6-DOF DESK-TOP OIE-OIL JOYSTIK S.E. Salcudean and N.R. Pake Depatment of Electical and ompute Engineeing Univesity of Bitish olumbia ancouve, B, 6T Z, anada f tims@ee.ubc.ca g ABSTRAT This pape pesents the design of a 6-DOF desk-top magnetically levitated foce-feedback joystick utilizing voice-coil actuation. Relative to pio designs (Hollis et. al., 99),(Salcudean et. al., 995),(Bekelman et. al., 996), this haptic inteface featues a novel geomety, a novel optical senso and optimized actuation. These allow fo all the electonics including the contol micopocesso to be integated in its base, with the device tapeing fom a handle 5.5" high to a footpint of 0.5"5.5". The device has a maximum tanslational motion ange of 3mm limited by the actuation gap, and a pedicted maximum otational motion ange of 5 limited by the senso motion ange. The moving mass of 60 gams will have maximum acceleations exceeding 0 g's, and will be able to exet continuous foces as lage as 6N. INTRODUTION A numbe of haptic inteface designs have been poposed fo vitual envionments and teleopeation systems. The eade is efeed to pio ASME-DS volumes, to (Stocco and Salcudean, 996) fo a detailed suvey, and to (Haywad and Astley, 995) fo pefomance measues. The need fo high acceleation in haptic intefaces has been demonstated in many studies and seems to have been accepted by designes. Although most epoted designs have tanslational wokspaces that exceed a cube with 0cm sides, it has not been demonstated that a wokspace of this magnitude is eally needed. Indeed, fo desk-top computing, input devices such as mice, tackballs o joysticks ae commonplace, and these devices have elatively small motion anges to avoid tiing the opeato. Futhemoe, designing high acceleation devices ove lage wokspaces is a non-tivial task equiing expensive actuatos, tansmissions and joints. As an altenative, the use of a small wokspace haptic device in ate mode o combined position/ate mode has been poposed and demonstated befoe (Salcudean et. al., 995). It has been agued in seveal papes (see, fo example, (Hollis and Salcudean, 993),(Salcudean et. al., 995)), that magnetically levitated (maglev) Loentz devices (Hollis et. al., 99) ae suitable small-motion haptic intefaces because of thei low mechanical impedance and high acceleation ability. Devices have been built at IBM (Hollis et. al., 99), Univesity of Bitish olumbia (Salcudean et. al., 995), and anegie-mellon Univesity (Bekelman et. al., 996). With espect to pio maglev designs, the haptic inteface pesented in this pape has the following novel featues: (i) a new cubic geomety leading to a smalle device with a pefectly conditioned tansfomation fom actuato cuents to esultant foces, (ii) a new, inexpensive, optical senso using thee linea position-sensing diodes and multiplexed plana infaed light beams, (iii) optimized voice-coil actuatos. These featues ae integated in a novel way into a device that is the st maglev haptic inteface that is inexpensive and small enough to t on the use's desk by awokstation o P. The pape is oganized as follows: st, the electomechanical design of this haptic inteface is pesented. A simple methodology fo voice-coil actuato optimization fo maximum eciency is discussed next. Then, the novel optical senso is pesented. Issues elated to the contol electonics and implementation follow. The pape concludes with the poject status and plans fo futue wok. ELETROMEHANIAL DESIGN The photogaph of the maglev haptic inteface pototype is shown in Figue. The use manipulates a mouse-like handle attached to a mobile oto shown in Figue. The oto
Figue : Photogaph of the maglev desk-top joystick: a sloped suppot allows the use to easily gasp the diskshaped handle. Figue 3: boad. Maglev joystick stato, oto and contolle can move within the connes of a stato that is attached by thee mounting posts to a plastic base. A pinted cicuit boad (PB) ts between the stato and the plastic base and caies the device sensing and powe electonics and a micocontolle. A photogaph of the main components - stato, oto and PB - is shown in Figue 3. The oto and stato of the device ae shown schematically in Figue. The basic actuato is the same as used befoe in a numbe of designs (Hollis et. al., 99) and is shown in Figue 5. Figue : Maglev joystick oto Six at coils t in the faces of the hollow cubic oto stuctue having an oute dimension equal to 53mm, a shell and coil thickness equal to d c =5mm, and a mass of 90 gams. The coils ae oiented along the diagonals of each cube face. Inside the oto shell, stato magnets matching the coils ae aanged on a cubic soft ion coe. Outside the oto shell, magnets matching the coils ae mounted on soft-ion etun plates aanged in a cubic stuctue. The magnet dimensions ae l m = 0mm, w m =8mm, t m =mm, and the magnetic gap is d =mm. The magnetic gaps allow the stuctue to tanslate 3mm in any diection in the absence of otation. The otational and tanslational wokspaces do not decouple in this design, unlike in the spheical geomety suggested in (Bekelman et. al., 996). Howeve, the angula motion of the device is substantial (at least 0 ) fom nominal, and is actually limited by the optical senso ange, not by mechanical intefeence. Because the oto coils ae aanged along the diagonals of a cube as shown, fou of the cube vetices can be cut away. Thee of these leave oom fo suppot posts to hold the inne cubic stuctue, and one leaves oom fo the optical senso, descibed late in the pape. A light handle can be mounted on a vetical shaft penetating the top vetex. The device modeling follows closely the appoach fom (Hollis et. al., 99) and will not be pesented in detail. The oto is epesented schematically in Figue 6. In the nominal position, the esultant wench vecto acting on the oto is computed by summing the foces f i and toques F i f i, whee f i is computed by taking the vecto poduct I i B i of the cuent vectos I ; :::; I 6 and the magnetic eld vectos B ; :::; B 6 (these ae outwad nomals to the faces of the cube and ae not dawn). These calculations ae st done with espect to the vetex coodinate system f;[i j k ]g, then ae tansfomed to the coodinate system ff; [i F j F k F ]g located at the cente of the cube and having k F aligned with the vetical (in Figue 6 the plane of vetices A ; B ; is hoizontal). A esultant 6 6 matix A mapping unit coil cuents to oto wenches can be obtained fom the device geomety, and the actuato foce gain of N/A pedicted fom calculations done late in the pape fo
w m tm lm Figue 5: Basic Flat oil Actuato I3 Figue : Haptic Inteface Assembly Schematic a coil esistance R =8: A = 6,:5 :3,:5,3:6 3:6 0,:00 0 :00,:00,:00 :00,3:7,3:7,3:7 0 0 0,0:0 0 0:0 0:03 0:03,0:07 0:06,0: 0:06,0:06 0:06 0 0 0 0 0:09 0:09 0:09 The st thee ows of A have units of N/A, the next thee Nm/A. It is wothwhile noting that A has two goups of equal singula values 5:66; 5:66; 5:66 N/A and 0:6; 0:6; 0:6 Nm/A coesponding to foces and toques, thei scaled values giving the maximum foces and toques that would be obtained with a given powe supply if all coil esistances wee identical. Thus this geomety distibutes the powe load acoss the actuatos in a unifom manne. With the optimized actuatos used in this design, the powe needed to actively levitate the cubic oto and a handle attached to it (total mass 60 gams) is only P lev = :6 W. ATUATOR OPTIMIZATION onside the actuato shown in Figue 5. Let d c be the coil width, d the gap between the magnets, and d = d, d c the coil 3 7 5 : A I k i j if 6 k F F j F I 3 I6 I5 5 I B Figue 6: oodinate assignments, coil centes and cuent vectos. \attle space". Let l wie be the coil wie length, and pack be the coil \packing eciency", i.e., pack = s eff =s wie, the atio of conducting to total wie coss-sectional aea. Note that pack depends on the wie coss-sectional shape (best packing achieved by at wie), and the atio of insulating mateial to conducting mateial. Let be the coil conducto esistivity and R be the coil esistance. Let P coil be the powe dissipated in the coil, and let I be the coil cuent. The actuato foce is given by Loentz's law. In obtaining the design fomula (6) below, it is assumed that (i) the ux cossing the coil is a constant B g, and, (ii) finging elds ae negligible, i.e., the ux outside the magnet pojection though the coil is negligible. Fo the actuato in Figue 5, given assumption (ii), the length of wie that poduces a foce is given by l eff = l mwmdc=swie. Then, with geom =l mwmdc=(swielwie) being an eciency facto detemined by the coil geomety, we ob-
. 0.55 0.5 Maximum foce <Newtons> 3.9 3.8 3.7 Magnetic Flux <Tesla> 0.5 0. 3.6 0.35 3.5 8 9 0 3 Magnetic gap <millimetes> Figue 7: Actuato foce vs gap with d = 6mm at P coil = 8W (l m = 0mm, w m = 8mm, and t m = mm), giving actuato gain at a cuent of A. tain the following expession fo the actuato foce: F (B g;d;lm;wm;tm) =B g I leff () P = coil B g R s = B g P coil l wie pack s wie = B g p pack P coil = B g p pack p geom P coil l mwmdc s wie () lmwmdc s wie (3) l mwmdc () s wielwie p wmlmdc (5) p p P = coil p B g pack geom wmlm(d, d ) : (6) Fo the coil shown in Figue 5, geom l mwm=(lmwm +w m), and is appoximately 0:6. Packing eciencies fo conventional (ound coppe wie) coils ae about 75%, with at coppe coils eaching values close to 95%. Assuming that the actuato ux in Figue 5 is steeed pefectly by the soft ion back-plates, the eld in the cente of the gap aligned with the cente of the magnet can be calculated by eplacing the actuato magnets with equivalent solenoids and using the Biot-Savat Law. It is given by (Magnet Sales, 996): B g(d; l m;wm;tm) = B w mlm [tan, p d d + lm + wm, tan, p w mlm ] ; (7) (t m + d) (t m + d) + lm + wm whee B is the magnetic mateial esidual ux. Substituting (7) in (6), one can elate the actuato dimensions to the esulting foce. An additional lowe bound of the fom t s w m can be imposed on the ion etun plates thickness in ode to avoid satuation. With appopiate inequality constaints to account 0.3 0 3 5 6 Offset fom Gap ente <mete> x 0 3 Figue 8: Pedicted gap eld at optimum gap (mm) fo the desied geometical dimensions, e.g.,t s+t m+d d max, t m, w m, l m, and d that maximize actuato foce can be obtained by solving a nonlinea pogam. The geometical eciency geom inceases with the atio l m=wm, while l m +w m will be bounded by oto size. In pactice, l m, w m ae selected sepaately as a function of oto geomety, desied motion and foce ange and desied foce lineaity. Then the magnet thickness t and the magnetic gap ae selected by plotting the actuato foce as a function of the magnetic gap d, as shown in Figue??, and choosing the maximizing d, i.e., the best coil-width fo a given attle space. In this paticula design, optimal actuato foces wee calculated fo a numbe of eadily available magnet dimensions fom plots such as the one shown in Figue 7. The dimensions l m = 0mm, w m = 8mm, and t m = mm wee selected as they show only a 5% loss of foce elative to olde designs (Hollis et. al., 99),(Salcudean et. al., 995) fo the same powe consumption, and ove fou times less magnetic mateial! Note that the coil width to gap atio is substantially lage in this design then in all othe epoted designs (Hollis et. al., 99),(Salcudean et. al., 995),(Bekelman et. al., 996). Futhemoe, note that the above fomulation does not involve the coil esistance, only the powe dissipated in it, its esistivity and geometical popeties. Thus the coil esistance can be selected fo maximum powe tansfe fom the powe amplie afte nding its dimensions. Not supisingly, the wie gauge in this design was selected to give R = 8 in ode to match available cuent dives. Note that the pedicted actuato foce is coect only in the middle of the gap, when the oto is in its nominal cente. The magnetic eld fomula (7) can be extended to give the eld along the magnet cente line (Magnet Sales, 996). The pedicted cuve fo the optimal gap (mm) obtained in Figue 7 is displayed in Figue 8. Note that the eld inceases nea the magnets, giving a non-unifom foce. This is aveaged, to a cetain extent, bythe thick coil. Pedicted foce and eld values have been compaed to expeimental ones with small eos (less than 5%) in seveal actuato designs of vaious sizes.
P P 5 k j P6 i P3 PSD 6 5 PSD 3 B A P P B PSD B B A PSD A PSD B LEDs geneating light plane A B A PSD A Figue 0: LED conguation fo optical senso Maglev Wokspace Fo 3 Degees Rotation OPTIAL SENSOR Figue 9: Optical senso schematic Anovel optical senso to compute the position and oientation osets of the oto with espect to the stato has been designed and ts unde the hoizontal coils of the oto. Its schematic epesentation is shown in Figue 9. Thee linea position sensing diodes (PSDs) ae placed on a hoizontal plane unde the oto. The PSDs ae mounted diectly on the device PB, so the plane is the PB plane tanslated upwads by the thickness of the PSDs. Thee light planes AB, B, and A, paallel to the oto faces (hee, fo simplicity, schematically shown to coincide with the oto faces) ae geneated by wide-angle infaed light emitting diodes (LEDs) attached to the oto unde the vetical coils and pojecting infaed light though naow slits towads the vetex,asshown schematically in Figue 0. These light planes ae tuned on in sequence, st AB, then B, then A, at high fequency, by the device micocontolle. When AB is ON, the positions of the light spots P and P ae detected by PSD A and PSD B, espectively, by measuing the PSD cuents in synchonization with the ashed light plane. When B is ON, the light spot positions P 3 and P ae detected by PSD B and PSD, espectively. When A is ON, the light spot positions P 5 and P 6 ae detected by PSD and PSD A, espectively. When the oto is in its nominal position with espect to the PSDs, points P and P 6 collapse into one point, and so do the pais P, P 3 and P, P 5 as shown in Figue 0. The position of the moving oto with espect to a xed coodinate system can be obtained fom the plane coodinates of the points P i, i =; :::; 6, by st computing the intesections A of P P with P 5P 6, B of P P with P 3P, and of P 3P with P 5P 6, then by computing as the point of intesection of thee sphees of diametes kabk; kbk; kak. Indeed, the loci of such that the angles ( A;B), d ( B;) d and ( ;A) d ae 90 ae Z (mm) 50 8 6 0 5 0 Y (mm) 5 6 X (mm) Figue : Optical senso tanslational wokspace fo abitay otations not exceeding 3 : the z-axis is the height of the vetex with espect to the PSD plane sphees with diagonals AB, B and A. Once is located, [i ;j ;k ] can be computed by nomalizing A;B;. Note that simila sensos can be constucted by using thee light planes that intesect thee linea PSDs (o linea Ds) and solving the associated diect kinematic equations numeically via an iteative method such as Newton's method. If the light planes ae along the faces of a pyamid, the intesection of thee thoi needs to be computed. This senso has a numbe of advantages. Unlike pio LED- PSD-based sensos used in pevious maglev wists (Hollis et. al., 99),(Bekelman et. al., 996), only linea, not twodimensional, PSDs ae necessay. Since LEDs ae inexpensive, cost savings fo a simila measued volume ae oughly one ode of magnitude (the optical senso descibed hee costs oughly US$60 in quantities, while a senso using two-dimensional PSDs would cost oughly US$600 in quantities, based on PSD pices fom the same manufactue). Since the PSDs ae in the same 0
plane, they can be mounted on a single pinted cicuit boad, with bette alignement and manufactuability than would be the case if a thee-dimensional PSD stuctue wee used. The senso wokspace is easy to quantify when the tanslation and otation ae decoupled. The tanslational wokspace at null oientation is the union of two symmetical pyamids, and becomes smalle as nite otations of abitay axis ae allowed (with PSDs with active aeas of mm each, the hoizontal side of the pyamid is oughly mm at null otation). The semidextous wokspace volume showing the achievable tanslations fo abitay axis oto otation of up to 3 is shown in Figue. ONTROLLER BOARD The contolle boad is a 0.6"x5" PB compising the following: - analog electonics to amplify the PSD cuents - LED tansisto dives - analog-to-digital convetes to ead the input fom the PSDs, with enough spae channels to accommodate the outputs of a six-degee-of-feedom foce senso that could be mounted on the oto - Pulse-Width-Modulation (PWM)-diven H-bidges fo the coils (3A continuous, 6A fo 00ms peaks, max foces and acceleation mentioned in the abstact and conclusion based on these specs and a 8 extenal powe supply). - one small fan fo occasional foced ai cooling, -two seial and one paallel communication pots. The seial pot can be used as a fast synchonous link allowing eal-time contol by a emote host. A second seial pot is povided fo the use of debugging tools. Seveal host communication methods ae being povided, even though they take a signicant amount of PB space, fo exibility and exploation of the best appoach to host connection. - a 50MHz Intel 8096NU micocontolle with associated EPROM and RAM. The micocontolle pefoms basic I/O communications with a host. It geneates the time-multiplexed light planes needed fo optical sensing and the PWM signals needed to dive the coils, and it computes the basic contol functions (diect kinematics, wench vecto computation accoding to a contol law fo mechanism emulation, and tansfomation of the contol wench into equivalent coil foces o cuents). The suppot posts shown in Figue locate the stato elative to the PB and senso, close to one of the PB sides, thus allowing a tapeed suface fo the use's foeam and wist to est on. The contolle boad has been built and its basic functions have been tested. The basic opeation of the optical senso has been successfully tested, although some changes ae equied to povide a unifom intensity light plane in ode to achieve the best esolution. uent dive outines, communication outines fo SGI machines and xed point kinematics outines have also been witten and tested, but to this date the oto has not yet been \own". ONLUSION The design of a small motion-ange 6-DOF haptic inteface was pesented, including novel geomety and packaging, optical senso, and actuato optimization. It is envisaged that the device will be used as (i) an intelligent haptic inteface emulating simple mechanisms fom its own libay o downloaded fom the host compute, such as limit stops, gimbals, slides, vaious fiction foces and simple geometic constaints that can be computed using its xed-point micocontolle, (ii) a \dumb" haptic inteface o teleopeation maste, with the micocontolle boad acting as an input-output boad and most calculations being pefomed by the host o anothe extenal compute. The fome mode does not equie high communication ates with the host compute, while the second one does, as low-level data such as stinesses and foces ae being passed between the host and the micocontolle boad. The chaacteistics of the device ae summaized in the following table: Moving mass 60 gams Motion ange 3 mm, 5 Maximum acceleation > 0 g Maximum continuous foce 6 N Peak foce 3 N Powe consumption fo levitation.6 W Optical senso esolution appox. 0 micons Isotopic design Optical senso one ode of magnitude cheape than used in pevious designs Optimized actuato ove 50% moe ecient than in pevious designs All electonics except powe supply integated in the base with a 0.5"x5.5" footpint Table : Summay of desk-top joystick chaacteistics. The haptic inteface has a motion ange that exceeds that of the successful passive \Space Mouse"/\Logitech Magellan" 6-DOF joystick designed in D. G. Hizinge's goup at DLR (Dietich and Plank, 988),(Hizingge et. al., 99), has high acceleation and foce capability, and ts, complete with all electonics and a micocontolle, into a small enclosue tapeing down fom a handle 5.5" high to a base oughly two thids the size of a sheet of pape. AKNOWLEDGEMENTS The authos wish to thank A. Kelley fo ealy design and othe discussions, S. Bachmann fo help with the mechanical design and senso testing, L. Welde fo help with the boad design, constuction and debugging, and D. Fletche and L. Kjolby fo machining. The oiginal contolle boad design was done by Y. Lehe unde the authos' supevision. This wok is suppoted by the anadian IRIS NE poject HMI-6 and an associated Bitish olumbia Povincial Infastuctue gant.
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