Journal of Experimental Psychology: Applied 2003, Vol. 9, No. 3, 175–186
Copyright 2003 by the American Psychological Association, Inc. 1076-898X/03/$12.00 DOI: 10.1037/1076-898X.9.3.175
Haptically Creating Affordances: The User–Tool Interface Jeffrey B. Wagman and Claudia Carello University of Connecticut Successful use of a hand-held tool requires overcoming the rotational inertia of the hand-plus-tool system. Where an object is grasped affects this rotational inertia. Appropriate choice of grip position may be crucial in the safe, effective, and efficient control of a hand-held tool. In 3 experiments, the authors investigated how choice of grip position on a tool was constrained by task demands. The results suggest that choice of grasp position serves to establish relationships among 3 variables derived from the inertial ellipsoid of the hand– object system (volume, symmetry, and eigenvector angle) in a way that specifically reflected the power or precision constraints of the given task. These variables have previously been shown to play a role in haptic perception of tool function. Changing grasp position on a tool is a way to exert control over the nuances of the user–tool interface.
2001; Vicente, 1995; Vicente & Rasmussen, 1990). A welldesigned interface is one that maps the structure of the work domain onto a visual representation such that both physical and functional 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 environmental state of affairs but also the path by which the operator might bring about a desired state of affairs (Norman, 1988; Vicente & Rasmussen, 1990; Warren, 1995; Zaff, 1995). Designing an interface that preserves the prospective nature of perception–action (see Turvey, 1992) is perhaps the most challenging aspect of interface design. One way to step into this problem is by investigating how users of decidedly less technologically advanced devices such as handheld tools choose to “create interfaces” (both between themselves and the tool and between the tool and the environment; see below). A hand-held tool can be considered an interface to the extent that it extends the tool user’s capacity for perception–action and improves the fit between animal and environment (see Beck, 1980; Burton, 1992, 1993; Gibson, 1979; McGrew, 1993; van LawickGoodall, 1970; Weir, Chappell, & Kacelink, 2002). A welldesigned tool, like a well-designed interface, serves to increase the opportunities for behavior—what Gibson (1979) called affordances (see also Bongers, 2001; Lockman, 2000; Shaw, Flascher, & Kadar, 1995; Smitsman, 1997). Successful tool use requires establishing a tool– environment interface (Kreifeldt & Hill, 1975; Mital & Sanghavi, 1986)—the functional relationship between the surfaces of the tool and the to-be-affected object (Bongers, 2001; Smitsman & Bongers, in press). It also requires an appropriate user–tool interface—the functional relationship between tool user and tool determined by how and where the user grasps the tool. Both of these interfaces depend on task constraints. For example, the tool– environment interface required for hammering is quite different from that required for poking (cf. Wagman & Carello, 2001). As a result, the two tasks may require different user–tool interfaces. Hammering may require a power grip, whereas poking may require a precision grip (Kroemer, 1986; Napier, 1993). Such grips allow for different sets of actions to be performed with the same tool. How such user–tool and tool– environment interfaces are selected, created,
The last decade or so has seen an explicit push to take an ecological approach to human factors (see Flach 1989, 1990; Flach, Hancock, Caird, & Vicente, 1995; Hancock, Flach, Caird, & Vicente, 1995; Vicente & Rasmussen, 1990), an approach rooted in theoretical contributions of James Gibson’s ecological psychology (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 of perception–action by attempting to understand how behaviorally relevant environmental properties lawfully structure energy arrays (Turvey, Shaw, Reed, & Mace, 1981). The enterprise devoted to uncovering such behaviorally relevant structure in stimulation patterns has been termed ecological physics (Gibson, 1961, 1979; Michaels & Carello, 1981). Its counterpart in human factors has been termed inverse ecological physics (Effken, Kim, & Shaw, 1997; Flach, 1990; Vicente, 1995) because it represents an attempt to design environments that give rise to behaviorally relevant structure in stimulation patterns. The emphasis is on seeking a generalizable model of the environment in addition to a generalizable model of the animal (Kirlik, 1995). One of the most successful applications of ecological principles in an explicitly applied setting is in the realm of interface design. The aim of ecological interface design is to build a display that allows for simultaneous monitoring and control of complex work environments (e.g., cockpits, power plants, operating rooms) without 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,
Jeffrey B. Wagman and Claudia Carello, Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut. This research was supported by National Science Foundation Grant BCS 00-04097 awarded to M. T. Turvey and Claudia Carello. We thank Alex Kirlik for comments on a previous version of this article. We thank Justin Bates and Len Katz for help with statistical analysis. Correspondence concerning this article should be addressed to Jeffrey B. Wagman, who is now at the Department of Psychology, Illinois State University, Campus Box 4620, Normal, Illinois 61790-4620. E-mail:
[email protected] 175
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and maintained has potential consequences for the likelihood of safe, effective, and efficient tool use by humans in various work settings (Armstrong, Radwin, Hansen, & Kennedy, 1986; Cochran & Riley, 1986; Drillis, 1963; Marras & Rockwell, 1986; Shaw et al., 1995). Sensitivity to these demands is evident from observation of children and animals. When faced with using spoons that have been bent in particular ways, toddlers choose a grasp type and position that preserves the functional act of scooping (Steenbergen, van der Kamp, Smitsman, & Carson, 1997; see also Lockman 2000). Chimpanzees, sea otters, and elephants have also been observed to vary their grip on an object depending on how that object 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 the principles that underlie these capabilities? Research on perceiving object properties by dynamic touch provides a starting point.
Dynamic Touch and User–Tool–Environment Interfaces Maintaining an appropriate user–tool– environment topology requires controlling the hand-plus-tool system to satisfy task constraints. Controlling an object requires exploiting the laws of rigid body motion and overcoming the translational and rotational inertia of the hand-plus-tool system with appropriate scaling and directing of muscularly generated forces and torques (Carello & Turvey, 2000; Shockley, Grocki, Carello, & Turvey, 2001; Turvey, 1996; see also Drillis, Schneck, & Gage, 1963). This impli-
cates dynamic touch, the type of touch used when an object is firmly grasped and wielded via muscular effort (Gibson, 1966). One line of inquiry suggests that perception of a multitude of geometric and functional object properties using dynamic touch is constrained by how that object resists rotational acceleration in different 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 suggested (e.g., Kingma, Beek, & van Diee¨ n, 2002; see below), an advantage of the inertial approach relevant to the present investigation is that resistance to rotational and translational acceleration provides a direct link to the level and patterning of forces required for task-specific movement. Resistance to rotational acceleration in different directions is quantified by the inertia tensor. When the inertia tensor is referred to the symmetry axes of the hand– object system, its eigenvalues, Ik, refer to the resistances to rotational acceleration about the symmetry axes, and the symmetry axes themselves are the eigenvectors, ek (see Figure 1A). Research on perception by dynamic touch has generally found that perceived magnitudes (e.g., length, width) are tied to Ik and perceived directions (e.g., the orientation of an object in the hand, the orientation of a limb, where the hand is on an object) are tied to ek (for reviews, see Carello & Turvey, 2000; Pagano & Turvey, 1998). A more explicitly functional setting for dynamic touch has been pursued recently with respect to the problem of perceiving heaviness, which has been shown to be 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 the object is not along the z-axis, the symmetry axes of the hand– object system (e1, e2, and e3) are not coincident with 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 example of one of the experimental stimuli (a hollow wooden rod containing a column of a particular volume of lead shot braced between two wooden dowels). The objects each appeared to be solid, homogeneous rods and were indistinguishable by sight or sound. (C) A participant settled on the grip position most appropriate for hammering. This position was measured as the distance from the bottom of the rod to the middle of the grasp.
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that mass as quantified by Ik (Amazeen, 1999; but see Kingma et al., 2002). There are two aspects to this functional setting. First, the relevant affordance characterization of heaviness seems to concern how movable an object is (Turvey, Shockley, & Carello, 1999). Second, the mass distribution is characterized with respect to two scalars (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. One should note that the exponent in the equation is such that the larger the value of V for a given object, the less force required to rotate that object about a rotation point (and vice versa). The symmetry of the inertial ellipsoid (see Figure 1A), S ⫽ 2I3/(I1 ⫹ I2),
(2)
is relevant to how those forces should be directed. The ellipsoid of a perfectly symmetric hand– object system (i.e., where S ⫽ 1.0) is spherical; it is as easy to rotate about one axis as it is to rotate about any other axis (Shockley, Grocki, et al., 2001; Turvey et al., 1999). In short, the current understanding of perceived heaviness implicates quantities that are relevant to how controllable the object is. Given the relevance of the perceived magnitudes and directions to constraining an object’s use, dynamic touch provides an appropriate context in which to investigate many aspects of tool use (Wagman & Carello, 2001). Research along these lines has shown that perception of the functional utility of an object for hammering or for poking is dependent on V but in seemingly opposite ways. Ratings of hammers show a negative relationship with V, suggesting that participants place a premium on the prospective transfer of force from the hammer to the struck surface. Ratings of pokers show a positive relationship with V and a further influence of angle of e3, suggesting that participants place a premium on the controllability of the object tip (see Wagman & Carello, 2001). In brief, although both V and ek are relevant to the regulation of one’s ability to maintain a tool– environment interface, they are relevant in different ways depending on task constraints. Other affordance-centered experiments have shown that people haptically perceive the location of the sweet spot of a striking implement, that is, the point on the implement at which it is most energetically efficient to strike another object such as a ball with a tennis racket (Carello, Thuot, Anderson, & Turvey, 1999; Carello, Thuot, & Turvey, 2000). As it happens, the sweet spot is also the location at which it feels best to strike another object (Brody, 1987). In a sense, the present experiments address whether people are sensitive to the sweet spot for grasping. Where does it feel best to grasp an object to be used for a given purpose? As Kirlik (1998) noted, during the first few minutes of driving a new car, drivers will often engage in putting the car through its paces to get a feel for its handling qualities. Our interest was in the outcome of a somewhat analogous process—putting a hand-held tool through its paces to determine its handling qualities. We were particularly interested in how grasp position affects the inertial properties of the hand-plus-object system and how such properties make the system (feel) more or less functional for a given task. In three experiments, we quantified the inertial consequences of chosen grip positions on a set of 12 objects to be used in various tasks with
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different functional constraints. The results may have relevance not only for tool design but also for interface design more generally.
Experiment 1 Where an object is grasped has consequences for how effectively the hand– object system can be controlled by the actor. Appropriately controlling the tool– environment interface would seem to require sensitivity to the rotational inertia of a hand-plustool system. In Experiment 1, we quantified the inertial consequences of chosen grip positions on objects to be used in a generic hammering task. In particular, we examined the functional relationships among the inertial variables that emerge at the chosen grip positions. Because perceivers are sensitive to higher order variables in determining the appropriateness of a tool (Wagman & Carello, 2001), we expected that perceivers would show sensitivity to the same variables in choice of grip position on a tool. We expected that together, V, S, and ek would account for a statistically significant portion of the variance in grip position. Moreover, we predicted that each variable would play a statistically significant role in multiple regression. We hypothesized that if perceivers are not sensitive to such variables in choice of grip position, these variables (either alone or in combination) will not constrain performance.
Method Participants. Eight introductory psychology students at the University of Connecticut participated in this experiment in partial fulfillment of a course requirement. Materials and apparatus. The 12 objects used in Experiments 1–3 are identified in Table 1. Objects consisted of 60-cm pine rods (with a 1.27-cm radius) with a 0.64-cm radius hole drilled lengthwise through each one (see Figure 1B). Wooden dowels (with a 0.64-cm radius) were inserted into one end 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 particular location (at the top, middle, or bottom of the rod; see Figure 1B). A specified volume of lead shot was then poured into the hole, and a second wooden dowel (0.64-cm radius) was inserted as a cap so that the column of 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 as the bottom, and black tape was wrapped around the end of each rod that was designated as the top (see Figure 1C). Procedure. Participants were seated and handed rods one at a time by the experimenter. Participants were asked to explore each object haptically, wielding it with one hand and repositioning it with the other hand, eventually choosing the position along its length at which they would grasp the object 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 (the portion below the hand of the participant) to the middle knuckle of the participant’s fist (see Figure 1C). Exploratory wielding was not restricted in any way except that participants were asked to refrain from striking anything with the rods as well as from flipping the rods (i.e., inverting the orientation of the designated top and bottom). Although participants were allowed to use their nonwielding hand to hold the rod while they explored the object, they were asked to make their perceptual report only with the hand that they would ordinarily use in a hammering task. The order of the rods was randomized, and each rod was encountered three times by each participant.
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Table 1 Grip 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 Hammer
% Fill 0 0 25 25 25 50 50 50 75 75 75 100
Hammer precision
Hammer power
Throw precision
Throw power
Fill location
Mass (g)
Center of mass (cm)
GP
SD
GP
SD
GP
SD
GP
SD
GP
SD
Bottom Middle Top Bottom Middle Top Bottom Middle Top Middle
128.0 146.3 344.2 344.2 344.2 542.2 542.2 542.2 740.1 740.1 740.1 938.0
30.0 30.0 16.8 30.0 43.2 18.8 30.0 41.2 23.8 30.0 36.2 30.0
10.0 8.9 8.1 13.3 19.1 10.2 17.1 22.0 15.4 18.8 22.5 21.5
3.4 4.3 4.9 3.5 4.4 4.1 4.4 5.0 4.9 3.7 5.2 7.0
18.2 18.1 13.5 19.5 25.0 16.2 22.0 26.2 19.9 22.0 25.8 24.3
3.2 5.2 3.7 4.1 5.3 4.4 3.5 8.5 4.9 2.9 6.9 6.7
7.3 6.8 6.8 8.0 11.4 8.3 11.3 12.7 9.5 12.0 14.4 13.3
5.3 6.5 5.6 4.5 7.3 5.8 4.2 9.2 6.5 4.2 6.5 5.3
10.9 11.7 9.9 14.1 19.0 10.8 14.9 22.5 14.4 18.3 20.7 17.9
5.3 8.1 7.6 5.8 8.9 6.9 6.6 11.5 8.1 7.3 9.8 11.3
14.6 17.2 14.0 18.2 27.0 15.3 21.9 29.5 20.6 25.6 26.7 26.8
5.5 5.7 5.5 4.9 5.7 6.2 4.0 6.6 3.9 3.8 4.1 5.2
Results and Discussion Participants were reasonably consistent in their elected grasp positions. In a correlation matrix, the responses of all but one pairing of participants were significantly correlated with one another. The mean r (on the basis of an r-to-z transform) was .86 (with raw correlations varying from .47 to .97). An overall impression of the task was obtained by first averaging grasp positions over trials and over participants to achieve a mean grasp position per object (see Table 1). Inertia tensors were calculated and diagonalized 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 inertial variables (log V, log S, and log ek) accounted for over 90% of the variance in log mean chosen grip position (R2 ⫽ .93, p ⬍ .01). The fact that stepwise regression selected log V, then log S, and then log ek (adding each in a successive step) suggests that V is playing the largest role in choice of grasp position, followed by S and then ek. At the level of the individual participants, log V, log S, and log ek accounted for between 47% and 92% of the variance in grip position (on average 75%). A Friedman two-way analysis of variance (ANOVA) by ranks (see Siegel, 1956) suggests that there are consistent differences in the ordering of the beta weights across participants, r2(2, N ⫽ 3) ⫽ 6.3, p ⬍ .05. In general, log V is weighted more strongly than log S, which is weighted more strongly than log ek. Moreover, the patterning of beta weights and standard errors is consistent with that of the preceding mean data. Generally, the beta weights for V and S were negative, and the beta weights for ek were positive. However, S and ek did not reach significance for most participants. This is consistent with the fact that participants were not given any information about what was to be hammered, how it was to be hammered, or what part of the object would be used to make the strike. The participant for whom V, S, and ek accounted for the least amount of variance (R2 ⫽ .47, ns) was examined further. This participant’s responses on Object 12 were aberrant. When Object 12 is removed from the analysis, V, S, and ek account for 80% of
the variance in grip position for this participant, and all three regressor variables are significant (or nearly so). It is unclear why this object was troublesome for this participant. Both at the level of the mean data as well as at the level of the individual participant data, the patterning of the coefficients on V, S, and ek is consistent with our hypotheses. Participants seem to be grasping so as to minimize V and S while simultaneously maximizing ek , and they are somewhat less consistent in regulating ek than in regulating V. This is consistent with the finding that V (and only V) played a determining role in haptic perception of the functional utility of an object for hammering (Wagman & Carello, 2001). As V and S decrease and as ek increases, a given object becomes less controllable and less horizontally oriented (with the center of mass located further from the rotation point)— qualities that when proportioned properly may yield an object suitable to hammering (one should recall that a smaller V means that more force is required to rotate an object). These notions support the idea that tool users are sensitive to Drillis’s (1963) quantitative measure of hammer efficiency. According to his analysis, an efficient hammer is one in which the center of mass of the hammer is located as close as possible to the point at which contact is to be made. A general goal of designers may be to design a hammer such that it minimizes the force required by the user yet maximizes force generated by the strike. In other words, a good hammer may be one that tends to “hammer itself.”
Analysis of Surrogate Data It should be noted that in analysis of the grip position data, the inertial variables (V, S, and ek) were calculated relative to a rotation point in the wrist at the (mean) chosen grip position on a given rod. These grasp positions were then regressed onto the inertial properties of the rods at these grip positions (see above). Superficially, at least, this technique runs the risk of circularity because the predictor variables (V, S, and ek) are not a priori statistically independent from the criterion variable (grasp position). On the contrary, they are derived from the criterion variable. This creates the possibility that relationships uncovered by the
USER–TOOL INTERFACE
multiple regression are a function of these preexisting relationships and not a function of task constraints. To show that the relationships between grip position and inertial variables uncovered in Experiment 1 are genuine, we enlisted the technique of surrogate data analysis, a relatively common technique 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, researchers are concerned with showing that some statistical measure of a time series (e.g., complexity) is a function of the temporal contiguity of a time series and not a property of random variation in the signal. Thus, they create a surrogate data set in which temporal contiguity is destroyed but other properties (e.g., mean, standard deviation) are preserved. For example, randomizing the data points with respect to time destroys temporal structure while preserving other statistical features. If the same meaningful structure appears in the surrogate data set as in the original data set, it is assumed that such structure is due to something other than the temporal contiguity of the signal. Thus, there is reason to doubt that any structure revealed in the original data set is genuine. Essentially, such a result suggests 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 is genuine, one must show that the statistical properties of the surrogate data set are significantly different from those of the original data set (see Hausdorff et al., 1995; Thelier et al., 1992; Webber & Zbilut, 1994, 1996). Ideally, structure present in the initial time series will be absent in the surrogate data. Rather than being expected to reflect a time dependency, however, the data presented in Experiment 1 are expected to reflect a functional dependency (i.e., grasping for the function of hammering). We can destroy this relationship (between grip position and mass distribution) while preserving the essential statistical features of the data set by randomly pairing each of the (mean) chosen grip positions with a different rod. By doing so, we destroy the intentionality of the task and create surrogate pairings of grip positions and object. These surrogate grip positions have the same statistical properties as the original grip positions—they are, in fact, the same set of numbers. They have simply been randomly reassigned to a different rod. As in the analysis of the original data set, surrogate grip positions can be used to generate surrogate inertial variables that describe the mass distribution at that (surrogate) grip position. We can then apply multiple regression to analyze the relationship between the surrogate grip positions and the inertial variables at those grip positions. If meaningful statistical structure appears in the multiple regression analysis of the surrogate variables, such structure is assumed to 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 is genuine. In contrast to the original grasp positions, the surrogate grasp positions were relatively uncorrelated across participants. The mean r for the surrogate grip positions (on the basis of an r-to-z transform) was .01 (with raw correlations varying from ⫺.06 to .51). At the level of the mean grip position, the surrogate inertial variables did not constrain surrogate grip position (R2 ⫽ .30, ns). One should recall that in the analysis of the original data, V, S, and
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ek accounted for over 90% of the variance in grip position (see above). This difference is statistically significant at the level of individual participants (original R2 ⫽ 75.4%, surrogate R2 ⫽ 36.6%, t[7] ⫽ 8.6, p ⬍ .01). In the surrogate analysis, the fact that stepwise regression did not choose any of the surrogate variables suggests that the surrogate inertial variables are not significantly related to surrogate grip position. Destroying the functional relationship between grip position and task significantly compromises the explanatory power of the three inertial variables implicated in the analysis of the original data set (e.g., at the level of the mean data, it renders beta weights of all three regressor variables nonsignificant). This suggests that the inertial dependencies established at the grip positions in the original data set are genuine. More conservatively put, it suggests that they are not random. However, one may further question whether a set of objects with cylindrical symmetry would allow adequate variation in Ik for the inertial dependencies to be evaluated meaningfully. To demonstrate that sufficient variation was, in fact, possible, we relativized the inertial variables generated at the chosen grip positions on each object with respect to the maximum possible inertial values on that object. The values of the inertial variables at the mean chosen grip positions on each object were divided by their respective maximum values on each rod. These values were then averaged over the 12 objects and multiplied by 100 to obtain the mean percentage of V, S, and ek retained at the mean grasp position (see Table 2). These values suggest that in grasping so as to hammer, participants are minimizing S while maximizing ek. This is consistent with analysis of beta weights and standard errors, particularly the fact that the beta weights for S and ek variables are opposite in sign. These values are perhaps most informative only in comparison with the percentages from the other conditions (see Table 2). Figure 2 represents how changes in grip positions on each of the 12 objects simultaneously affect V, S, and ek. Each trajectory represents the possible variation among the variables V, S, and ek on each of the 12 rods (at all possible grip positions). Each symbol on a trajectory represents the mean chosen grasp position in a given condition in what amounts to VSe space. The fact that the symbols representing the chosen grip positions in the generic hammering task (gray circles) are located toward the right and toward the vertical peak of each trajectory is indicative of the fact that participants are grasping so as to maximize ek while minimizing S in this condition (see Figure 2).
Table 2 Percentage of V, S, and ek Retained on Average When Objects Were Grasped Under the Functional Constraints in Each of the Five Conditions Across the Three Experiments Condition
V
S
ek
Hammer precision Throw precision Hammer Hammer power Throw for power
86 85 74 73 62
57 54 31 30 17
78 82 94 94 (ns) 90 (ns)
Note.
V ⫽ volume; S ⫽ symmetry; ek ⫽ eigenvector angle.
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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 dependent on the properties of the objects themselves. Each trajectory represents the possible variation among the variables V, S, and ek on each of the 12 rods. They represent the simultaneous changes in these three variables at all possible grip positions. The upper end-point of each trajectory corresponds to the relationship among these variables when that object is grasped at the end designated as the bottom. The inflection point corresponds to the relationship among the same variables when that object is grasped at its center of mass. The lower end-point of each trajectory corresponds to the relationship among these variables when that object is grasped at the end designated as the top. The symbols indicate mean chosen grip positions on each object in each of the five conditions. The thickness of a given trajectory indicates where it sits along the Volume axis. Thinner trajectories are located further in depth from the viewer than thicker trajectories. Because trajectories for some objects overlap, fewer than 12 trajectories are visible.
Before proceeding, we should address the issue of alternative variables. We have been focusing on configurations of the mass distribution that have consequences for movement (Ik). Calculations of these quantities involve mass and center of mass (in particular, its distance from the rotation point). Not surprisingly, these component variables (as well as others such as static moment) are also strongly related to elected grasp position in Experiment 1. However, research has shown systematically (in experiments designed to disentangle the variety of components) that the influence of these variables is typically carried by the higher order inertial variables (i.e., Ik; see Fitzpatrick, Carello, & Turvey, 1994; Shockley, Carello, & Turvey, 2001, 2003; Solomon & Turvey, 1988; Stroop, Turvey, Fitzpatrick, & Carello, 2000). Moreover, the tensorial characterization has the advantage of providing a unified account of the perception of a wide variety of properties in a wide variety of circumstances. Intentions to perceive length, width, weight, and orientation all yield a dependence on Ik but with different, predictable parsings (see Carello & Turvey, 2000).
Furthermore, these dependencies do not depend on whether the object is being held vertically or horizontally or on whether it is being wielded quickly or slowly. Other accounts, in contrast, assume that perceivers use different strategies to perceive different properties or even different strategies to perceive the same property under different orientations (e.g., Kingma et al., 2002). For us, the latter approach is insufficiently constrained. The tensorial characterization, through its link to controlling movement, rationalizes the particular parsings that are revealed. It is expected that the different functional constraints under consideration here should be consistent with this characterization.
Experiment 2 The results of Experiment 1 suggest that in grasping an object to be used in a generic hammering task, the actor establishes a relation among a particular set of inertial variables (V, S, and ek) in a way that seems to reflect functional task constraints. In Experi-
USER–TOOL INTERFACE
ment 2, we compared the inertial consequences of chosen grip positions on objects to be used in a precision hammering task with those on the same objects to be used in a power hammering task. Because perceivers show sensitivity to ek in determining the appropriateness of a particular tool for a precision task (but not for a power task; Burton & McGowan, 1997; Wagman & Carello, 2001), we expected that perceivers would show sensitivity to ek in choice of grasp position in a precision tool-use task but not in a power tool-use task. That is, we expected that V, S, and ek would be required to account for a statistically significant portion of the variance in grip position in the precision task, but only V and S would be required to do so in the power task. We hypothesized that if perceivers do not show differential sensitivity to ek in choosing a grip position across tasks, then there will be no such differences across conditions.
Method Participants. Seven students at the University of Connecticut participated in this experiment. All were compensated $8 for their participation. Materials and apparatus. The objects used in Experiment 2 were the same objects used in Experiment 1 and are identified in Table 1. In addition, a large spike (25 cm long, 1 cm in diameter) partially embedded into 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 were used to provide the constraints on the hammering task in the power and precision conditions, respectively. Procedure. The procedure was the same as in Experiment 1 with the exception that a style of hammering was specified. Participants were asked to explore each object haptically, eventually choosing a grip position best suited to hammering the spike or the finishing nail. Grip position was reported and recorded as before. All participants completed both conditions in blocked fashion, and the order of conditions was counterbalanced across participants.
Results and Discussion As in Experiment 1, participants were reasonably consistent in their elected grasp positions. In both conditions, the responses of all pairings were significantly correlated with one another. In the power condition, the mean r (on the basis of an r-to-z transform) was .80 (with raw correlations varying from .22 to .93). In the precision 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 the log of the three inertial variables (V, S, and ek) accounted for 90% of the variance in log mean grip position (R2 ⫽ .90, p ⬍ .01). The fact that stepwise regression selected log V, then log S, and then log ek (adding each in a successive step) suggests that V is playing the largest role in choice of grasp position, followed by S and then ek. In the power condition, multiple regression revealed that log V and log S accounted for nearly 90% of the variance in log mean grip position (R2 ⫽ .88, p ⬍ .01). The influence of log ek was not significant in this condition. The fact that stepwise regression selected 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 grasp position and that the role of ek is minimal, at most. At the level of the individual participants, V, S, and ek accounted for between 34% and 88% of the variance in grip position in the power condition (on average 64%) and between 62% and 96% of
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the variance in grip position in the precision condition (on average 74%). Unlike in Experiment 1, a Friedman two-way ANOVA by ranks suggested that there were not consistent differences in the ordering of the beta weights across participants in either condition. In general, the patterning of beta weights and standard errors at the level of the individual participants are consistent with that of the mean data. Generally, in both conditions, the beta weights for both V 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 lowest amount of variance in Experiment 2, specifically in the power condition (R2 ⫽ .34, ns), tended to choke up (i.e., grasp closer to the top) on each object more than any other participant and showed an expanded range of grasp positions. These tendencies may have been detrimental to the functional specificity of grasp position in this condition. At the level of the mean data but less clearly at the level of the individual 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 generic hammer. In the current experiment, participants were asked to grasp so as to create specific hammers— ones that would be appropriate for precision and power tasks, respectively. In a power hammering task, participants grasped so as to regulate the forces required to control a given object as well as the directions in which those forces are required (as indexed by V and S, respectively). However, in a precision hammering task, participants grasped not only so as to regulate these relationships but also so as to regulate the perceived orientation of the object with respect to the hand (as indexed by ek). That is, behavior in Experiment 1 seems more comparable with behavior in the precision condition in the current experiment than with behavior in the power condition. An increased sensitivity to ek may allow for better control of the object tip in the precision task (Burton & McGowan, 1997; Wagman & Carello, 2001).
Analysis of Surrogate Data In Experiment 2, the surrogate grasp positions were again relatively uncorrelated across participants in each condition. The mean r for the surrogate grip positions in the power condition (on the basis of an r-to-z transform) was .02 (with raw correlations varying from ⫺.70 to .70). In the precision condition, the mean r (on the basis of an r-to-z transform) was .05 (with raw correlations varying from ⫺.36 to .54). Furthermore, the surrogate inertial variables did not constrain surrogate grip position in either the power condition (R2 ⫽ .33, ns) or in the precision condition (R2 ⫽ .56, ns). These differences are statistically significant at the level of the individual participants (in the precision condition: original R2 ⫽ 75.4%, surrogate R2 ⫽ 36.6%, t[6] ⫽ 3.5, p ⬍ .05; in the power condition: original R2 ⫽ 64.4%, surrogate R2 ⫽ 36.9%, t[6] ⫽ 8.6, p ⬍ .05). This fact, in combination with the fact that stepwise regression did not choose any of the surrogate variables in the power condition and chose only ek in the precision condition, suggests that (as in Experiment 1) the surrogate inertial variables are not significantly related to surrogate grip position. As in Experiment 1, we see important consequences of destroying the functional relationship between grip position and task. As in Experiment 1, this suggests that the inertial dependencies
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achieved at the grip positions described above are genuine (i.e., a function of task constraints). Using the method described in Experiment 1, we calculated the mean 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 is more strictly defined to emphasize its precision constraints over its power constraints, participants tend to grasp the object so as to maximize V and S while minimizing ek. This may serve to maximize the object’s controllability while serving to regulate the force transference capacity of the hand– object system such that it is appropriate for a precision task. These trends are apparent in Figure 2 in that the symbols representing the chosen grip position in hammering with power (black circles) and those representing hammering 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 object to be used as a hammer, tool users establish a relationship among V, S, and ek in a way that depends on the relative precision constraints of the hammering task. In Experiment 3, we compared the inertial consequences of chosen grip positions on objects to be used in other tasks that seem to share these same functional constraints. Specifically, we compared the inertial consequences of grasp position in a precision-throwing task with those in a powerthrowing task. We expected participants to show sensitivity to V, S, and ek in choice of grip position on objects to be used in a throwing task. We hypothesized that if perceivers are not sensitive to such variables in choice of grip position in such a task, these variables (either alone or in combination) will not constrain performance. Furthermore, because perceivers show sensitivity to ek in grasping a tool to be used in a precision-hammering task but not in a powerhammering task, we expected them to show the same sensitivity to ek in a precision-throwing task but not in a power-throwing task. That is, we expected that together, V, S, and ek would account for a statistically significant portion of the variance in grip position in the precision task, but only V and S would be required to do so in the power task. We hypothesized that if perceivers do not show differential sensitivity to ek across tasks, there will be no such differences across conditions.
Method Participants. Ten students at the University of Connecticut participated in this experiment. All were compensated $8 for their participation. Materials and apparatus. The objects used in Experiment 3 were the same 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 floor 1.5 m from the seated participant. Procedure. As in Experiments 1 and 2, participants were seated and handed rods one at a time by the experimenter. In the power condition, participants were asked to haptically explore each object, eventually choosing the position along its length at which they would grasp it if they were asked to throw it as far as possible. In the precision condition, participants were asked to haptically explore each object, eventually choosing the position along its length at which they would grasp it if they were asked to throw it so that it landed completely within the boundaries of the cloth circle. Grip position was reported and recorded as before. All participants
completed both conditions in blocked fashion, and the order of conditions was counterbalanced across participants.
Results and Discussion Participants were again reasonably consistent in their elected grasp positions. The mean r in the power condition (on the basis of an r-to-z transform) was .60 (with raw correlations varying from .06 to .89). In the precision condition, the mean r (on the basis of an r-to-z transform) was .59 (with raw correlations varying from ⫺.52 to .99). In the precision condition, multiple regression revealed that the log of the inertial variables (V, S, and ek) accounted for over 90% of the variance in log mean grip position (R2 ⫽ .94, p ⬍ .01). That stepwise regression selected log ek , log S, and then log V (in successive steps) highlights the enhanced role of ek in choice of grasp position in this task relative to its role in the task in Experiment 1. In the power condition, multiple regression revealed that log V and log S accounted for nearly 90% of the variance in log mean grip position (R2 ⫽ .89, p ⬍ .01). Log ek was not significant in this condition. That stepwise regression selected log V, then log S, but not log ek suggests that V is playing the largest role in choice of grasp position, followed by S but that ek does not play a significant role in choice of grasp position. At the level of the individual participants, these three variables accounted for between 2.5% and 88% of the variance in grip position for precision throwing (on average 36%) and between 10% and 92% of the variance in grip position for power throwing (on average 56%). A Friedman two-way ANOVA by ranks suggests that there are consistent differences in the ordering of the beta weights across participants in both conditions (precision: r2[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 or ek. The patterning of beta weights and standard errors was again consistent with the mean data in both conditions. Generally, in both conditions, beta weights for V and S were negative, and beta weights for ek were positive. However, V, S, and ek were generally not significant at the level of the individual participants. The participants for whom V, S, and ek accounted for the lowest amount 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 a compressed range of grip positions. As in Experiment 2, these variations may have been detrimental to the functional specificity of grasp position across objects. The cause of the discrepancy for these participants, however, is less straightforward. We can only speculate that these participants adopted a different style of throwing than did the other participants (e.g., underhand or sidearm as opposed to overhand). In Experiment 2, participants grasped the 12 objects so as to create specific hammers— ones that would be appropriate for a precision task and ones that would be appropriate for a power task. In doing so, they showed functionally specific sensitivity to higher order inertial properties. In the current experiment, participants were expected to grasp so as to create specific projectiles— ones that would be appropriate for a precision task and ones that would be appropriate for a power task. At the level of the mean data, but less clearly at the level of individual participant data, the patterning
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of the coefficients on V, S, and ek support our hypotheses. The lack of clarity may simply indicate that throwing is a less restricted task than hammering—throwers may have more options in how to pattern forces applied to the thrown object so as to accomplish the goal of the throwing task. Nonetheless, grasp positions for power and precision throwing were distinct from one another and paralleled distinctions in grasp positions for power and precision hammering.
Analysis of Surrogate Data As in Experiments 1 and 2, in Experiment 3 the surrogate grasp positions were again relatively uncorrelated across participants in each condition. The mean r for the surrogate grip positions in the power condition (on the basis of an r-to-z transform) was ⫺.01 (with raw correlations varying from ⫺.51 to .72). In the precision condition, the mean r (on the basis of an r-to-z transform) was ⫺.03 (with raw correlations varying from ⫺.46 to .44). The surrogate inertial variables accounted for only 20% of the variance in surrogate grip position in the power condition (R2 ⫽ .20, ns) and 27% of the variance in surrogate grip position in the precision condition (R2 ⫽ .27, ns). One should note that in analysis of the original data, V, S, and ek accounted for over 90% of the variance in grip position in throwing with precision, and V and S accounted for nearly same amount of variance in throwing with power. This difference is statistically significant at the level of the individual participants in the power condition (original R2 ⫽ 56.3%, surrogate R2 ⫽ 28.6%, t[9] ⫽ 3.7, p ⬍ .01) but not in the precision condition (original r2 ⫽ 36.5%, surrogate R2 ⫽ 42.4%, t[9] ⫽ ⫺.57, p ⫽ .58). Furthermore, stepwise regression on the surrogate variables did not choose any of variables in either condition. Using the method described in Experiments 1 and 2, we calculated the mean percentage that S and V are being retained from their maximum values when participants grasp objects in each condition in this experiment (see Table 2). When data from all three experiments are considered, we see a more convincing demonstration of the pattern that emerged in earlier analyses. As a task (regardless of whether it is a hammering task or a poking task) is more strictly defined to emphasize precision constraints over power constraints, participants grasp an object to be used in that task so as to maximize V and S while simultaneously minimizing ek. That is, they grasp the object so as to make it more controllable and less asymmetric. Conversely, as a task (regardless of whether it is a hammering task or a poking task) is more strictly defined to emphasize power constraints over precision constraints, participants grasp an object to be used in that task so as to minimize V and S without showing any regard for ek. That is, they grasp the object so as to make it more asymmetric and enhance the potential energy available just prior to the release. This is apparent in Figure 2 in that the symbols representing the chosen grip position in throwing with power (black squares) are located to the far right of each trajectory, whereas the symbols representing the chosen grip position in throwing with precision (white squares) are located to the far left (relatively speaking) of each trajectory.
General Discussion The inertial characteristics of an object make that object more or less functionally appropriate for a given task (Cochran & Riley,
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1986; Drillis, 1963; Drillis et al., 1963; Marras & Rockwell, 1986; Pagano & Turvey, 1998; Wagman & Carello, 2001). When the inertial properties of an object cannot be altered by adjusting or modifying the object itself (see Hart & Hart, 1994; Hart et al., 2001; Weir et al., 2002), perceivers–actors can modulate the inertial properties of the hand– object system by changing their grasp on 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 interface. In general, they were asked to exhibit prospective control of their behavior (cf. Turvey, 1992). Our goals in these experiments were twofold: (a) to uncover the inertial variables that constrain grip position in certain tasks and (b) to determine whether (and how) these variables reflect functional task constraints. Our expectations were that participants would grasp so as to minimize V in tasks that require power and maximize V while minimizing ek in tasks that require precision. In short, we expected to demonstrate that abstract assertions about the functional role of Iij are realizable in real-world behaviors.
Functional Specificity and User–Tool–Environment Interfaces The data suggest that when participants grasp objects so as to perform various functions with them, they show sensitivity to higher order inertial variables (V, S, and ek). These variables (or a subset of them) account for between 88% and 94% of the variance in mean chosen grasp position across the five tasks in the three experiments. Moreover, not only do participants seem to exploit the inertia tensor in choosing an appropriate grasp position on a given object, they show sensitivity to specific parsings of the tensor so as to grasp in a functionally specific manner. V and S play a role in choice of grasp position in all tasks. This is consistent with recent research that has focused on the relationship between the inertia tensor and controlling movement (Shockley et al., 2001; Turvey et al., 1999; Wagman & Carello, 2001). As noted, V and S are related to, respectively, the forces required to control a given object and the directions in which those forces are required. Presumably, all five tasks required regulating such aspects of the hand– object system to satisfy task demands. In addition to V and S, ek plays a role in constraining grip position in those tasks in which the (implicit or explicit) precision constraints seemingly outweigh the power constraints. Its contribution was apparent in a generic hammering task (Experiment 1), a precision hammering task (Experiment 2), and a precision throwing task (Experiment 3). Such a role for ek echoes that seen in research on perception of object orientation with respect to the hand (see Pagano & 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 a tool, participants establish relationships among the same inertial variables but in a way that reflects these specific task constraints. As the explicit or implied precision constraints of a task are emphasized, participants grasp so as to preserve V and S while simultaneously reducing ek (see Figure 2 and Table 2). Overall, these transformations of the mass distribution relative to the rotation point serve to enhance controllability of the hand– object system at the expense of the potential energy available prior to the hammer stroke or throw.
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When an object is grasped and wielded, time-varying forces produce time-varying motions of the object and the limb. The forces and motions are coupled by time-invariant parameters, of which, for present purposes, the most notable are the moments of the 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 the zeroth, first, and second moments. These moments are proportional to the forces needed to, respectively, hold the grasped object vertically still, hold it horizontally still, or wave it about in three dimensions. Typically, these three moments are correlated, and identifying their particular contributions to constraining perception requires objects specially designed to disentangle them. At present, that evidence seems to favor the second moment (e.g., compare Kingma et al., 2002, with Stroop, Turvey, Fitzpatrick, & Carello, 2000, and Shockley, Carello, & Turvey, 2001, 2003). We did not use such objects here, so the first moment would also serve to constrain grasp choices. But as noted earlier, the larger advantage of the second moment (and its derived scalars) that we tried to exploit in the present experiments is the systematicity of various parsings as they relate to particular properties. Perception of properties including length, width, heaviness, orientation, shape, grasp location, length in front of the grasp, and length behind the grasp are all constrained by the inertia tensor with different patterns of dependencies. It is unclear how the first moment could provide the same generality or richness.
Concluding Remarks: Structured Energy Arrays and Points of Observation It has been argued that stimulation rich enough to support complex behaviors (e.g., locomotion and tool use) can only be found in structured energy arrays (Gibson, 1966, 1979). Just as the optic array consists of differences in light intensities in different directions ambient to an observation point, the inertial array consists of different resistances to rotational acceleration in different directions ambient to a rotation point (Cooper, Carello, & Turvey, 2000). Just as changes in the point of observation open vistas in the optic array, changes in the point of rotation (of a hand-held object) open vistas in the inertial array. In both cases, such changes are accompanied by changes in the affordance structure available to an organism (see Benedikt, 1979; Gibson, 1979; Steenbergen et al., 1997). As soon as a perceiver–actor grasps an object (as soon as a user–tool interface is created), the dynamics of the prehensile system 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 emergent possibilities for action for the tool user (see Gibson, 1979; Steenbergen et al., 1997; van Leeuwen, Smitsman, & van Leeuwen, 1994; Wagman & Carello, 2001). The possibilities for action are a function of the mass distribution of the object relative to the rotation point (i.e., the wrist of the perceiver–actor). The user–tool interface is this relationship, and as we have demonstrated experimentally here, such an interface reflects many of the functional constraints 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 of grasp position on an object must accommodate not only the func-
tional constraints of the task but also these physical constraints. In some sense, the inertial properties inherent to the object set the initial conditions from which the perceiver–actor builds the user– tool– environment interface (see Figure 2). In grasping an object in a particular location, a tool user places additional limits on how that object can be moved. Before an object is grasped, it can become any one of a number of functional objects depending on how and where it is grasped. In grasping that object in a particular location, the tool user is selecting the functional object that seems appropriate given the task constraints. We have shown here that the higher order inertial variables that underlie haptic perception of object function (see Wagman & Carello, 2001) also underlie haptic creation of object function.
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Received July 18, 2002 Revision received May 14, 2003 Accepted May 15, 2003 䡲
