Haptically creating affordances: The user-tool interface

Haptically Creating Affordances: The User–Tool Interface

Jeffrey B. Wagman and Claudia CarelloUniversity of Connecticut

Successful use of a hand-held tool requires overcoming the rotational inertia of the hand-plus-toolsystem. Where an object is grasped affects this rotational inertia. Appropriate choice of grip position maybe crucial in the safe, effective, and efficient control of a hand-held tool. In 3 experiments, the authorsinvestigated how choice of grip position on a tool was constrained by task demands. The results suggestthat choice of grasp position serves to establish relationships among 3 variables derived from the inertialellipsoid of the hand–object system (volume, symmetry, and eigenvector angle) in a way that specificallyreflected the power or precision constraints of the given task. These variables have previously beenshown to play a role in haptic perception of tool function. Changing grasp position on a tool is a way toexert control over the nuances of the user–tool interface.

The last decade or so has seen an explicit push to take anecological approach to human factors (see Flach 1989, 1990;Flach, Hancock, Caird, & Vicente, 1995; Hancock, Flach, Caird, &Vicente, 1995; Vicente & Rasmussen, 1990), an approach rootedin theoretical contributions of James Gibson’s ecological psychol-ogy (see Gibson, 1979; Lombardo, 1987; Michaels & Carello,1981; Reed, 1996; Shaw & Turvey, 1999; Turvey & Shaw, 1999).A general ecological approach seeks a law-based account ofperception–action by attempting to understand how behaviorallyrelevant environmental properties lawfully structure energy arrays(Turvey, Shaw, Reed, & Mace, 1981). The enterprise devoted touncovering such behaviorally relevant structure in stimulationpatterns has been termed ecological physics (Gibson, 1961, 1979;Michaels & Carello, 1981). Its counterpart in human factors hasbeen termed inverse ecological physics (Effken, Kim, & Shaw,1997; Flach, 1990; Vicente, 1995) because it represents an attemptto design environments that give rise to behaviorally relevantstructure in stimulation patterns. The emphasis is on seeking ageneralizable model of the environment in addition to a general-izable model of the animal (Kirlik, 1995).

One of the most successful applications of ecological principlesin an explicitly applied setting is in the realm of interface design.The aim of ecological interface design is to build a display thatallows for simultaneous monitoring and control of complex workenvironments (e.g., cockpits, power plants, operating rooms) with-out an excessive cognitive load on the operator (see Effken et al.,1997; Jacob, Siebert, McFarlene, & Muller, 1994; Hinkley,Pausch, Proffitt, & Kassell, 1998; Koike, Sato, & Kobayashi,

2001; Vicente, 1995; Vicente & Rasmussen, 1990). A well-designed interface is one that maps the structure of the workdomain onto a visual representation such that both physical andfunctional aspects of the work domain are specified. In doing so,such displays extend the operator’s perception–action capability.However, an interface must specify not only the current environ-mental state of affairs but also the path by which the operatormight bring about a desired state of affairs (Norman, 1988; Vicente& Rasmussen, 1990; Warren, 1995; Zaff, 1995). Designing aninterface that preserves the prospective nature of perception–action(see Turvey, 1992) is perhaps the most challenging aspect ofinterface design.

One way to step into this problem is by investigating how usersof decidedly less technologically advanced devices such as hand-held tools choose to “create interfaces” (both between themselvesand the tool and between the tool and the environment; see below).A hand-held tool can be considered an interface to the extent thatit extends the tool user’s capacity for perception–action and im-proves the fit between animal and environment (see Beck, 1980;Burton, 1992, 1993; Gibson, 1979; McGrew, 1993; van Lawick-Goodall, 1970; Weir, Chappell, & Kacelink, 2002). A well-designed tool, like a well-designed interface, serves to increase theopportunities for behavior—what Gibson (1979) called affor-dances (see also Bongers, 2001; Lockman, 2000; Shaw, Flascher,& Kadar, 1995; Smitsman, 1997).

Successful tool use requires establishing a tool–environmentinterface (Kreifeldt & Hill, 1975; Mital & Sanghavi, 1986)—thefunctional relationship between the surfaces of the tool and theto-be-affected object (Bongers, 2001; Smitsman & Bongers, inpress). It also requires an appropriate user–tool interface—thefunctional relationship between tool user and tool determined byhow and where the user grasps the tool. Both of these interfacesdepend on task constraints. For example, the tool–environmentinterface required for hammering is quite different from that re-quired for poking (cf. Wagman & Carello, 2001). As a result, thetwo tasks may require different user–tool interfaces. Hammeringmay require a power grip, whereas poking may require a precisiongrip (Kroemer, 1986; Napier, 1993). Such grips allow for differentsets of actions to be performed with the same tool. How suchuser–tool and tool–environment interfaces are selected, created,

Jeffrey B. Wagman and Claudia Carello, Center for the EcologicalStudy of Perception and Action, Department of Psychology, University ofConnecticut.

This research was supported by National Science Foundation Grant BCS00-04097 awarded to M. T. Turvey and Claudia Carello. We thank AlexKirlik for comments on a previous version of this article. We thank JustinBates and Len Katz for help with statistical analysis.

Correspondence concerning this article should be addressed to JeffreyB. Wagman, who is now at the Department of Psychology, Illinois StateUniversity, Campus Box 4620, Normal, Illinois 61790-4620. E-mail:[email protected]

Journal of Experimental Psychology: Applied Copyright 2003 by the American Psychological Association, Inc.2003, Vol. 9, No. 3, 175–186 1076-898X/03/$12.00 DOI: 10.1037/1076-898X.9.3.175

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and maintained has potential consequences for the likelihood ofsafe, effective, and efficient tool use by humans in various worksettings (Armstrong, Radwin, Hansen, & Kennedy, 1986; Cochran& Riley, 1986; Drillis, 1963; Marras & Rockwell, 1986; Shaw etal., 1995).

Sensitivity to these demands is evident from observation ofchildren and animals. When faced with using spoons that havebeen bent in particular ways, toddlers choose a grasp type andposition that preserves the functional act of scooping (Steenbergen,van der Kamp, Smitsman, & Carson, 1997; see also Lockman2000). Chimpanzees, sea otters, and elephants have also beenobserved to vary their grip on an object depending on how thatobject is to be used (Boesch-Acherman & Boesch, 1993; Hall &Schaller, 1964; Hart & Hart, 1994; Hart, Hart, McCoy, & Sarath,2001; Tomasello & Call, 1997). But how is one to understand theprinciples that underlie these capabilities? Research on perceivingobject properties by dynamic touch provides a starting point.

Dynamic Touch and User–Tool–Environment Interfaces

Maintaining an appropriate user–tool–environment topology re-quires controlling the hand-plus-tool system to satisfy task con-straints. Controlling an object requires exploiting the laws of rigidbody motion and overcoming the translational and rotational in-ertia of the hand-plus-tool system with appropriate scaling anddirecting of muscularly generated forces and torques (Carello &Turvey, 2000; Shockley, Grocki, Carello, & Turvey, 2001; Tur-vey, 1996; see also Drillis, Schneck, & Gage, 1963). This impli-

cates dynamic touch, the type of touch used when an object isfirmly grasped and wielded via muscular effort (Gibson, 1966).One line of inquiry suggests that perception of a multitude ofgeometric and functional object properties using dynamic touch isconstrained by how that object resists rotational acceleration indifferent directions about a rotation point in the wrist (for reviews,see Carello & Turvey, 2000; Turvey, 1996; Turvey & Carello,1995). Although alternative mechanical variables have been sug-gested (e.g., Kingma, Beek, & van Dieen, 2002; see below), anadvantage of the inertial approach relevant to the present investi-gation is that resistance to rotational and translational accelerationprovides a direct link to the level and patterning of forces requiredfor task-specific movement.

Resistance to rotational acceleration in different directions isquantified by the inertia tensor. When the inertia tensor is referredto the symmetry axes of the hand–object system, its eigenvalues,Ik, refer to the resistances to rotational acceleration about thesymmetry axes, and the symmetry axes themselves are the eigen-vectors, ek (see Figure 1A). Research on perception by dynamictouch has generally found that perceived magnitudes (e.g., length,width) are tied to Ik and perceived directions (e.g., the orientationof an object in the hand, the orientation of a limb, where the handis on an object) are tied to ek (for reviews, see Carello & Turvey,2000; Pagano & Turvey, 1998). A more explicitly functionalsetting for dynamic touch has been pursued recently with respectto the problem of perceiving heaviness, which has been shown tobe constrained jointly by an object’s mass and the distribution of

Figure 1. (A) The ellipsoid of inertia for the hand–object system shown. Because the center of mass of theobject is not along the z-axis, the symmetry axes of the hand–object system (e1, e2, and e3) are not coincidentwith the geometric axes (x, y, and z). The formulae for ellipsoid volume (V) and symmetry (S) are also provided.The angle between e3 and the z-axis is the eigenvector of interest in the current investigation. (B) An exampleof one of the experimental stimuli (a hollow wooden rod containing a column of a particular volume of lead shotbraced between two wooden dowels). The objects each appeared to be solid, homogeneous rods and wereindistinguishable by sight or sound. (C) A participant settled on the grip position most appropriate forhammering. This position was measured as the distance from the bottom of the rod to the middle of the grasp.

176 WAGMAN AND CARELLO

that mass as quantified by Ik (Amazeen, 1999; but see Kingma etal., 2002). There are two aspects to this functional setting. First, therelevant affordance characterization of heaviness seems to concernhow movable an object is (Turvey, Shockley, & Carello, 1999).Second, the mass distribution is characterized with respect to twoscalars (see Figure 1A) derived from Ik (Shockley, Grocki, et al.,2001; Turvey et al., 1999). The volume of the inertial ellipsoid,

V � 4�/3(I1 � I2 � I3)�1/2, (1)

quantifies the mean level of force required to rotate an object. Oneshould note that the exponent in the equation is such that the largerthe value of V for a given object, the less force required to rotatethat object about a rotation point (and vice versa). The symmetryof the inertial ellipsoid (see Figure 1A),

S � 2I3/(I1 � I2), (2)

is relevant to how those forces should be directed. The ellipsoid ofa perfectly symmetric hand–object system (i.e., where S � 1.0) isspherical; it is as easy to rotate about one axis as it is to rotateabout any other axis (Shockley, Grocki, et al., 2001; Turvey et al.,1999). In short, the current understanding of perceived heavinessimplicates quantities that are relevant to how controllable theobject is.

Given the relevance of the perceived magnitudes and directionsto constraining an object’s use, dynamic touch provides an appro-priate context in which to investigate many aspects of tool use(Wagman & Carello, 2001). Research along these lines has shownthat perception of the functional utility of an object for hammeringor for poking is dependent on V but in seemingly opposite ways.Ratings of hammers show a negative relationship with V, suggest-ing that participants place a premium on the prospective transfer offorce from the hammer to the struck surface. Ratings of pokersshow a positive relationship with V and a further influence of angleof e3, suggesting that participants place a premium on the control-lability of the object tip (see Wagman & Carello, 2001). In brief,although both V and ek are relevant to the regulation of one’sability to maintain a tool–environment interface, they are relevantin different ways depending on task constraints.

Other affordance-centered experiments have shown that peoplehaptically perceive the location of the sweet spot of a strikingimplement, that is, the point on the implement at which it is mostenergetically efficient to strike another object such as a ball with atennis racket (Carello, Thuot, Anderson, & Turvey, 1999; Carello,Thuot, & Turvey, 2000). As it happens, the sweet spot is also thelocation at which it feels best to strike another object (Brody,1987). In a sense, the present experiments address whether peopleare sensitive to the sweet spot for grasping. Where does it feel bestto grasp an object to be used for a given purpose? As Kirlik (1998)noted, during the first few minutes of driving a new car, driverswill often engage in putting the car through its paces to get a feelfor its handling qualities. Our interest was in the outcome of asomewhat analogous process—putting a hand-held tool through itspaces to determine its handling qualities. We were particularlyinterested in how grasp position affects the inertial properties ofthe hand-plus-object system and how such properties make thesystem (feel) more or less functional for a given task. In threeexperiments, we quantified the inertial consequences of chosengrip positions on a set of 12 objects to be used in various tasks with

different functional constraints. The results may have relevancenot only for tool design but also for interface design moregenerally.

Experiment 1

Where an object is grasped has consequences for how effec-tively the hand–object system can be controlled by the actor.Appropriately controlling the tool–environment interface wouldseem to require sensitivity to the rotational inertia of a hand-plus-tool system. In Experiment 1, we quantified the inertial conse-quences of chosen grip positions on objects to be used in a generichammering task. In particular, we examined the functional rela-tionships among the inertial variables that emerge at the chosengrip positions.

Because perceivers are sensitive to higher order variables indetermining the appropriateness of a tool (Wagman & Carello,2001), we expected that perceivers would show sensitivity to thesame variables in choice of grip position on a tool. We expectedthat together, V, S, and ek would account for a statistically signif-icant portion of the variance in grip position. Moreover, we pre-dicted that each variable would play a statistically significant rolein multiple regression. We hypothesized that if perceivers are notsensitive to such variables in choice of grip position, these vari-ables (either alone or in combination) will not constrainperformance.

Method

Participants. Eight introductory psychology students at the Universityof Connecticut participated in this experiment in partial fulfillment of acourse requirement.

Materials and apparatus. The 12 objects used in Experiments 1–3 areidentified in Table 1. Objects consisted of 60-cm pine rods (with a 1.27-cmradius) with a 0.64-cm radius hole drilled lengthwise through each one (seeFigure 1B). Wooden dowels (with a 0.64-cm radius) were inserted into oneend of the rod such that an unfilled portion of the rod (one quarter, one half,three quarters, or the entire volume of the rod) remained in a particularlocation (at the top, middle, or bottom of the rod; see Figure 1B). Aspecified volume of lead shot was then poured into the hole, and a secondwooden dowel (0.64-cm radius) was inserted as a cap so that the columnof shot was contained between the two dowels (see Table 1 and Figure 1B).White tape was wrapped around the end of each rod that was designated asthe bottom, and black tape was wrapped around the end of each rod thatwas designated as the top (see Figure 1C).

Procedure. Participants were seated and handed rods one at a time bythe experimenter. Participants were asked to explore each object haptically,wielding it with one hand and repositioning it with the other hand, even-tually choosing the position along its length at which they would grasp theobject if they were asked to use it as a hammer. Once this choice was made,the experimenter measured the distance from the bottom of the rod (theportion below the hand of the participant) to the middle knuckle of theparticipant’s fist (see Figure 1C). Exploratory wielding was not restrictedin any way except that participants were asked to refrain from strikinganything with the rods as well as from flipping the rods (i.e., inverting theorientation of the designated top and bottom). Although participants wereallowed to use their nonwielding hand to hold the rod while they exploredthe object, they were asked to make their perceptual report only with thehand that they would ordinarily use in a hammering task. The order of therods was randomized, and each rod was encountered three times by eachparticipant.

177USER–TOOL INTERFACE

Results and Discussion

Participants were reasonably consistent in their elected grasppositions. In a correlation matrix, the responses of all but onepairing of participants were significantly correlated with one an-other. The mean r (on the basis of an r-to-z transform) was .86(with raw correlations varying from .47 to .97). An overall im-pression of the task was obtained by first averaging grasp positionsover trials and over participants to achieve a mean grasp positionper object (see Table 1). Inertia tensors were calculated and di-agonalized for the mean grip positions on each of the 12 objects.S, V, and ek were then calculated at the mean grip positions.Multiple regression revealed that the log of the three inertialvariables (log V, log S, and log ek) accounted for over 90% of thevariance in log mean chosen grip position (R2 � .93, p � .01). Thefact that stepwise regression selected log V, then log S, and thenlog ek (adding each in a successive step) suggests that V is playingthe largest role in choice of grasp position, followed by S andthen ek.

At the level of the individual participants, log V, log S, and logek accounted for between 47% and 92% of the variance in gripposition (on average 75%). A Friedman two-way analysis ofvariance (ANOVA) by ranks (see Siegel, 1956) suggests that thereare consistent differences in the ordering of the beta weights acrossparticipants, �r

2(2, N � 3) � 6.3, p � .05. In general, log V isweighted more strongly than log S, which is weighted morestrongly than log ek. Moreover, the patterning of beta weights andstandard errors is consistent with that of the preceding mean data.Generally, the beta weights for V and S were negative, and the betaweights for ek were positive. However, S and ek did not reachsignificance for most participants. This is consistent with the factthat participants were not given any information about what was tobe hammered, how it was to be hammered, or what part of theobject would be used to make the strike.

The participant for whom V, S, and ek accounted for the leastamount of variance (R2 � .47, ns) was examined further. Thisparticipant’s responses on Object 12 were aberrant. When Object12 is removed from the analysis, V, S, and ek account for 80% of

the variance in grip position for this participant, and all threeregressor variables are significant (or nearly so). It is unclear whythis object was troublesome for this participant.

Both at the level of the mean data as well as at the level of theindividual participant data, the patterning of the coefficients on V,S, and ek is consistent with our hypotheses. Participants seem to begrasping so as to minimize V and S while simultaneously maxi-mizing ek , and they are somewhat less consistent in regulating ek

than in regulating V. This is consistent with the finding that V (andonly V) played a determining role in haptic perception of thefunctional utility of an object for hammering (Wagman & Carello,2001). As V and S decrease and as ek increases, a given objectbecomes less controllable and less horizontally oriented (with thecenter of mass located further from the rotation point)—qualitiesthat when proportioned properly may yield an object suitable tohammering (one should recall that a smaller V means that moreforce is required to rotate an object). These notions support theidea that tool users are sensitive to Drillis’s (1963) quantitativemeasure of hammer efficiency. According to his analysis, anefficient hammer is one in which the center of mass of the hammeris located as close as possible to the point at which contact is to bemade. A general goal of designers may be to design a hammer suchthat it minimizes the force required by the user yet maximizesforce generated by the strike. In other words, a good hammer maybe one that tends to “hammer itself.”

Analysis of Surrogate Data

It should be noted that in analysis of the grip position data, theinertial variables (V, S, and ek) were calculated relative to arotation point in the wrist at the (mean) chosen grip position on agiven rod. These grasp positions were then regressed onto theinertial properties of the rods at these grip positions (see above).Superficially, at least, this technique runs the risk of circularitybecause the predictor variables (V, S, and ek) are not a prioristatistically independent from the criterion variable (grasp posi-tion). On the contrary, they are derived from the criterion variable.This creates the possibility that relationships uncovered by the

Table 1Grip Positions (GP) and Their Standard Deviations for Five Tasks (Across the Three Experiments) for Each of 12 Objects

Object attributes Grip positions (cm) and SD

% FillFill

location Mass (g)Center ofmass (cm)

HammerHammerprecision

Hammerpower

Throwprecision

Throwpower

GP SD GP SD GP SD GP SD GP SD

0 128.0 30.0 10.0 3.4 18.2 3.2 7.3 5.3 10.9 5.3 14.6 5.50 146.3 30.0 8.9 4.3 18.1 5.2 6.8 6.5 11.7 8.1 17.2 5.7

25 Bottom 344.2 16.8 8.1 4.9 13.5 3.7 6.8 5.6 9.9 7.6 14.0 5.525 Middle 344.2 30.0 13.3 3.5 19.5 4.1 8.0 4.5 14.1 5.8 18.2 4.925 Top 344.2 43.2 19.1 4.4 25.0 5.3 11.4 7.3 19.0 8.9 27.0 5.750 Bottom 542.2 18.8 10.2 4.1 16.2 4.4 8.3 5.8 10.8 6.9 15.3 6.250 Middle 542.2 30.0 17.1 4.4 22.0 3.5 11.3 4.2 14.9 6.6 21.9 4.050 Top 542.2 41.2 22.0 5.0 26.2 8.5 12.7 9.2 22.5 11.5 29.5 6.675 Bottom 740.1 23.8 15.4 4.9 19.9 4.9 9.5 6.5 14.4 8.1 20.6 3.975 Middle 740.1 30.0 18.8 3.7 22.0 2.9 12.0 4.2 18.3 7.3 25.6 3.875 Top 740.1 36.2 22.5 5.2 25.8 6.9 14.4 6.5 20.7 9.8 26.7 4.1

100 Middle 938.0 30.0 21.5 7.0 24.3 6.7 13.3 5.3 17.9 11.3 26.8 5.2


multiple regression are a function of these preexisting relationshipsand not a function of task constraints.

To show that the relationships between grip position and inertialvariables uncovered in Experiment 1 are genuine, we enlisted thetechnique of surrogate data analysis, a relatively common tech-nique for the validation of observed structure in time-series data(for general information, see Hausdorff, Peng, Ladin, Wei, &Goldberger, 1995; Thelier, Eubank, Longtin, Galrikian, & Farmer,1992; Webber & Zbilut, 1994, 1996). In such analyses, researchersare concerned with showing that some statistical measure of a timeseries (e.g., complexity) is a function of the temporal contiguity ofa time series and not a property of random variation in the signal.Thus, they create a surrogate data set in which temporal contiguityis destroyed but other properties (e.g., mean, standard deviation)are preserved. For example, randomizing the data points withrespect to time destroys temporal structure while preserving otherstatistical features. If the same meaningful structure appears in thesurrogate data set as in the original data set, it is assumed that suchstructure is due to something other than the temporal contiguity ofthe signal. Thus, there is reason to doubt that any structure re-vealed in the original data set is genuine. Essentially, such a resultsuggests that the original data set is (at least in certain ways)indistinguishable from a random process.

To show that the structure revealed by the original analysis isgenuine, one must show that the statistical properties of the sur-rogate data set are significantly different from those of the originaldata set (see Hausdorff et al., 1995; Thelier et al., 1992; Webber &Zbilut, 1994, 1996). Ideally, structure present in the initial timeseries will be absent in the surrogate data.

Rather than being expected to reflect a time dependency, how-ever, the data presented in Experiment 1 are expected to reflect afunctional dependency (i.e., grasping for the function of hammer-ing). We can destroy this relationship (between grip position andmass distribution) while preserving the essential statistical featuresof the data set by randomly pairing each of the (mean) chosen grippositions with a different rod. By doing so, we destroy the inten-tionality of the task and create surrogate pairings of grip positionsand object. These surrogate grip positions have the same statisticalproperties as the original grip positions—they are, in fact, the sameset of numbers. They have simply been randomly reassigned to adifferent rod. As in the analysis of the original data set, surrogategrip positions can be used to generate surrogate inertial variablesthat describe the mass distribution at that (surrogate) grip position.We can then apply multiple regression to analyze the relationshipbetween the surrogate grip positions and the inertial variables atthose grip positions.

If meaningful statistical structure appears in the multiple regres-sion analysis of the surrogate variables, such structure is assumedto be due to something other than functional constraints of the task(e.g., random variation or a statistical artifact). If this is the case,there is reason to doubt that the structure in the original data set isgenuine.

In contrast to the original grasp positions, the surrogate grasppositions were relatively uncorrelated across participants. Themean r for the surrogate grip positions (on the basis of an r-to-ztransform) was .01 (with raw correlations varying from �.06 to.51). At the level of the mean grip position, the surrogate inertialvariables did not constrain surrogate grip position (R2 � .30, ns).One should recall that in the analysis of the original data, V, S, and

ek accounted for over 90% of the variance in grip position (seeabove). This difference is statistically significant at the level ofindividual participants (original R2 � 75.4%, surrogate R2 �36.6%, t[7] � 8.6, p � .01). In the surrogate analysis, the fact thatstepwise regression did not choose any of the surrogate variablessuggests that the surrogate inertial variables are not significantlyrelated to surrogate grip position.

Destroying the functional relationship between grip position andtask significantly compromises the explanatory power of the threeinertial variables implicated in the analysis of the original data set(e.g., at the level of the mean data, it renders beta weights of allthree regressor variables nonsignificant). This suggests that theinertial dependencies established at the grip positions in the orig-inal data set are genuine. More conservatively put, it suggests thatthey are not random.

However, one may further question whether a set of objects withcylindrical symmetry would allow adequate variation in Ik for theinertial dependencies to be evaluated meaningfully. To demon-strate that sufficient variation was, in fact, possible, we relativizedthe inertial variables generated at the chosen grip positions on eachobject with respect to the maximum possible inertial values on thatobject. The values of the inertial variables at the mean chosen grippositions on each object were divided by their respective maxi-mum values on each rod.

These values were then averaged over the 12 objects and mul-tiplied by 100 to obtain the mean percentage of V, S, and ek

retained at the mean grasp position (see Table 2). These valuessuggest that in grasping so as to hammer, participants are mini-mizing S while maximizing ek. This is consistent with analysis ofbeta weights and standard errors, particularly the fact that the betaweights for S and ek variables are opposite in sign. These valuesare perhaps most informative only in comparison with the percent-ages from the other conditions (see Table 2).

Figure 2 represents how changes in grip positions on each of the12 objects simultaneously affect V, S, and ek. Each trajectoryrepresents the possible variation among the variables V, S, and ek

on each of the 12 rods (at all possible grip positions). Each symbolon a trajectory represents the mean chosen grasp position in agiven condition in what amounts to VSe space. The fact that thesymbols representing the chosen grip positions in the generichammering task (gray circles) are located toward the right andtoward the vertical peak of each trajectory is indicative of the factthat participants are grasping so as to maximize ek while minimiz-ing S in this condition (see Figure 2).

Table 2Percentage of V, S, and ek Retained on Average When ObjectsWere Grasped Under the Functional Constraints in Each of theFive Conditions Across the Three Experiments

Condition V S ek

Hammer precision 86 57 78Throw precision 85 54 82Hammer 74 31 94Hammer power 73 30 94 (ns)Throw for power 62 17 90 (ns)

Note. V � volume; S � symmetry; ek � eigenvector angle.


Before proceeding, we should address the issue of alternativevariables. We have been focusing on configurations of the massdistribution that have consequences for movement (Ik). Calcula-tions of these quantities involve mass and center of mass (inparticular, its distance from the rotation point). Not surprisingly,these component variables (as well as others such as static mo-ment) are also strongly related to elected grasp position in Exper-iment 1. However, research has shown systematically (in experi-ments designed to disentangle the variety of components) that theinfluence of these variables is typically carried by the higher orderinertial variables (i.e., Ik; see Fitzpatrick, Carello, & Turvey, 1994;Shockley, Carello, & Turvey, 2001, 2003; Solomon & Turvey,1988; Stroop, Turvey, Fitzpatrick, & Carello, 2000). Moreover, thetensorial characterization has the advantage of providing a unifiedaccount of the perception of a wide variety of properties in a widevariety of circumstances. Intentions to perceive length, width,weight, and orientation all yield a dependence on Ik but withdifferent, predictable parsings (see Carello & Turvey, 2000).

Furthermore, these dependencies do not depend on whether theobject is being held vertically or horizontally or on whether it isbeing wielded quickly or slowly. Other accounts, in contrast,assume that perceivers use different strategies to perceive differentproperties or even different strategies to perceive the same prop-erty under different orientations (e.g., Kingma et al., 2002). For us,the latter approach is insufficiently constrained. The tensorialcharacterization, through its link to controlling movement, ratio-nalizes the particular parsings that are revealed. It is expected thatthe different functional constraints under consideration here shouldbe consistent with this characterization.

Experiment 2

The results of Experiment 1 suggest that in grasping an object tobe used in a generic hammering task, the actor establishes arelation among a particular set of inertial variables (V, S, and ek) ina way that seems to reflect functional task constraints. In Experi-

Figure 2. Changes in grip position on each of the 12 objects create changes in the inertial variables of volume(V), symmetry (S), and eigenvector angle (ek). The degree to which these values can vary is highly dependenton the properties of the objects themselves. Each trajectory represents the possible variation among the variablesV, S, and ek on each of the 12 rods. They represent the simultaneous changes in these three variables at allpossible grip positions. The upper end-point of each trajectory corresponds to the relationship among thesevariables when that object is grasped at the end designated as the bottom. The inflection point corresponds tothe relationship among the same variables when that object is grasped at its center of mass. The lower end-pointof each trajectory corresponds to the relationship among these variables when that object is grasped at the enddesignated as the top. The symbols indicate mean chosen grip positions on each object in each of the fiveconditions. The thickness of a given trajectory indicates where it sits along the Volume axis. Thinner trajectoriesare located further in depth from the viewer than thicker trajectories. Because trajectories for some objectsoverlap, fewer than 12 trajectories are visible.


ment 2, we compared the inertial consequences of chosen grippositions on objects to be used in a precision hammering task withthose on the same objects to be used in a power hammering task.

Because perceivers show sensitivity to ek in determining theappropriateness of a particular tool for a precision task (but not fora power task; Burton & McGowan, 1997; Wagman & Carello,2001), we expected that perceivers would show sensitivity to ek inchoice of grasp position in a precision tool-use task but not in apower tool-use task. That is, we expected that V, S, and ek wouldbe required to account for a statistically significant portion of thevariance in grip position in the precision task, but only V and Swould be required to do so in the power task. We hypothesized thatif perceivers do not show differential sensitivity to ek in choosinga grip position across tasks, then there will be no such differencesacross conditions.

Method

Participants. Seven students at the University of Connecticut partici-pated in this experiment. All were compensated $8 for their participation.

Materials and apparatus. The objects used in Experiment 2 were thesame objects used in Experiment 1 and are identified in Table 1. Inaddition, a large spike (25 cm long, 1 cm in diameter) partially embeddedinto a wooden block and a finishing nail (2.3 cm long, 0.1 cm in diameter)partially embedded in a (6.5 cm � 15 cm) section of wooden molding wereused to provide the constraints on the hammering task in the power andprecision conditions, respectively.

Procedure. The procedure was the same as in Experiment 1 with theexception that a style of hammering was specified. Participants were askedto explore each object haptically, eventually choosing a grip position bestsuited to hammering the spike or the finishing nail. Grip position wasreported and recorded as before. All participants completed both conditionsin blocked fashion, and the order of conditions was counterbalanced acrossparticipants.


As in Experiment 1, participants were reasonably consistent intheir elected grasp positions. In both conditions, the responses ofall pairings were significantly correlated with one another. In thepower condition, the mean r (on the basis of an r-to-z transform)was .80 (with raw correlations varying from .22 to .93). In theprecision condition, the mean r (on the basis of an r-to-z transform)was .81 (with raw correlations varying from .60 to .93).

In the precision condition, multiple regression revealed that thelog of the three inertial variables (V, S, and ek) accounted for 90%of the variance in log mean grip position (R2 � .90, p � .01). Thefact that stepwise regression selected log V, then log S, and thenlog ek (adding each in a successive step) suggests that V is playingthe largest role in choice of grasp position, followed by S andthen ek.

In the power condition, multiple regression revealed that log Vand log S accounted for nearly 90% of the variance in log meangrip position (R2 � .88, p � .01). The influence of log ek was notsignificant in this condition. The fact that stepwise regressionselected log V and log S (in successive steps) but not log ek

suggests that V is playing a larger role than S in choice of graspposition and that the role of ek is minimal, at most.

At the level of the individual participants, V, S, and ek accountedfor between 34% and 88% of the variance in grip position in thepower condition (on average 64%) and between 62% and 96% of

the variance in grip position in the precision condition (on average74%). Unlike in Experiment 1, a Friedman two-way ANOVA byranks suggested that there were not consistent differences in theordering of the beta weights across participants in either condition.In general, the patterning of beta weights and standard errors at thelevel of the individual participants are consistent with that of themean data. Generally, in both conditions, the beta weights for bothV and S were negative and the beta weights for ek were positive.Again, S and ek did not reach significance for most participants.

The participant for whom V, S, and ek accounted for the lowestamount of variance in Experiment 2, specifically in the powercondition (R2 � .34, ns), tended to choke up (i.e., grasp closer tothe top) on each object more than any other participant and showedan expanded range of grasp positions. These tendencies may havebeen detrimental to the functional specificity of grasp position inthis condition.

At the level of the mean data but less clearly at the level of theindividual participant data, the patterning of the coefficients on V,S, and ek is consistent with our hypotheses. In Experiment 1,participants grasped the 12 objects so as to create a generichammer. In the current experiment, participants were asked tograsp so as to create specific hammers—ones that would beappropriate for precision and power tasks, respectively. In a powerhammering task, participants grasped so as to regulate the forcesrequired to control a given object as well as the directions in whichthose forces are required (as indexed by V and S, respectively).However, in a precision hammering task, participants grasped notonly so as to regulate these relationships but also so as to regulatethe perceived orientation of the object with respect to the hand (asindexed by ek). That is, behavior in Experiment 1 seems morecomparable with behavior in the precision condition in the currentexperiment than with behavior in the power condition. An in-creased sensitivity to ek may allow for better control of the objecttip in the precision task (Burton & McGowan, 1997; Wagman &Carello, 2001).


In Experiment 2, the surrogate grasp positions were again rel-atively uncorrelated across participants in each condition. Themean r for the surrogate grip positions in the power condition (onthe basis of an r-to-z transform) was .02 (with raw correlationsvarying from �.70 to .70). In the precision condition, the mean r(on the basis of an r-to-z transform) was .05 (with raw correlationsvarying from �.36 to .54). Furthermore, the surrogate inertialvariables did not constrain surrogate grip position in either thepower condition (R2 � .33, ns) or in the precision condition (R2 �.56, ns). These differences are statistically significant at the levelof the individual participants (in the precision condition: originalR2 � 75.4%, surrogate R2 � 36.6%, t[6] � 3.5, p � .05; in thepower condition: original R2 � 64.4%, surrogate R2 � 36.9%, t[6]� 8.6, p � .05). This fact, in combination with the fact thatstepwise regression did not choose any of the surrogate variablesin the power condition and chose only ek in the precision condition,suggests that (as in Experiment 1) the surrogate inertial variablesare not significantly related to surrogate grip position.

As in Experiment 1, we see important consequences of destroy-ing the functional relationship between grip position and task. Asin Experiment 1, this suggests that the inertial dependencies


achieved at the grip positions described above are genuine (i.e., afunction of task constraints).

Using the method described in Experiment 1, we calculated themean percentage of V, S, and ek retained at the mean grasp position(see Table 2 and Figure 2). We see that as the hammering task ismore strictly defined to emphasize its precision constraints over itspower constraints, participants tend to grasp the object so as tomaximize V and S while minimizing ek. This may serve to maxi-mize the object’s controllability while serving to regulate the forcetransference capacity of the hand–object system such that it isappropriate for a precision task. These trends are apparent inFigure 2 in that the symbols representing the chosen grip positionin hammering with power (black circles) and those representinghammering with precision (white circles) are located, respectively,to the far right and the far left of each trajectory.

Experiment 3

Experiments 1 and 2 demonstrated that when grasping an objectto be used as a hammer, tool users establish a relationship amongV, S, and ek in a way that depends on the relative precisionconstraints of the hammering task. In Experiment 3, we comparedthe inertial consequences of chosen grip positions on objects to beused in other tasks that seem to share these same functionalconstraints. Specifically, we compared the inertial consequences ofgrasp position in a precision-throwing task with those in a power-throwing task.

We expected participants to show sensitivity to V, S, and ek inchoice of grip position on objects to be used in a throwing task. Wehypothesized that if perceivers are not sensitive to such variablesin choice of grip position in such a task, these variables (eitheralone or in combination) will not constrain performance. Further-more, because perceivers show sensitivity to ek in grasping a toolto be used in a precision-hammering task but not in a power-hammering task, we expected them to show the same sensitivity toek in a precision-throwing task but not in a power-throwing task.That is, we expected that together, V, S, and ek would account fora statistically significant portion of the variance in grip position inthe precision task, but only V and S would be required to do so inthe power task. We hypothesized that if perceivers do not showdifferential sensitivity to ek across tasks, there will be no suchdifferences across conditions.

Method

Participants. Ten students at the University of Connecticut partici-pated in this experiment. All were compensated $8 for their participation.

Materials and apparatus. The objects used in Experiment 3 were thesame as those used in Experiments 1 and 2 and are identified in Table 1.In addition, a black cloth circle (30 cm in diameter) was placed on the floor1.5 m from the seated participant.

Procedure. As in Experiments 1 and 2, participants were seated andhanded rods one at a time by the experimenter. In the power condition,participants were asked to haptically explore each object, eventually choos-ing the position along its length at which they would grasp it if they wereasked to throw it as far as possible. In the precision condition, participantswere asked to haptically explore each object, eventually choosing theposition along its length at which they would grasp it if they were asked tothrow it so that it landed completely within the boundaries of the clothcircle. Grip position was reported and recorded as before. All participants

completed both conditions in blocked fashion, and the order of conditionswas counterbalanced across participants.


Participants were again reasonably consistent in their electedgrasp positions. The mean r in the power condition (on the basis ofan r-to-z transform) was .60 (with raw correlations varying from.06 to .89). In the precision condition, the mean r (on the basis ofan r-to-z transform) was .59 (with raw correlations varying from�.52 to .99).

In the precision condition, multiple regression revealed that thelog of the inertial variables (V, S, and ek) accounted for over 90%of the variance in log mean grip position (R2 � .94, p � .01). Thatstepwise regression selected log ek , log S, and then log V (insuccessive steps) highlights the enhanced role of ek in choice ofgrasp position in this task relative to its role in the task in Exper-iment 1.

In the power condition, multiple regression revealed that log Vand log S accounted for nearly 90% of the variance in log meangrip position (R2 � .89, p � .01). Log ek was not significant in thiscondition. That stepwise regression selected log V, then log S, butnot log ek suggests that V is playing the largest role in choice ofgrasp position, followed by S but that ek does not play a significantrole in choice of grasp position.

At the level of the individual participants, these three variablesaccounted for between 2.5% and 88% of the variance in gripposition for precision throwing (on average 36%) and between10% and 92% of the variance in grip position for power throwing(on average 56%). A Friedman two-way ANOVA by ranks sug-gests that there are consistent differences in the ordering of thebeta weights across participants in both conditions (precision:�r

2[2, N � 3] � 3.8, p � 0.01; power: �r2[2, N � 3] � 9.6, p � .05).

In both conditions, V was weighted more strongly than either S orek. The patterning of beta weights and standard errors was againconsistent with the mean data in both conditions. Generally, inboth conditions, beta weights for V and S were negative, and betaweights for ek were positive. However, V, S, and ek were generallynot significant at the level of the individual participants.

The participants for whom V, S, and ek accounted for the lowestamount of variance in the precision condition tended to either (a)choke up on each and show an expanded range of grip positions or(b) grasp closer to the bottom object of the objects and show acompressed range of grip positions. As in Experiment 2, thesevariations may have been detrimental to the functional specificityof grasp position across objects. The cause of the discrepancy forthese participants, however, is less straightforward. We can onlyspeculate that these participants adopted a different style of throw-ing than did the other participants (e.g., underhand or sidearm asopposed to overhand).

In Experiment 2, participants grasped the 12 objects so as tocreate specific hammers—ones that would be appropriate for aprecision task and ones that would be appropriate for a power task.In doing so, they showed functionally specific sensitivity to higherorder inertial properties. In the current experiment, participantswere expected to grasp so as to create specific projectiles—onesthat would be appropriate for a precision task and ones that wouldbe appropriate for a power task. At the level of the mean data, butless clearly at the level of individual participant data, the patterning


of the coefficients on V, S, and ek support our hypotheses. The lackof clarity may simply indicate that throwing is a less restricted taskthan hammering—throwers may have more options in how topattern forces applied to the thrown object so as to accomplish thegoal of the throwing task. Nonetheless, grasp positions for powerand precision throwing were distinct from one another and paral-leled distinctions in grasp positions for power and precisionhammering.


As in Experiments 1 and 2, in Experiment 3 the surrogate grasppositions were again relatively uncorrelated across participants ineach condition. The mean r for the surrogate grip positions in thepower condition (on the basis of an r-to-z transform) was �.01(with raw correlations varying from �.51 to .72). In the precisioncondition, the mean r (on the basis of an r-to-z transform) was�.03 (with raw correlations varying from �.46 to .44). Thesurrogate inertial variables accounted for only 20% of the variancein surrogate grip position in the power condition (R2 � .20, ns) and27% of the variance in surrogate grip position in the precisioncondition (R2 � .27, ns). One should note that in analysis of theoriginal data, V, S, and ek accounted for over 90% of the variancein grip position in throwing with precision, and V and S accountedfor nearly same amount of variance in throwing with power. Thisdifference is statistically significant at the level of the individualparticipants in the power condition (original R2 � 56.3%, surro-gate R2 � 28.6%, t[9] � 3.7, p � .01) but not in the precisioncondition (original r2 � 36.5%, surrogate R2 � 42.4%, t[9] ��.57, p � .58). Furthermore, stepwise regression on the surrogatevariables did not choose any of variables in either condition.

Using the method described in Experiments 1 and 2, we calcu-lated the mean percentage that S and V are being retained fromtheir maximum values when participants grasp objects in eachcondition in this experiment (see Table 2). When data from allthree experiments are considered, we see a more convincing dem-onstration of the pattern that emerged in earlier analyses. As a task(regardless of whether it is a hammering task or a poking task) ismore strictly defined to emphasize precision constraints overpower constraints, participants grasp an object to be used in thattask so as to maximize V and S while simultaneously minimizingek. That is, they grasp the object so as to make it more controllableand less asymmetric. Conversely, as a task (regardless of whetherit is a hammering task or a poking task) is more strictly defined toemphasize power constraints over precision constraints, partici-pants grasp an object to be used in that task so as to minimize Vand S without showing any regard for ek. That is, they grasp theobject so as to make it more asymmetric and enhance the potentialenergy available just prior to the release. This is apparent inFigure 2 in that the symbols representing the chosen grip positionin throwing with power (black squares) are located to the far rightof each trajectory, whereas the symbols representing the chosengrip position in throwing with precision (white squares) are locatedto the far left (relatively speaking) of each trajectory.

General Discussion

The inertial characteristics of an object make that object more orless functionally appropriate for a given task (Cochran & Riley,

1986; Drillis, 1963; Drillis et al., 1963; Marras & Rockwell, 1986;Pagano & Turvey, 1998; Wagman & Carello, 2001). When theinertial properties of an object cannot be altered by adjusting ormodifying the object itself (see Hart & Hart, 1994; Hart et al.,2001; Weir et al., 2002), perceivers–actors can modulate the iner-tial properties of the hand–object system by changing their graspon the object—by changing the user–tool interface.

In three experiments, participants were asked to create a user–tool interface by virtue of anticipating a tool–environment inter-face. In general, they were asked to exhibit prospective control oftheir behavior (cf. Turvey, 1992). Our goals in these experimentswere twofold: (a) to uncover the inertial variables that constraingrip position in certain tasks and (b) to determine whether (andhow) these variables reflect functional task constraints. Our ex-pectations were that participants would grasp so as to minimize Vin tasks that require power and maximize V while minimizing ek intasks that require precision. In short, we expected to demonstratethat abstract assertions about the functional role of Iij are realizablein real-world behaviors.

Functional Specificity and User–Tool–EnvironmentInterfaces

The data suggest that when participants grasp objects so as toperform various functions with them, they show sensitivity tohigher order inertial variables (V, S, and ek). These variables (or asubset of them) account for between 88% and 94% of the variancein mean chosen grasp position across the five tasks in the threeexperiments. Moreover, not only do participants seem to exploitthe inertia tensor in choosing an appropriate grasp position on agiven object, they show sensitivity to specific parsings of thetensor so as to grasp in a functionally specific manner.

V and S play a role in choice of grasp position in all tasks. Thisis consistent with recent research that has focused on the relation-ship between the inertia tensor and controlling movement (Shock-ley et al., 2001; Turvey et al., 1999; Wagman & Carello, 2001). Asnoted, V and S are related to, respectively, the forces required tocontrol a given object and the directions in which those forces arerequired. Presumably, all five tasks required regulating such as-pects of the hand–object system to satisfy task demands. In addi-tion to V and S, ek plays a role in constraining grip position in thosetasks in which the (implicit or explicit) precision constraints seem-ingly outweigh the power constraints. Its contribution was appar-ent in a generic hammering task (Experiment 1), a precisionhammering task (Experiment 2), and a precision throwing task(Experiment 3). Such a role for ek echoes that seen in research onperception of object orientation with respect to the hand (seePagano & Turvey, 1998), using a long cane to guide locomotion(Burton & McGowan, 1997), and poking a target (Wagman &Carello, 2001). In general, the results suggest that in grasping atool, participants establish relationships among the same inertialvariables but in a way that reflects these specific task constraints.As the explicit or implied precision constraints of a task areemphasized, participants grasp so as to preserve V and S whilesimultaneously reducing ek (see Figure 2 and Table 2). Overall,these transformations of the mass distribution relative to the rota-tion point serve to enhance controllability of the hand–objectsystem at the expense of the potential energy available prior to thehammer stroke or throw.


When an object is grasped and wielded, time-varying forcesproduce time-varying motions of the object and the limb. Theforces and motions are coupled by time-invariant parameters, ofwhich, for present purposes, the most notable are the moments ofthe object’s mass distribution. Mass (total mass), static moment(Mass � The Distance From An Origin), and moment of inertia(Mass � The Squared Distance From An Origin), constitute thezeroth, first, and second moments. These moments are propor-tional to the forces needed to, respectively, hold the grasped objectvertically still, hold it horizontally still, or wave it about in threedimensions. Typically, these three moments are correlated, andidentifying their particular contributions to constraining perceptionrequires objects specially designed to disentangle them. At present,that evidence seems to favor the second moment (e.g., compareKingma et al., 2002, with Stroop, Turvey, Fitzpatrick, & Carello,2000, and Shockley, Carello, & Turvey, 2001, 2003). We did notuse such objects here, so the first moment would also serve toconstrain grasp choices. But as noted earlier, the larger advantageof the second moment (and its derived scalars) that we tried toexploit in the present experiments is the systematicity of variousparsings as they relate to particular properties. Perception of prop-erties including length, width, heaviness, orientation, shape, grasplocation, length in front of the grasp, and length behind the graspare all constrained by the inertia tensor with different patterns ofdependencies. It is unclear how the first moment could provide thesame generality or richness.

Concluding Remarks: Structured Energy Arrays andPoints of Observation

It has been argued that stimulation rich enough to supportcomplex behaviors (e.g., locomotion and tool use) can only befound in structured energy arrays (Gibson, 1966, 1979). Just as theoptic array consists of differences in light intensities in differentdirections ambient to an observation point, the inertial array con-sists of different resistances to rotational acceleration in differentdirections ambient to a rotation point (Cooper, Carello, & Turvey,2000). Just as changes in the point of observation open vistas in theoptic array, changes in the point of rotation (of a hand-held object)open vistas in the inertial array. In both cases, such changes areaccompanied by changes in the affordance structure available to anorganism (see Benedikt, 1979; Gibson, 1979; Steenbergen et al.,1997).

As soon as a perceiver–actor grasps an object (as soon as auser–tool interface is created), the dynamics of the prehensilesystem are immediately altered (Bongers, 2001; Smitsman, 1997).The perceiver–actor instantaneously becomes a perceiver–actor–tool complex. In this way, the addition of the tool creates emergentpossibilities for action for the tool user (see Gibson, 1979; Steen-bergen et al., 1997; van Leeuwen, Smitsman, & van Leeuwen,1994; Wagman & Carello, 2001). The possibilities for action are afunction of the mass distribution of the object relative to therotation point (i.e., the wrist of the perceiver–actor). The user–toolinterface is this relationship, and as we have demonstrated exper-imentally here, such an interface reflects many of the functionalconstraints of the task for which the object was grasped.

The ways in which an object can be moved are, of course,limited by the inertial properties of the object itself. Choice ofgrasp position on an object must accommodate not only the func-

tional constraints of the task but also these physical constraints. Insome sense, the inertial properties inherent to the object set theinitial conditions from which the perceiver–actor builds the user–tool–environment interface (see Figure 2). In grasping an object ina particular location, a tool user places additional limits on howthat object can be moved. Before an object is grasped, it canbecome any one of a number of functional objects depending onhow and where it is grasped. In grasping that object in a particularlocation, the tool user is selecting the functional object that seemsappropriate given the task constraints. We have shown here thatthe higher order inertial variables that underlie haptic perception ofobject function (see Wagman & Carello, 2001) also underlie hapticcreation of object function.

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Received July 18, 2002Revision received May 14, 2003

Accepted May 15, 2003 �


Haptically creating affordances: The user-tool interface

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