Friction And Curvature Judgement - ResearchGate

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Friction and curvature judgementChris Christou (1) and Alan Wing (2)(1) Optometry and Neuroscience, UMIST / Unilever Research (2) Behavioural Brain Sciences Centre,The University of BirminghamAbstractLocal shape is an important attribute that canbe sensed by exploratory movements of thefinger. Normally this involves a blend of tactileand proprioceptive cues. A curved surface willdeform the pad of a single finger and so tactilecues can indicate whether a surface is convexor concave or whether it slopes one way oranother. When more subtle discriminationsmust be made between different degrees ofcurvature, scanning motions are made inwhich the finger sweeps along the surface. Inthis case the cue to curvature is the change inposition of the finger tip over time and hereproprioceptive input is important. We havebeen examining how curvature judgements areaffected by the force reflected back from thecurved surface during scanning. Normallywhen you run your finger over a surface, youexperience resistance to motion due to friction.This resistance creates a force vector whichvaries in direction with friction. But the vectoralso varies in direction with the curvature ofthe surface traversed by the finger. We used atwo-alternative forced-choice (2AFC) task inan adaptive staircase in which subjects madecomparisons between various test curvaturesand a reference curvature in order to find thepoint of subject equality (PSE) between thetwo. Differences in friction between referenceand test stimuli were found to alter the PSE ina consistent manner. In particular, we foundthat the reference curvature was only closelymatched when no frictional disparity existedbetween reference and test surface. Referencesurfaces that exerted high frictional forcesproduced smaller curvatures as PSEs whilesurfaces with low friction produced highcurvature matches. These results suggest thatforces experienced in palpating a surface maybe utilised in the comparison of curvature.1. Introduction.Curvature is an important local shapedescriptor that may vary continuously acrossthe surface of an object. In terms of thesensation of touch, curvature may be assessedby either the cutaneous receptors of theglabrous skin (finger pads or palm) of the handor through proprioception supported by severaltypes of receptors in the muscles of the hand,or both. Evidence for the former type ofsensitivity to curvature has been provided byLaMotte et al (1998); see also Bisley et al(2000) who showed that slowly adapting type1 mechanoreceptors in the monkey handrespond to the curvature of a raised bump onan otherwise flat surface. Psychophysicalexperiments have also shown that humansubjects are very good at judging curvatureusing only the finger pads (Goodwin et al,1991; Goodwin & Wheat, 1992). Evidence forthe ability to perceive curvature throughproprioceptionhas been studied usingpsychophysical experiments on humans. Suchexperiments involved curvature discriminationbased on active touch or passive deformationof the whole hand (e.g. Vogels et al, 1999;Pont et al, 1998). Surface curvature, it seems,may be assessed equally well by both staticplacement of the hand across the surface or byactive touch with the hand or fingers (Pont etal, 1999). However, it has been arguedelsewhere that active touch is better thanpassive touch in the discrimination of shapeand recognition of objects because the formercan yield continual pick-up of informationfrom the surface (Gibson, 1966). Differencesin the discrimination of curvature in differentparts of the hand were also studied by Pont etal (1997) who found that the palmar side of thehand is more adept at this task than the dorsalside. Pont et al. attribute this to thepreponderance of cutaneous input from thepalm although the task clearly involves both(cutaneous and proprioceptive) types of input.A notable feature of the visual sense is thatof maintaining shape invariance or shapeconstancy. That is, a shape may be encoded ingeometrical terms equally well regardless ofwhich visual cues are being used to depict it.There is active debate in the vision communitywhether this is the case with human vision andwe may ask whether such an ability is found inactive touch as well. So what physical factorsmight influence the perception of shape from

visually unaided active touch? Imagine that aconvex bump on a flat surface is being strokedby a single finger that does not providecutaneous input. Both the horizontal, scanningand vertical velocity of the finger and thereactive force of the surface acting on thefinger may be affected by the object impedingmotion of the finger. These physical variablesmay be encoded by the mechanoreceptors tothe muscles of the upper limb and therefore, ifcurvature can be encoded by throughproprioception, then it may be through changesin these variables. Surfaces of real objects alsoexert an additional, frictional force on thefinger in a direction opposite to the direction ofmotion. If the force applied through the fingeris greater than the tangential force exerted byfriction the finger starts to slide across thesurface. In this case, dynamic frictional forcesact on the finger to impede its motion. Thisresistive force depends on the normal force atthe contact surface but is also a function of thecoefficient of dynamic friction of the surface.It is therefore possible that the perception ofsurface curvature is influenced by the frictionalproperties of the surface.We isolated proprioceptive cues tocurvature by using the Phantom hapticinterface. The Phantom is essentially a robotarm controlled by three motors and connectedto a computer that can control the exertion ofreactive forces to a single finger placed in athimble. These forces can be used to simulatesolid objects, friction and viscosity. The usefulfeature of using the Phantom is that sensoryinput is provided by active palpation withoutlocal tactile information and this in turnallowed us to focus on the contribution ofproprioceptive cues.2. Method.2.1 Simulation of Solid Shape.The Phantom is a haptic rendering systemthat uses 3D force feedback to generate theimpression of 3D solid shape, viscosity,friction and surface texture. The hapticrendering process is similar to that in computergraphics (Salisbury et al. 1995; see also Ho etal, 1999). For instance in the rendering of solidshape the position of the cursor or stylus istracked at a frequency of 1 kHz until anintersection with a virtual surface is detected.Once an intersection is detected various forcescan be applied to the finger to give not only theimpression of solidity but also of surfacecompliance, texture and surface friction. Itshould be noted that the perception of solidshape is generated only as a function of theobservers active movements of a single fingerinserted into a thimble. If there is nomovement (and therefore no exerted force)then no haptic feedback can be provided. Thisallowed us to isolate the proprioceptive sensethat results from active movement.As well as generating the impression ofsolid shape the Phantom can also beprogrammed to simulate static and dynamicfriction (Salisbury et al. 1995). Friction issimulated by detecting the collision betweenthe finger/stylus and an object in the scene andapplying an appropriate tangential force to thefinger. The tangential force serves to restorethe finger to an initial position as the fingerattempts to slide across the surface. Thus thefinger sticks on the surface. If the tangentialforce required to restore the finger becomesgreater than the normal force times thecoefficient of static friction then slidingoccurs. During sliding a tangential force(proportional to the coefficient of dynamicfriction) is applied to the finger in the directionopposite to the direction of motion, whichprovides the sensation of dynamic friction. Inthis manner, the surface is made to feel eitherslippery like ice (i.e. low friction) and feelssticky like rubber (i.e. high friction).2.2 Stimulus definition.The curvature (or more correctly the normalcurvature) of a surface at a point is thecurvature of a section of the surface in a givendirection and perpendicular to the tangentplane at that point. On a sphere the normalcurvature is the same in all directions. On acylindrical surface, which is what we shall beusing here, the normal curvature is zero alongthe elongated axis and maximal in a directionperpendicular to this axis. Cross sections of aright circular cylinder are circular in form andthe maximal normal curvature of the cylinderis therefore given by the curvature of a circularsection which is inversely dependent on theradius.The stimulus in this experiment was avirtual cylinder that the subject was allowed tostroke twice. This virtual surface wasgenerated by the Phantom force-feedbacksystem. This was implemented using theapplication programming interface GHOST.The Phantom was programmed to generatecylinders with variable cross-section and it wasthe radius of these cross sections that served asthe independent variable in these experiments.The cylindrical surface was defined within avirtual space measuring 5cmx20cmx20cm (seefigure) with the X axis set as the horizontalaxis perpendicular to the desk at which the

subject sat. The Y axis was the gravitationalvertical axis and the Z (depth) axis defined theforward-backward direction with respect to thesubject. The principal axis of the cylindricalsegment was oriented along the X axis and thesubject stroked the segment from the top in theforward-backward (Z) direction. Movement inthe X direction was restricted so that strokesacross the surface followed a similar trajectoryeach time.estimated as the average of six reversals. Inorder to bring the test stimulus quickly to thePSE each staircase measurement was precededby 4 ‘reducing reversals’ in which theincrement or decrement of the test was variedas a function of the reducing reversal number.The influence of dynamic friction wastested by introducing disparities in simulatedfriction coefficient between the reference andtest stimuli. Two friction coefficients wereused (µ 0.2 and µ 0.8) for both the referenceand test stimuli. The µ 0.2 stimuli feltslippery, rather like moving ice on ice. Theµ 0.8 stimuli felt rubbery. In both cases thefriction coefficients were low enough thatsmooth and uninterrupted movement of thefinger across the strip was still possible.2.4 Design.Figure 1: Schematic representation of objectsurfaces created by haptic rendering.2.3 Task.The aim of this experiment was todetermine how well a subject coulddiscriminate between the curvature of twocircular strips and to test whether this ability isaffected by friction. The only curvatureinformation was through proprioceptivesources arising from the Phantom. Wemeasured the point of subjective equality(PSE) for two curvatures (0.013/cm and0.008/cm). The curvature was manipulated byvarying the radius of the cross sections of acircular cylinder (i.e. 75mm and 125mm)however for a constant position of the centre ofcurvature this manipulation of radius wouldhave resulted in an additional height cue in they direction (see Figure 1). This was controlledby allowing the centre of curvature to move upor down in the Y direction so that the maximalheight of the cylinder remained constant.The subject was asked to determine whichof two (sequentially presented) curvatures wasgreater. One of the two stimuli was theconstant reference (radius 75mm or 125mm)and the other varied according to a 1-up/1down adaptive staircase. After having strokedboth strips the subject had to respond using acomputer keyboard which had the greatercurvature. Using this method the PSE wasThe two sizes of reference stimulus and thetwo friction values for both test and referenceresulted in 8 distinct conditions in a balanceddesign. That is, each condition consisted of aunique value of reference radius (either 75mmor 125mm), reference friction (either 0.2 or0.8) and test friction (either 0.2 or 0.8). MeanPSEs were collected for each of these 8conditions in random order and repeated 5times for each subject.2.5 Subjects.Four subjects participated in this experimentand were rewarded with gift vouchers. Allsubjects were spent several minutes training onthe task prior to the actual data collection.Subjects’ view of their hands was occludedduring the experiment and they were asked toclose their eyes.Figure 2: Effects of reference radius andsurface friction on point of subjective equality(PSE)

3. Results.The dependent measure for this experimentwas the PSE radius which is defined as theradius of the test surface that subjects equatewith the magnitude of a given reference radiusregardless of frictional differences. We reportresults mainly in terms of the radius ofcurvature because it involves more intuitiveand manageable dimensions of size in terms ofmillimetres rather fractional curvaturequantities although it should be rememberedthat a smaller radius of curvature produces alarger surface curvature. Figure 2 shows thePSE radius averaged across all 4 subjects andplotted as a function of the reference radius.The four lines correspond to the fourconditions used. The reference radius wasmatched closely only when the frictioncoefficients for test and reference stimuli wasthe same (i.e. when µr µt). When there weredisparities between the test and referencestimulus friction systematic errors in meanPSE were observed. For example, when thereference friction coefficient was greater thanthe test stimulus friction (i.e. when µr µt) themean PSE radius obtained was at least 25%higher than the actual reference radius whichmeant an underestimation of the radius ofcurvature of the reference stimulus (that is thereference appeared more curved than it reallywas). For trials in which the reference surfacefriction was less than the test surface friction(i.e. when µr µt) the mean PSE radius wasfound to be at least 11% lower than that of thereference stimulus. These results mean that theradius of curvature of the reference stimuluswas underestimated for high friction surfacesand overestimated for low friction surfaces.An analysis of variance was performed onthe data with three repeated measures(reference friction µr, test friction µt andreference radius) and mean PSE radius asdependent variable. Assuming an α 0.05 asour level of significance we found a significantmain effect of reference friction [F1,3 11.42,p 0.05], an almost significant effect of teststimulus friction [F1,3 11.42, p 0.09], and ahighly significant main effect of radius. Noneof the interactions (i.e. between µr and radius)was significant.In terms of repeatability, we use thestandard deviation of settings to assessdifferences in relative difficulty. Standarddeviations were calculated for the five repeatedsettings made by subjects for each of the 8 datapoints. The mean standard deviations(averaged across all subjects) for the 75mmand 125mm circular segments were 11mm and21mm respectively. A paired comparisonstudents t-test showed that this difference inmeans was significant. The increased varianceof settings for the 125mm radius strip reflectsgreater difficulty in assessing a shallowercurvature (larger radius of curvature).4. Conclusions.We have described an experiment in whichsubjects made curvature comparisons betweensequentially presented curved strips, simulatedusing the Phantom haptic interface. The resultsshow clearly that simulated curved strips canbe accurately discriminated using kinestheticinformation derived from the hand joints as thefinger is deflected by the surface duringstroking. Our results also highlight theimportance of friction, and consequently ofreactive forces, on the curvature discriminationprocess. We found that the radius of strips witha higher frictional coefficient than thecomparison stimulus was overestimated. Theradius of strips with a lower ated. In terms of curvature, thismeans that the curvature of rough or highfriction surfaces is underestimated relative tolow friction surfaces and our results show thatthe converse of this is also true. When thefriction coefficients of the reference and teststimuli were the same subjects settings of thetwo radii, and therefore curvatures, were aclose match. It remains for us to explainexactly why disparities in friction cause underand over-estimates in curvature in theseexperiments and we are investigating threepotential sources:1) The subjects use tangential forces toencode curvature and tangential forcesarising from friction disrupt this encoding.2) It is not force but change in velocity that isused to encode curvature. The frictionaldifferences disrupt direct velocitycomparisons.3) The result is an artifact of the process ofgenerating virtual shapes and virtualfrictional forces.5. References.Bisley JW, Goodwin AW, Wheat HE (2000)Slowly adapting type I afferents from the sidesand end of the finger respond to stimuli on thecenter of the fingerpad. Journal ofNeurophysiology, 84: 57-64.Gibson, J J (1962) Observations on active touch.Psychological Review, 69, 477-91Goodwin AW, John KT, Marceglia AH (1991)Tactile discrimination of curvature by humansusing only cutaneous information from the

fingerpads. Experimental Brain Research, 86:(3) 663-672.Goodwin AW, Wheat HE (1992) Human tactilediscrimination of curvature when contact areawith the skin remains constant, ExperimentalBrain Research, 88: 447-450.Ho C, Basdogan C & Srinivasan M A (1999)Efficient point-based rendering techniques forhaptic display of virtual objects. Presence, 8,477-491.LaMotte RH, Friedman RM, Lu C, Khalsa PS,Srinivasan MA (1998) Raised object on aplanar surface stroked across the fingerpad:Responses of cutaneous mechanoreceptors toshape and orientation. , Journal ofNeurophysiology, 80, 2446-2466.Salisbury K, Brock D, Massie N, Swarup N & ZillesC (1995) Haptic rendering: Programming touchinteraction with virtual objects. ACMSymposium on Interactive 3D Graphics,Monterey CA USA.Pont SC, Kappers AML, Koenderink JJ (1999)Similar mechanisms underlie curvaturecomparison by static and dynamic touch.Perception & Psychophysics, 61: 874-894.Vogels IMLC, Kappers AML, Koenderink JJ (1999)Influence of shape on haptic curvatureperception. Acta Psychologica, 100: 267-289.

Friction and curvature judgement Chris Christou (1) and Alan Wing (2) (1) Optometry and Neuroscience, UMIST / Unilever Research (2) Behavioural Brain Sciences Centre,

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