Trjectory of Contct Region On the Fingerpd Gives the Illusion of Hptic Shpe Hnif Dostmohmed nd Vincent Hywrd Astrct When one explores solid oject with fingertip, contct region is usully defined. When the trjectory of this region on the fingerpd is rtificilly controlled so s to resemle the trjectory tht is normlly present while exploring rel oject, the experience of shpe is creted. In order to generte pproprite locl deformtion trjectories, we uilt servo-controlled mechnism tht rolled flt plte on the fingerpd during the mnul explortion of virtul surfces so tht the plte ws kept tngent to virtul shpe t the point of virtul contct. An experiment ws then designed to test which mode of explortion mximized the shpe informtion gin: ctive versus semi-ctive explortion, where semictive explortion is when one hnd touches pssively nd the other moves the trget oject, nd the use of single versus multiple points of contct. We found tht sujects were le to perform curvture discrimintion t levels comprle to those chieved when using direct mnul contct with rel ojects, nd tht the highly simplified stimulus provided y the device ws sufficient cue to give the illusion of touching three dimensionl surfces. Keywords Hptic Perception. Illusory Perception. Shpe Discrimintion. Introduction When n oject is ctively explored, cues such s proprioceptive cues, locl cutneous deformtion, friction, etc., re integrted together to yield the unified experience of n oject. This is the cse when the oject is sttionry nd when the exploring hnd is the sme s the hnd through which the shpe is experienced. When explortion involves two hnds: one to move the oject nd the other to touch it, similr cues re expected to contriute to the experience of shpe. In this cse however, the cues cn e expected to comine differently or with different weights. The understnding of these elementry cues nd of their contriutions to n overll percept is therefore essentil to the understnding of hptic shpe perception. Artificil stimuli produced with the id of hptic interfces hve lredy provided some insight in wht these cues might e nd how they comine (Roles-De-L-Torre nd Hywrd, 2001; Drewing nd Ernst, 2003). However, most ville hptic interfce devices To whom correspondence should e ddressed. Hptics Lortory, Centre for Intelligent Mchines, 3480 University Street, McGill University, H3A 2A7, Cnd, hywrd@cim.mcgill.c, Fx. +1-514-398-7348. This reserch ws supported iris, the Institute for Rootics nd Intelligent Systems, nd nserc the Nturl Sciences nd Engineering Reserch Council of Cnd. The uthors thnk A. M. Smith nd G. Roles- De-L-Torre for insightful comments on erlier drfts of the mnuscript. 1
rely shpe informtion through the use of force feedck nd ssume tht virtul proe serves s n intermediry etween the stimulus nd the opertors finger(s). Previous studies hve indicted tht direct fingerpd contct is criticl nd in fct key to mny hptic tsks due to the distriuted fingerpd deformtion tht occurs (Peine nd Howe, 1998). With displys relying on the virtul proe ssumption, however, judging shpe nd curvture informtion is clerly t est s inefficient s in the rel condition of eing forced to explore nd judge the shpe of rel oject thought the use of stylus (Ledermn nd Kltzky, 1999; Christou nd Wing, 2001; Kirkptrick nd Dougls, 2002). The contriutions of elementry cues to curvture perception hve rrely een studied in isoltion, however, mny relted spects of tctile shpe perception hve een documented in the pst. Severl studies hve shown tht cutneous receptors, nd in prticulr Type I SA receptors, in the glrous regions of the hnd re highly tuned to curvture informtion (Srinivsn nd LMotte, 1991; LMotte nd Srinivsn, 1993; Vierck, 1979). Pont et l. (1997) clssified the vrious roles plyed y different prts of the hnd for the hptic discrimintion of curvture. They found tht not only is cutneous stimultion importnt for curvture perception, ut the size of the re of the skin in contct with the stimuli lso plys significnt prt in incresing discrimintion performnce. Goodwin et l. (1991) showed tht constnt curvture informtion could e judged from sttic curvture informtion presented to fingerpd to high degree of precision. When physicl ojects with constnt curvture were presented to sujects, they found the detection threshold to e +4.9 m 1 for convex shpes presented to the fingerpd nd 5.4 m 1 for concve shpes. In the present study, we were interested in demonstrting tht curvture nd shpe informtion could e perceived through the sole production of contct region trjectory on the fingerpd designed to resemle tht cused y the interction with physicl oject. To test this, we uilt device tht rolled flt plte on the fingerpd of suject during the explortion of the surfce of virtul oject. The principle of this technique is illustrted y Fig. 1. It shows how plte cn cuse deformtion trjectory on the fingerpd tht resemles the pttern creted y the explortion of rel oject, simply y driving the plte to e tngent to the surfce of the virtul shpe eing explored. Figure 1: ) Trversl of fingerpd over physicl oject. ) A fingerpd deformtion trjectory similr to when trversing rel oject cn e creted y rolling plte on it. This cn e ccomplished y rotting the plte round point locted t the pex of the one of the distl phlnx (dshed circle), nd y keeping the plte tngent to the virtul shpe t the point of virtul contct. Although the entire set of the cues used y humns to cquire shpe y touch is not known, those tht were relily eliminted y our experimentl method include: proprioceptive cues due to verticl finger movement during explortion of surfce, ll force cues correlted to oject geometry, ll cues relted to skin deformtion within the re of 2
contct, s well s ll cues due to sliding. The only cue left ws the contct trjectory. With this method, we investigted whether vrying modes of explortion hd n effect on the overll performnce of curvture discrimintion. Doing so, we found tht sujects were le to perform typicl shpe discrimintion tsk t levels of performnce which were similr to those which hve lredy een reported in the literture for sujects exploring ctul ojects (Goodwin et l., 1991). Active touch ws defined y Gison (1962) to e where the suject ctively controlled the movement over trget surfce nd pssive touch to e where the suject remined sttionry nd stimulus ws imposed. These two modes of explortion hve een studied y vrious groups, demonstrting tht significnt differences exist in judging the ttriutes of physicl stimuli when compring ctive versus pssive touch (Loomis nd Ledermn, 1986; Ledermn nd Kltzky, 1987; Pont et l., 1999). The mjority of studies in this re hve shown tht self-controlled explortory movements generlly ply role in incresing performnce in the judgment of oject ttriutes. To these previously descried modes, we suggest dding third tht we termed semictive touch, where suject uses one hnd to touch pssively, nd uses the other hnd to hold nd move the trget oject. This hppens frequently when n oject is smll enough to e held with one hnd nd explored y the other. It is lso mode often used when deling with flimsy ojects. To pprecite the fltness of sheet of metl, for exmple, it is quite prcticl to touch the sheet with one hnd nd to use the other to slide it under the sttionry finger(s). The specific ims of the present study were (1) to demonstrte tht three dimensionl shpes cn e experienced through the movement of the deformed region of contct re on the fingerpd s suject trverses over virtul shpe in mnner tht is similr to trversing over rel physicl oject, (2) to find the threshold of curvture detection t which sujects could identify the stimuli presented s either convex or concve with n ccurcy of 75%, (3) to exmine the effect of ctive versus semi-ctive explortion using our device, nd (4) to exmine the effect of using single versus multiple points of contct. Mterils nd Methods Apprtus A device ws designed to orient flt plte round fixed point under servo control. This ws ccomplished through the use of sphericl five-r prllel linkge hving the property of constrining its links to move on sphericl surfces (see Appendix A for more detil). The links drove high-dhesion non-slip plte round fixed point which we locted 3 mm ove its upper surfce. As illustrted in Fig. 1, this situted the center of rottion inside the suject s fingerpd when resting on the plte, thus reducing the finger s rigid motion to smll mount, perhps less thn 1 mm (it would e very difficult to eliminte it completely). Fig. 2 illustrtes how the plte cn interct with the fingertip. In first mode of explortion, the device, see Fig. 3, ws mounted on gntry rolling without friction on tle in the x nd y directions s shown in Fig. 3. The gntry llowed sujects to explore ritrrily lrge virtul ojects. The position over virtul surfce ws 3
Figure 2: ) Nominl finger position. ) Exggerted finger position to show how the plte cn roll on the fingertip with dshed white lines to show center of rottion. mesured y the opticl trcking system of computer mouse (Logitech TM M-BJ69 800 dpi opticl mouse) ttched to the underside of the plte supporting the device. In second mode, the device rested on tle. In this configurtion, sujects used computer mouse to explore virtul ojects with their free hnd. Figure 3: ) Servo controlled sphericl linkge device. ) The device mounted on lightweight gntry used for ctive explortion. The device operted y servoing the plte orienttion to e tngentil to the virtul surfce eing explored t given point. In the first mode, explortion ws ccomplished y moving the entire device in the horizontl plne with one or two fingerpds nd experiencing the results with the sme finger(s). This mode pproximted closely the condition illustrted y Fig. 1 where the finger movements hve no verticl component. In the second mode, the device ws sttionry nd the virtul contct point with the surfce ws determined y the position of the mouse tht ws moved using the hnd tht ws not touching the plte. This mode ws equivlent to the ctul cse where one hnd would slide n oject under the sttionry fingerpd(s) of the other hnd. In this second mode the, touching finger experienced no significnt rigid motion, just deformtion. 4
Sujects Seven sujects prticipted in the experiment. They were right hnded individuls with no known perceptul or motor disorders. Two femle nd five mle sujects in their twenties prticipted. Six of the sujects were nive s to the purpose nd design of the experiment wheres one of the sujects hd knowledge of the device from working in the sme lortory s the uthors. No suject hd ny prior informtion regrding the experimentl protocol or the purpose of the experiments. All sujects gve informed consent for prticiption in the experiments nd were compensted for their time. The procedures were pproved y the McGill University s Fculty of Eduction Ethics Review Committee. Stimuli The stimuli consisted of virtul sections of spheres with vrying curvtures (where curvture is defined s the inverse of the rdius). Both positive nd negtive curvtures were utilized (i.e. convex nd concve shpes). Curvtures of the virtul spheres presented rnged from ±2.5 to ±10 m 1 (i.e. 1/r = ±2.5, 2.85, 3.33, 4.00, 4.50, 5.0, 5.5, 6.67, 8.33, 10.0 m 1 ; spheres of rdii rnging from 0.4 m to 0.1 m) in order to rcket the discrimintion threshold which for most sujects ws out 4.0 m 1 in the ctive conditions nd 5.0 m 1 in the semictive conditions. The rnge of curvtures to e used were sed on decision mde from the results of pilot study tht ws conducted with 3 sujects nd from comprison with rel ojects such s glss condenser lenses. Experimentl Setup Sujects were seted in front of tle with their forerm resting on the tle nd their fingerpd(s) resting on the plte of the device. A curtin plced etween the suject s ody nd their forerm prevented them from seeing their hnd. The computer ws plced out of the sight of the sujects. The virtul stimuli presented were rendered with personl computer running the Linux r operting system with rel-time extensions. The thred tht updted the orienttion of the device rn t frequency of 1 khz. The virtul shpes were presented to the sujects fingerpd(s) in 25 25 mm window using the device descried ove. If the oundry ws exceeded, then the plte ws rought to rest. Although the device ws le to trverse rnge of 280 280 mm, we limited the stimulus window ecuse previous studies hve shown tht the sptil length of stimulus tht is hpticlly explored cn directly influence the judgment of hptic curvture discrimintion (Pont et l., 1996). Another importnt considertion ws to limit the effect of proprioceptive cues since previous studies hve demonstrted these cues cn ffect hptic shpe identifiction performnce (Voisin nd Chpmn, 2002). Sujects were instructed to keep their rm stright so tht the nil(s) of their digit(s) would remin fcing upwrd nd sttionry. Becuse it ws not prcticl in this study to constrin the explortory trjectories, sujects were free to move the mouse (when the gntry ws not used) or the entire device (when the gntry ws used) to explore the virtul surfce in ny prticulr direction they chose. Commonly used explortion movements were fore-ft, lterl nd spirl motions. In ll of the cses however, the fingerpd(s) remined 5
sttionry on the plte nd did not undergo ny significnt rigid motion with respect to the mechnism s ground link. Trining Phse The experimentl phse ws preceded y rief trining phse in which sujects were presented with 12 trils of convex stimuli nd 12 trils of concve stimuli. Its purpose ws to fmilirize them with the condition under which they were to e e tested nd with the virtul shpes. During the trining, sujects were given eforehnd list of the sphere sizes tht were to e presented so they knew wht profiles would e presented, however, no feedck ws given. Sujects were sked to experience the rndomly presented virtul stimuli (using the experimentl condition tht would e immeditely following the trining) nd to judge whether they felt convex or concve. Once they were redy to mke decision, they entered their response y pressing keys on keyord. One key ws mrked with symol of convex shpe, nd nother key ws mrked with the symol of concve shpe. No time limit ws imposed, however sujects were instructed to respond s soon s they were redy to mke choice nd were timed. This ws mesured y the time etween which new profile ws presented to the suject signled y computer generted ell sound to the time when the suject entered their response. Experimentl Phse : Effect of mode of explortion Active explortion conditions were creted when the device ws mounted on top of the gntry so the hnd used to experience the shpe ws the sme s the hnd tht ws used to move the device over the virtul surfce. Semi-ctive explortion ws in effect when the device ws immoilized (i.e. the gntry ws not used) nd the sujects used their left hnd to move the mouse cursor over virtul surfce while experiencing the surfce with the right hnd. A single point of contct condition ws when the suject used the fingerpd of the index finger to experience the virtul surfce, nd multiple points of contct ws defined to e the cse when the suject used the fingerpds of the index finger nd of the middle finger to experience the virtul surfces. Comining these cses led to four conditions illustrted in Fig. 4. Condition 1: Active explortion using single point of contct, Condition 2: Active explortion using multiple points of contct, Condition 3: Semi-ctive Explortion using single point of contct, nd Condition 4: Semi-ctive explortion using multiple points of contct. These four conditions entiled four trining phses nd four experimentl phses. Sujects were first tested in Condition 1 (ctive explortion, single point of contct), then in Condition 3 (ctive explortion, two points of contct), then in Condition 2 (semictive explortion, single point of contct), nd finlly in Condition 4, (semi-ctive explortion, two points of contct). Sujects were given five minute rest fter completion of ech experimentl phse. Similr to the trining phse, during the experimentl trils for ech condition, sujects were sked to judge the curvtures presented nd enter their responses (convex or concve) 6
c d Figure 4: The four conditions tht were employed:,c) Moving the device over the virtul surfce with one or two fingers,,d) moving mouse with the free hnd of over the virtul surfce nd touching the sttionry device with one or two fingers. using the mrked keys on the keyord. This phse differed from the trining however in tht no prior informtion ws given, nd profiles were rndomly presented. One experimentl tril consisted of either convex or concve profile hving specific curvture which the sujects were sked to judge. Blocks of trils were dministered under one specified condition. In order to mximize the dt nd minimize the time required from the prticipnts, the numer of times stimuli were presented for ech curvture ctegory ws vried. Curvtures which from the pilot study which were oserved to e esier to discriminte (i.e. curvtures greter thn 5.5 m 1 ) were presented less often thn those tht were more difficult to discriminte. Ech lock consisted of 110 trils nd ws dedicted to one of the four explortion methods. Dt collection nd nlysis We clculted the proility of correctly clssifying stimuli to e either convex or concve for ech curvture level under ech of the four conditions for ll sujects. The proilities were verged for ech independent conditions (within sujects) since the numer of stimuli presented vried cross curvtures s descried ove. The dt for ech suject were then fit to Weiull psychometric function in order to determine the thresholds of curvture detection t the 75% ccurcy level. The psychometric function prmeters were otined using mximum likelihood estimtion nd susequent Monte Crlo simultions 7
were run in order to ssess the goodness of fit. These nlysis were crried out using the spss TM pckge nd the psignifit toolox (Wichmnn nd Hill, 2001; Wichmnn nd Hill, 2001). Representtive exmples of how the threshold vlues were otined from fitted psychometric functions re illustrted in Fig. 5. A two fctor with repeted mesures nlysis of vrince test (nov) ws then crried out in order to ssess whether differences etween methods used for explortion of the virtul surfces were significnt. Results Tle 1 summrizes the performnce of sujects under Conditions 1 4. A trend could e oserved in the thresholds t which sujects were le to identify the stimuli presented t n ccurcy of 75%. Tle 1 lso shows the time sujects required to judge the vrious virtul stimuli. The percentge of correct responses tht sujects gve were tulted for ech suject nd verged cross sujects. The men score for prticipnt ccurcy re lso presented in Tle 1. The numer of contct points s well s semi-ctive nd ctive modes for the explortion of the virtul stimuli were found to hve n effect on the overll performnce for curvture discrimintion. The two fctor repeted mesures nov showed tht significnt difference existed etween the use of single nd multiple points of contct when sujects explored the virtul surfces [F (1, 6) = 5.69, p = 0.05]. The two fctor repeted mesures nov lso showed significnt difference etween the use of ctive nd semi-ctive modes of explortion of curvture [F (1, 6) = 13.69, p < 0.05]. On verge, when ctively exploring the stimuli, sujects could detect smller curvtures using multiple points of contct thn when using one point of contct (i.e. 3.96 m 1 vs 4.40 m 1 ). Similrly, during semi-ctive explortion, the threshold of curvture detection decresed when using multiple points of contct compred to those detected with single point of contct (i.e. 5.02 m 1 vs 5.18 m 1 ). Fig 5 shows the psychometric functions for verge dt cross sujects otined under the four conditions of the experiment. The thresholds t which sujects were le to correctly identify 75% of the stimuli were found to e T 75 = 3.96 when using multiple points of contct nd ctive explortion, T 75 = 4.40 when using single point of contct nd ctive explortion, T 75 = 5.02 when using multiple points of contct nd semi-ctive explortion, nd T 75 = 5.18 when using single point of contct nd semi-ctive explortion. Discussion This study hs shown tht the single cue of trjectory of the contct region on the fingerpd(s) could e integrted over time y the rin to give rise to the experience of curvture. The thresholds t which curvtures could e discriminted nd the time required using this cue lone were oserved to e impressive. The consistently short times required for sujects to mke decision coupled with the fct tht most of the sujects hd never seen or herd of the device efore the experiments mkes it very unlikely tht cognitive processes could hve een t ply. Goodwin et l. (1991) conducted study similr to ours in which the gol ws to 8
Tle 1: Performnce (in m 1 ) t T 75, verge time (in seconds) for ech suject, nd score verged cross sujects under ll conditions. Conditions ctive ctive semi-ctive semi-ctive two finger one finger two finger one finger T 75 Time T 75 Time T 75 Time T 75 Time Suject m 1 s m 1 s m 1 s m 1 s A 3.96 10.7 4.14 14.2 3.91 17.3 4.47 13.7 B 3.78 8.6 4.37 16.2 4.17 16.2 4.58 13.0 C 4.04 10.6 4.40 11.7 4.20 10.2 5.01 13.0 D 4.02 10.0 3.96 9.3 4.29 12.4 4.74 12.2 E 3.33 12.1 3.83 15.8 5.38 15.5 3.96 10.4 F 4.26 12.7 5.35 11.2 5.81 9.7 6.71 13.5 G 4.72 7.7 5.01 9.4 5.52 12.8 6.71 10.0 v. 10.3 12.5 13.4 12.3 s.d. 1.7 2.9 3.0 1.5 v. 4.01 4.44 4.75 5.16 v. 3.96 4.40 5.02 5.18 s.d. 0.43 0.56 0.78 1.10 rdii c 0.25 0.23 0.20 0.19 v. score 73% 74% 65% 63% Thresholds from simple verge of T 75 vlues for ech suject cross ech condition. Thresholds from Weiull function fit otined from verging individul proilities cross sujects nd conditions. c Rdii of the virtul spheres corresponding to the curvture thresholds. clssifiction correct pro. 1.0 0.9 0.8 0.7 0.6 0.5 2 4 6 8 10 curvture clssifiction correct pro. 1.0 0.9 0.8 0.7 0.6 0.5 2 4 6 8 10 curvture ctive - two finger ctive - one finger semi-ctive - two finger semi-ctive - one finger Figure 5: )Representtive smple of the Weiull psychometric function fit to dt points representing suject s performnce with vrying curvture when exploring the virtul surfce. ) Averge dt otined from sujects in the four conditions. 9
rcket the threshold of curvture detection when rel physicl ojects were stticlly presented to the fingerpd. To our knowledge, this is the only other study tht hs quntified the threshold for curvture detection of lrge stimuli in this mnner, nd so it ws used s enchmrk for compring the results tht we otined. The study reported tht sujects could discriminte curved surfces from flt surfces with discrimintion thresholds of +4.9 m 1 nd 5.4 m 1 t n ccurcy of 75% when pssively touched. Although we did not nlyze convex nd concve stimuli seprtely, we otined similr results in terms of discrimintion thresholds when exploring virtul stimuli using our device under the semictive condition. We my ttriute the differences to the stimuli delivery methods. In our study, for the semi-ctive condition, while the right hnd of the suject remined sttionry nd pssively received the stimuli (s in the Goodwin study), we llowed the suject to move over the virtul shpe with their free hnd. Although still pssively experiencing the stimuli, the sujects hd control over how they were explored. Furthermore, our stimulus delivery method gve no informtion relted to shpe vi skin deformtion in the re of contct. Such deformtion occurs when using physicl stimuli s it ws the cse in previous studies. A smll, ut significnt dvntge ws oserved with the use multiple points of contct compred to the use of single one during the ctive nd semi-ctive explortion of stimuli. We hypothesize tht this ws due to numer of comined fctors such s lrger popultion of cutneous fferents tht re stimulted when more thn one fingerpd is used, nd smll differentil verticl motion etween the two fingers tht occurs when two fingers contct the plte simultneously. In our study, we did not find ny significnt differences in the mount of time needed to rrive t judgments cross the four different conditions, however, the time required to rrive t judgment ws oserved to e much shorter thn reported in similr studies using hptic devices for shpe perception (Kirkptrick nd Dougls, 2002). Active versus pssive explortion hs previously een studied for tctile recognition of ojects (Gison, 1962; Loomis nd Ledermn, 1986; Ledermn nd Kltzky, 1987; Pont et l., 1999). Wheres the lrge mount of literture on this topic suggests tht selfcontrolled explortory finger movements increse performnce, Pont et l. concluded the opposite: tht similr mechnisms underlie sttic nd dynmic curvture comprison for curvtures rnging from 4 m 1 to +4 m 1. Our study, however, confers with the former view nd demonstrtes tht ctively exploring surfce provides significnt dvntge on the performnce of curvture discrimintion over pssive explortion of the sme stimuli. Differences etween our study nd tht of Pont s my e ccounted for y the fct tht certin cues such s friction nd speed of explortion re vrile ttriutes etween the explortion of rel nd virtul stimuli. We would like to investigte this possiility s source of discrepncy. In our study we tried to minimize the mount of joint movement in order to limit the use of proprioceptive informtion for the curvture discrimintion tsks. Studies hve previously reported tht cutneous informtion nd in prticulr compression of the fingerpd is mjor contriuting fctor in discrimintion of two dimensionl ngles (Voisin et l., 2002). They dd tht proprioceptive cues re importnt in incresing performnce. In future work, we would like to incorporte these proprioceptive cues in controlled mnner into the design 10
of our device in order to e le to quntify their contriutions. Kppers nd Koenderink (1996) found tht dynmic curvture discrimintion of cylindricl surfces did not follow Weer lw nd tht performnce incresed s did curvtures. Using our device, we lso oserved similr phenomenon: sujects performnce incresed s the curvtures of the virtul spheres decresed. We however hve not yet tested for the threshold t which ojects with lrge curvtures cn e perceived t the 75% level ccurcy s ws done for stimuli with low curvtures. We suspect tht the conditions which would enhnce sujective performnce using smller stimuli would e quite different from those conditions which were seen to e optiml for the perception of stimuli with smll curvtures. We would like to investigte these questions in future work s well. Appendix A The device ws mde of closed-loop five-r sphericl mechnism, hving two degrees-offreedom, Fig. 6. While mny mechnisms nd structures cn orient plte round point, this design is prticulrly prsimonious nd efficient. The sttionry link is leled Link-0. The plte of the device is ssigned to Link-3. We gve the nme of Morpheotron to this device ecuse of its ility to deform (morph) the skin in mnner tht elicits senstion of shpe. The center of rottion, shown in the figure t the intersection of the xes of the motors, is such tht the xes of ll five joints lwys meet there. It ws set t 3 mm ove the upper surfce of the plte. Plte orienttion resulted from controlling the motors ngles vi proportionl-derivtive feedck control nd kinemtic trnsformtions. The motors were Mxon TM 3 W dc motor with 19:1 ger-hed reduction. They produced torques tht were lrgely sufficient to counterct the lod creted y the suject s finger. The Morpheotron ws used sttionry or mounted on light weight rolling gntry schemtized in Fig. 6. Link-0 M-2 M-1 Link-2 Link-1 Link-3 Link-4 Figure 6: ) Schemtic kinemtic rrngement. ) Rolling gntry sketch. The plte tilted round point locted inside the fingertip s function of ny of the explortion movements. For instnce, if the suject were to move 25 mm from the right to the left, the plte would chnge y the sme mount when the suject moved 25 mm using the fore-ft motion, or long ny of the meridin trjectories. As nother exmple, circulr trjectory long prllel of the virtul sphere would cuse the plte to undergo 11
full cycle t constnt inclintion with respect to the verticl xis, therey creting closed trjectory of the contct point on the fingertip. These chnges in tilt of the plte, therefore simulted the explortion of sphere. Similrly, in the cse of semi-ctive explortion, the plte tilted y n mplitude tht corresponded to the distnce trversed y the left hnd. To give scle, when the suject moved to the right extreme of the 25 25 mm oundry, the plte tilted 2.86 o when virtul curvture of 0.4 m 1 ws present. References Christou, C. nd Wing, A. M. (2001). Friction nd curvture judgement. In Proc. Eurohptics, University of Birminghm, UK. Drewing, K. nd Ernst, M. O. (2003). Integrtion of force nd position cues in hptic curvture perception. Astr. Psych. Soc., 44:112. Gison, J. (1962). Oservtions on ctive touch. Psychologicl Review, 69:447 491. Goodwin, A., John, K., nd Mrcegli, A. (1991). Tctile discrimintion of curvture y humns using only cutneous informtion from the fingerpds. Exp. Brin Res., 86:663 672. Kppers, A. nd Koenderink, J. (1996). Hptic unilterl nd ilterl discrimintion of curved surfces. Perception, 25:739 749. Kirkptrick, A. E. nd Dougls, S. A. (2002). A shpe recognition enchmrk for evluting usility of hptic environment. In Brewster, S. nd Murry-Smith, R., editors, Proc. First Interntionl Workshop on Hptic Humn-Computer Interction, pges 151 156. Berlin:Springer Verlg. LMotte, R. nd Srinivsn, M. (1993). Response of cutneous mechnoresceptors to the shpe of ojects pplied to the primte fingerpd. Act Psychologic, 84:41 51. Ledermn, S. nd Kltzky, R. (1987). Hnd movements: A window into hptic oject recognition. Cognitive Psychology, 19:342 368. Ledermn, S. nd Kltzky, R. (1999). Sensing nd displying sptilly distriuted fingertip forces in hptic interfces for teleopertor nd virtul environment systems. Presence: Teleopertors nd Virtul Environments, 8(1):86 103. Loomis, J. nd Ledermn, S. (1986). Tctul perception. In Boff, K., Kufmn, L., nd Thoms, J., editors, Hndook of Perception nd Humn Performnce, volume 2. Peine, W. nd Howe, R. (1998). Do humns sense finger deformtion or distriuted pressure to detect lumps in soft tissue? In Proc. ASME Dyn. Sys. nd Control Div., volume DSC-64, pges 273 278, Anheim, Cliforni. 12
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