Prog. In Quantitative NDE,, to be published [3] Dodd C.V. and Deeds W.E., 1968, Analytial solutions to eddy-urrent probe-oil problems, J. Appl. Phys., 39(6), [33] Smith C.H., Shneider R.W., Dogaru T., and Smith S.T., 00, GMR magneti sensor arrays for NDE eddy urrent sensing, Rev. Prog. In Quantitative NDE,, [34] Dogaru T., Smith C.S., Shneider R.W. and Smith S.T., 001, New diretions in eddy urrent sensing tehnology, Sensors Magazine, 18(6), [35] Yound R.D., 1966, Field emission ultramirometer, Rev. Si. Instrum., 37(3), [36] Young R.D., Ward J. and Sire F., 197, The topografiner, An instrument for measuring surfae mirotopography, Rev. Si. Instrum., 40(1), [37] Binnig G., Rohrer H., Gerber Ch. And Weibel E., 198, Tunneling through a ontrollable vauum gap, Appl. Phys. Letts., 40(1), [38] Binnig G. and Rohrer H., 198, Sanning tunneling mirosopy, Helv. Phys. Ata, 55,

59 [39] Chetwynd D.G. and Smith S.T., 1991, High preision surfae profilometry: From stylus to STM, in From Instruments to Nanotehnology, ed. Gardner J.W. and Hingle H.T., Gordon and Breah, London, [40] Binnig G., Quate C.F. and Gerber Ch., 1986, Atomi fore mirosope, Phys. Rev. Letts., 56(9), [41] See for eample Matthais Sherge and Stanislav N. Gorb, 001, Biologial miroand nanotribology: Nature s solutions, Springer-Verlag, Berlin, ISBN Sarid D., 1994, Sanning fore mirosopy: With appliations to eletri, magneti and atomi fores, Oford University Press. [4] Mavroidis C., Pfeiffer C. and Mosley M., 1999, Conventional atuators, shape memory alloys, and eletrorheologial fluids, in Automation, miniature robotis and sensors for non-destrutive testing and evaluation, ed. Bar-Cohen Y., hapter 5. [43] Spadaini, C., Zhang, X., Cadou, C., Miki, N., and Waitz, N., 003, Preliminary Development of a Hydroarbon Fueled Catalyti Miro Combustor, Sensors and Atuators, 103, pg [44] Whalen, S., Thompson, M., Bahr, D., Rihards, C. and Rihards, R., 003, Design, Fabriation and Testing of the P3 Miro Heat Engine, Sensors and Atuators, 104, pg [45] Anderson, B., 00, Piezoeletri atuators move preisely and powerfully, Laser Fous World, 38 (9), pg [46] Bittle, S. D. and Kurfess, T. R., 1997, An Ative Piezoeletri Probe for Preision Measurement on a CMM, Mehatronis, 7 (4), pg

60 [47] Mitrovi, M., Carman, G. P. and Straub, F. K., 001, Response of piezoeletri stak atuators under ombined eletro-mehanial loading, International journal of solids and strutures, 38 (4-5), pg [48] Harb, S. Smith, S. T. and Chetwynd, D. G., 199, Subnanometer behavior of a apaitive feedbak, piezoeletri displaement atuator, Rev. Si. Instrum., 63 (), pg [49] Samuelson, M., et al., 1997, Atuator systems for preision motion ontrol, Advanes in the Astronautial Sienes, 94, Proeedings of the 1997 Annual AAS Roky Mountain Guidane and Control Conferene, Feb , Brekenridge, CO, USA, pg [50] Binnig, G. and Smith, D.P.E., 1986, Single-tube-3-dimensional sanner for sanning tunneling mirosopy, Rev. Si. Instrum., 57 (8), pg [51] Chen, C. J., 199, Eletromehanial defletions of piezoeletri tubes with quartered eletrodes, Appl. Phys. Lett., 60 (1), pg [5] Wang, Z., Jouaneh, M. K. and Dornfeld, D. A., 1990, Design and haraterization of a linear motion piezoeletri miropositioner, IEEE Control Systems Magazine, 10 (), pg [53] Park, J., et al., 001, Development of a ompat displaement aumulation atuator devie for both large fore and large displaement, Sensors and Atuators, A: Physial, A 90, pg [54] Kim, S-C. and Kim, S. H., 001, A preision linear atuator using piezoeletrially driven frition fore, Mehatronis, 11 (8), pg

61 [55] Kim, J-D. and Nam, S., 1997, Development of a miro-depth ontrol system for an ultr-preision lathe using a piezoeletri atuator, Int. J. Mah. Tools Manufat., 37 (4), pg [56] Gao, P. and Swei, S., 1999, A si-degree-of-freedom miro-manipulator based on piezoeletri translators, Nanotehnology, 10 (4), pg [57] Gao, P., Swei, S-M. and Yuan, Z., 1999, A new piezodriven preision miropostioning stage utilizing fleure hinges, Nanotehnology, 10 (4), pg [58] Janoha, H. and Kuhnen, K., 000, Real-time ompensation of hysteresis and reep in piezoeletri atuators, Sensors and Atuators, A: Physial, 79 (), pg [59] Xu, Y. and Jones, B., 1997, A simple means of prediting the dynami response of eletromagneti atuators, Mehatronis, 7 (7), pg [60] Janoha, H., 001, Appliation potential of magneti field driven new atuators, Sensors and Atuators, A: Physial, 91 (1-), pg [61] Awabdy, B. A., Shih, W-C. and Auslander, D. M., 1998, Nanometer Positioning of a Linear Motion Stage Under Stati Loads, IEEE/ASME Transations on Mehatronis, 3 (), pg [6] Smith, S. T. and Chetwynd, D. G., 1990, An optimized magnet-oil fore atuator and its appliation to preision elasti mehanisms, Proeedings of the Institution of Mehanial Engineers, Part C: Mehanial Engineering Siene, 04 (4), pg [63] Hadfield D., 196, Permanent magnets and magnetism, John Wiley and Sons, In., London. 59

62 [64] Kiang, M.-H., Solgaard, O., Lau, K. Y. and Muller, R. S., 1998, Eletrostati Combdrive-Atuated Miromirrors for Laser-Beam Sanning and Positioning, Journal of Miromehanial Systems, 7 (1), pg [65] Kallenbah, E., et al., 1999, New polarized eletromagneti atuators as integrated mehatroni omponents design and appliation, Mehatronis, 9 (7), pg [66] Chen, F., Xie, H. and Fedder, G.K., 001, A MEMS-Based Monolithi Eletrostati Miroatuator for Ultra-Low Magneti Disk Head Fly Height Control, IEEE Transations on Magnetis, 37 (4), pg [67 ] Feddeme J.T., Warne L.K., Johnson W.A., Ogden A.J. and Armour D.L., 00, Assembly of LIGA using eletri fields, Sand report, sand , see also [68] Bobbio S., Goodwin-Johansson J., DuBois T., Tranjan F., Smith S., Fair R., Ball C., Jaobson J., Bartlett C., Eleyan N., Makki H. and Gupta R., 1996, Integrated fore array: Positioning drive appliations, Pro SPIE, 7, the higher work densities quoted in this paper are based on a private ommuniation and represent more reent work arried out in 00. [69] Kim K.J. and Shahinpoor M., 00, Appliations of polyeletrolytes in ioni polymeri sensors and artifiial musles, in Handbook of Polyeletrolytes and their Appliations, ed. Tripathy S.K., Kumar J. and Nalwa H.S., vol. 3:Appliations of Polyeletrolytes and Theoretial Models, Amerian Sientifi Publishers, ISBN

63 [70] Taylor, G. W., et. al., 1985, Piezoeletriity, Ferroeletriity and Related Phenomena Vol. 4, Gordon and Breah Siene Publishers, New York, NY, ISBN: [71] Zhuang, Z. and Shi, H., 1993, Temperature-stable high eletrostritive strain relaor ferroeletri eramis for servo-atuator appliations, Sensors and Atuators, A: Physial, 35 (3), pg [7] Uhino, K., 1995, Advanes in erami materials, Materials Letters, (1-), pg [73] Cross, E. L., 1996, Ferroeletri materials for eletromehanial transduer appliations, Materials Chemistry and Physis, 43 (), pg [74] Lu, T. J. and Evans, A. G., 00, Design of a high authority fleural atuator using an eletro-stritive polymer, Sensors and Atuators, A: Physial, 99 (3), pg [75] See for eample Etrema Produts In., 500 North Loop Drive, Ames, Iowa, IO [76] Portman V., Sandler B.Z., 1999, High-stiffness preision atuator for small displaements, Int. J. Mahine Tools and Manuf., 39, [77] Gravesen, P., 1993, Mirofluidis a review, Journal of Miromehanis and Miroengineering, 3 (4), pgs [78] Andersson, H. and van der Berg, A., 003, Mirofluidi devies for ellomis: a review, Sensors and Atuators, B: Chemial, 9(3), [79] Harmon, M. E., Tang, M., and Frank, C. F., 003, A mirofluidi atuator based on thermosponsive hydrogels, Polymer, 44(16),

64 [80] Chong, J. M. and MaDonald, N.C., 1998, Suspended moving hannels and hannel atuators for mirofluidi appliations, Amerian Soiety of Mehanial Engineers, Dynami Systems and Control Division, 66, Miro-Eletro-Mehanial Systems (MEMS), [81] See for eample Zemansky M.W., 1957, Heat and Thermodynamis, MGraw-Hill, NY, hapter 9. [8] Henning, A.K., 1998, Mirofluidi MEMS, In Proeedings, IEEE Aerospae Conferene, Paper 4.906, IEEE Press, Pisataway, NJ, 1998, [83] Butefish, S., and Buttgenbah, S., A New Pneumatially Atuated Miniature Gripper for Miro Assembly,. [84] Grosjean C. and Tai Y.A., Thermopneumati Peristalti Miropump, Calteh Miromahining Lab, Calteh EE , Pasadena, CA [85] Meng E., Wang X., Mak H., and Tai Y., A Chek-Valved Silione Diaphragm Pump Calteh Miromahining Lab, , Calteh, Pasadena, CA [86] Bridgeman P.W., 1949, The physis of high pressure, G. Bell and Sons, Ltd, London, hapter 6, ompressibility of solids. 6

65 [87] Mihalz, I., 001, Fundamental Charateristis and Design Method for Nikel- Titanium Shape Memory Alloy, Periodia Polytehnia, Mehanial Engineering, 45 (1), pgs [88] Webb, G., Wilson, L., Lagoudas, D. and Rediniotis, O., 000, Adaptive Control of Shape Memory Alloy Atuators for Underwater Biomimeti Appliations, AIAA Journal, 38 (), pgs [89] Otsuka, K. and Kakeshita, T., 00, Siene and Tehnology of Shape-Memory Alloys; New Developments, MRS Bulletin, 7 (), pg [90] Bergamaso, M., Dario, P. and Salsedo, F., 1990, Shape Memory Alloy Miroatuators, Sensors and Atuators, A: Physial, 1 (1-3), pgs [91] Gordaninejad, F. and Wu, W., 001, A two-dimensional shape memory alloy/elastomer atuator, International Journal of Solids and Strutures, 38 (19), pgs [9] Krulevith, P., et al., 1996, Thin Film Shape Memory Alloy Miroatuators, Journal of Miroeletromehanial Systems, 5 (4), pg [93] Rivin E.I., Sayal G., Johal P.R.S. and Singh R.P.G., 004, Strutural appliations of SMA/superelasti materials, Pro. 004 NSF Design, Servie and Manufaturing Grantees and Researh Conferene, Dallas, TX. [94] Samuelson, M., et al., 1997, Atuator systems for preision motion ontrol, Advanes in the Astronautial Sienes, 94, Proeedings of the 1997 Annual AAS Roky Mountain Guidane and Control Conferene, Feb , Brekenridge, CO, USA, pg

66 [95] Liang, C and Rogers, C.A., 199, Design of Shape Memory Alloy Atuators, Journal of Mehanial Design, 114 (), pg [96] Otsuka, K. and Wayman, C.M., 1998, Shape Memory Materials, Cambridge University Press, Cambridge, UK, 84 Pgs., ISBN: [97] Srinivasan, A.V. and MFarland, D.M., 001, Smart Strutures: Analysis and Design, Cambridge University Press, Cambridge, UK, 8 Pgs., ISBN: