Scaling affordances for human reach actions

Human Movement Science 23 (2004) 785–806 www.elsevier.com/locate/humov

Scaling affordances for human reach actions Hyeg Joo Choi, Leonard S. Mark

*

Department of Psychology, Miami University, Oxford, OH 45056, USA Received 18 March 2004; revised 3 August 2004; accepted for publication 7 August 2004 Available online 13 October 2004

Abstract A methodology developed by Cesari and Newell [Cesari, P., & Newell, K. M. (1999). The scaling of human grip configuration. Journal of Experimental Psychology: Human Perception and Performance 25, 927–935; Cesari, P., & Newell, K. M. (2000). The body-scaling of grip configurations in children aged 6–12 years. Developmental Psychobiology 36, 301–310] was used to delineate the roles of an objectÕs weight (W) and distance (D) as well as the actorÕs strength (S) in determining the macroscopic action used to reach for the object. Participants reached for objects of five different weights placed at 10 distances. The findings of a single discriminant analysis revealed that when object weight is scaled in terms of each individualÕs strength and reach distance is scaled in terms of each individualÕs maximum-seated reach distance, a single discriminant analysis was able to predict 90% of the reach modes used by both men and women. The result of the discriminant analysis was used to construct a body-scaled equation, K = ln D + ln(W/S)/36, similar in form to the one derived by Cesari and Newell, accurately predicted the reach action used. Our findings indicate that Cesari and NewellÕs method can identify a complex relationship between geometric and dynamic constraints that determine the affordances for different reach actions.
2004 Elsevier B.V. All rights reserved. PSYCINFO classification: 2230; 2323 Keywords: Critical boundary; Affordances; Reaching; Dimensional analysis

*

Corresponding author. Tel.: +1 513 529 2417; fax: +1 513 529 2420. E-mail address: [email protected] (L.S. Mark).

0167-9457/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.humov.2004.08.004

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1. Introduction Reaching is a fundamental, goal-directed activity. Humans reach to pickup objects either as goals or as the means to attain a desired goal. People reach for objects that afford a myriad of possibilities for action, such as eating, drinking, writing, throwing, reading, etc. Such commonplace reach actions are not only essential to our daily existence, but are performed so seamlessly that people are unaware of just how often and on how many scales reaching takes place. But at the heart of every reach action is a scaling problem. Prospective actors have to perceive the existing arrangement of substances and surfaces in the environment relative to their own reach capabilities. Is an object close enough for a person to reach from her current seated position, or will the prospective actor have to stand up and, perhaps, locomote toward the target object? To reach successfully, actors must scale the distance of the object in terms of their effective reach actions, which are constrained by both geometric measures, notably aspects of their body scale (e.g., arm length) and biodynamic capabilities (e.g., strength, limb mobility and joint flexibility). When prospective actors scale reach distance with respect to their body scale, they are perceiving what James Gibson called an affordance (Gibson, 1979), a concept that was introduced to capture this intrinsic relationship between the personÕs action capabilities and relevant properties of the environment needed to support a particular action. The detection of the affordance for a particular mode of reaching entails perceiving whether the reach action will fit (can be performed successfully in) the existing layout of the environment. This means that prospective actors must be able to perceive critical reach distances, beyond which a particular reach action is no longer afforded and a transition to another reach mode must occur. This paper focuses on the critical boundaries between different modes of reaching and how those boundaries should be measured. Following WarrenÕs (1984) seminal study delineating the critical boundaries for the affordance of bipedal stair climbing, research on the location of critical reach boundaries has largely focused on the role of geometric constraints, specifically aspects of the actorÕs body size, in determining critical reach distance for specific reach actions. Carello, Grosofsky, Reichel, Solomon, and Turvey (1989; also Heft, 1992; Mark, Nemeth, Gardner, Dainoff, Paasche, Duffy, & Grandt, 1997) found that the critical boundary for a reach involving simple arm extension without any other body movement, what we will refer to as an arm-only reach, is a nearly invariant proportion of the actorÕs arm length. Beyond this critical boundary, actors must change to a reach action involving shoulder extension (arm-and-shoulder reach) or leaning forward (arm-and-torso reach) because an arm-only reach is no longer afforded. At a still farther distance, a seated reach is no longer afforded and actors will have to stand (standing reach) in order to pick up the object. Fig. 1 illustrates this taxonomy of reach actions developed by Gardner, Mark, Ward, and Edkins (2001). Mark et al. (1997) and Gardner et al. (2001) also examined how people actually reached when they were not constrained as to what type of reach action to use. Both studies reported that transitions between reach modes typically occurred at distances

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Fig. 1. The taxonomy of macroscopic reach actions developed by Gardner et al. (2001).

closer than the absolute critical boundary, that is, the distance beyond which a reach mode is no longer afforded. They referred to the location at which transitions actually occur as the preferred critical boundary. Gardner et al.Õs (2001) results also highlighted the importance of task constraints in determining the locations of critical boundaries. Mark et al.Õs (1997) findings emphasized the roles of postural dynamics and comfort of the reach action in determining the location of preferred critical reach boundaries. However, neither study attempted to incorporate non-geometric factors into a model of the affordance boundary for reaching. Thus, like most investigations of affordances, the focus of affordance research on reaching was on delineating critical boundaries that were measurable using a geometric dimension (distance). Biodynamic considerations were not incorporated either into the research design or models of the critical reach boundaries. The choice of actions studied using WarrenÕs (1984) affordance paradigm appeared to be limited to those situations in which geometric constraints were an overwhelming determinant of the critical boundary for the affordance. One reason for doing so may have been the ease with which dimensionless numbers or p-numbers could be produced by scaling environmental properties (e.g., surface height) in terms of geometric measures of the actorÕs body scale (e.g., leg length). Warren recognized the importance of incorporating biodynamic terms, such as strength, joint mobility, energy expenditure, etc., into a measure of the critical boundary and even demonstrated the relevance of energy efficiency for selecting a preferred climbable riser height. He argued that the principles of dimensional analysis, borrowed from physical biology, constitute a tool for modeling the fit of the actorÕs capabilities to the environment. Konczak, Meeuwsen, and Cress (1992) used a regression analysis to show that the perceived absolute critical boundary for bipedal climbing was constrained by the perceiverÕs leg strength and joint flexibility as well as leg length. However, neither of these investigations presented a specific model relating geometric and biodynamic constraints to the critical boundary for bipedal climbing. For this reason, Cesari and NewellÕs (1999, 2000) application of principles of dimensional analysis to delineate critical boundaries in grasping constitutes an important advance in the study of affordances. Cesari and Newell (1999) studied grip configurations used to pick up cubes of various lengths and masses (densities). In an earlier study Newell, Scully, Tennebaum, and Hardiman (1989) found that young children and adults used only a limited number of grips (2-finger, 3-finger, 4-finger, 5-finger, and 2-handed) in picking up objects

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of various sizes. Their investigation determined that as cube length increased, transitions between grip configurations occurred at particular (dimensionless) ratios of cube length to hand size. These ratios were nearly constant across their diverse group of participants. However, Newell et al.Õs (1989) analysis of critical boundaries was limited to geometric properties of the cube (length) and the actor (hand size). Cesari and Newell (1999) wanted to determine the location of these transitions between grip configurations when the cubes varied not only in size, i.e., length (L), but also in dynamic properties, mass (M) and density (ML
3). Their participants picked up 62 cubes of varying lengths and densities in random order using whatever grip configuration they wanted. Each cube was picked up 10 times, thus enabling the investigators to identify a preferred grip for each cube as the grip used on at least 80% of the trials. For each participant Cesari and Newell (1999) plotted the natural logarithms (ln) of the mass (Y-axis) and length (X-axis) of each cube using symbols that were specific to the preferred grip for that cube (see their fig. 2). They were then able to graphically fit a set of four parallel lines that demarcated the graph area into five regions, each of which corresponded to the locations of cubes that were grasped by one of the five grip configurations. These lines had a common slope of
9 for each of the five male participants and a slope of
6 for each of the five women. Cesari and Newell were able to write equations describing those straight lines for men : for women :

ln M ¼ b0
9 ln L; ln M ¼ b0
6 ln L;

ð1Þ ð2Þ

where M, refers to the cube mass, L, the cube length and b0 the y-intercept. Because each of the lines had a common slope, a constant, K, could be defined for men (Km = (b0/9)) and women (Kf = (b0/6)) such that K m ¼ ln L þ ðln M=9Þ;

ð3Þ

K f ¼ ln L þ ðln M=6Þ:

ð4Þ

It is important to appreciate three things about these equations: First, the obtained difference in slopes between men and women reflects anthropometric differences in their respective hand sizes and masses and differences in strength. Second, the constant, K, describes a relationship between cube length and mass that effectively constrains the grip configuration used to pick up a single cube. Eqs. (3) and (4) show that cube length contributes in total to K, whereas the effect of cube mass on K is modulated by the slope, which reflects differences of hand length and mass. The constant, K, organizes the grips used across the 62 cubes. When Cesari and Newell plotted grip configuration as a function of the value of K for each of the cubes (their fig. 4), with a few exceptions the transitions between grip configurations occurred at specific values of K. Cesari and Newell also reported that these transition values of K were nearly identical for both men and women. (See their fig. 5.) Third, the power of these equations for predicting grip configuration rests on the assumption that the lines separating the grip configurations are parallel.

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Cesari and Newell obtained empirical confirmation from their discriminant analyses that the slopes were nearly identical. By assuming that the slopes were identical, Cesari and Newell were able to derive the constants for men (Km = (b0/9)) and women (Kf = (b0/6)) from which Eqs. (3) and (4) were constructed. To be sure, there is nothing in their method, per se, or in conventional dimensional analysis that would require the slopes to be parallel. However, by making this assumption powerful equations could be derived that could predict the grip configuration used on almost 90% of all trials. (Our analysis of reaching is grounded on the same assumption.) In a follow up study of the development of prehension, Cesari and Newell (2000) presented a general equation that captured both the geometric and biodynamic constraints on prehension independently of the actorÕs sex K ¼ ln Lo þ ððln M o Þ=ða þ bM h þ cLh ÞÞ;

ð5Þ

where Lo and Mo are the length and mass of the object, Lh and Mh are the length and mass of the hand, and a, b, and c are empirically obtained constants. Unlike Eqs. (3) and (4), Eq. (5) is applicable to all individuals – women and men, children and adults. Thus, borrowing the tool of dimensional analysis from the domain of physical biology, Cesari and Newell (1999, 2000; see also 2002) devised a method for delimiting the critical boundaries associated with affordances. What was responsible for the difference in slopes between men and women in Cesari and NewellÕs fig. 2? In their discussion Cesari and Newell noted that the ratio of the obtained slopes, 9:6, roughly corresponded to ratios of reported strength measures for males and females (Holloway, 1994). They suggested that the scaling differences between men and women, as reflected by the slopes in their fig. 2, were likely due to differences in participantsÕ hand size and strength, rather than their sex. Cesari and Newell (1999) did not measure the strength of their participants. As a result, their analyses were presented by sex of participants, thereby requiring separate equations for men and women that differed in terms of their slopes. However, Cesari and Newell did measure the hand length for each of the participants and they estimated hand mass. They plotted these measures on a single graph (their fig. 3). This revealed a marked gap between men and women on both dimensions. Using the measures of hand mass, Cesari and Newell (1999) might have rescaled the cube mass with respect to each participantÕs hand mass, thereby creating an intrinsic measure of cube mass. Had they replotted their fig. 2a and b on a single graph using intrinsically scaled masses for each participant, the resultant plot would have been difficult to interpret as well as see the grip regions demarcated by the fitted lines because of the density of the target objects in the space. An alternate strategy that they might have tried (one that we will use in presenting our reach data) would have been to use the mean hand masses for men and women to intrinsically rescale the cube masses. Although we are unsure about the units Cesari and Newell used to express hand mass on the ordinate of their fig. 3, the measured hand mass for the women appears to be roughly 50% of that for the men. If their fig. 2 is instrinsically rescaled using such a transformation, the slopes for the men and women would have been more similar.

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Before focusing on our application of Cesari and NewellÕs work to our investigation of reaching, we offer a final observation about their fig. 2. Cesari and Newell chose to express the relevant properties of their cubes in terms of cube length (abscissa) and cube mass (ordinate). However, the quantity of matter of each cube, its mass, is not the crucial dynamic property of the object needed to guide action. Rather, it is the objectÕs weight, that is, the force by which the earth attracts the object toward its center. To pick up an object, the prospective actor has to generate sufficient forces with her or his muscles in order to lift the target object off of the surface of support. Force is related to mass through gravitational acceleration: Force = mass * gravitational acceleration. Thus, Cesari and Newell might have expressed cube mass as a force. (For reference, 1 lb = 453.59 g [mass] = 455 dynes [force] = 4.55 N [force]). Doing so would not have changed the essential outcome demonstrated by their fig. 2 or the overall structure of Eqs. (1)–(4). However, the use of force on the ordinate makes the relationship between cube mass and the actorÕs strength easier to discern. More importantly, expressing mass in terms of the inertial forces opens up the possibility of scaling object mass with respect to the actorÕs strength, that is, the potential for generating forces. With respect to our investigation of critical reach boundaries, Cesari and NewellÕs (1999, 2000) work establishes a methodology for examining how the target objectÕs dynamic properties, such as mass or weight, as well as geometric properties, such as distance, affect the type of reach action used. We report here our attempt to use this method to delineate critical reach boundaries that takes both reach distance and object weight into account. In doing so, we attempted to construct an affordance space (analogous to the one depicted in Cesari and NewellÕs fig. 2) in which both reach distance and object weight (expressed as a force) were measured intrinsically, that is, with respect to each participantÕs reach capabilities and strength. Participants reached for objects of five different weights, each placed at 10 distances scaled in terms of each participantÕs maximum-seated (arm-and-torso) reach. (We chose not to use extrinsically scaled distances to avoid the possibility of having either very big or small participants for whom our range of distances would not include their critical boundary. Had we tried to prevent this by increasing the number of distances, the number of trials would have become excessive. As is, the experiment, though a bit monotonous for the participant, was exhausting for the experimenters who stood for almost 90 min, during which they had to concentrate on placing the object at the proper distance.) Beginning from a seated posture, they reached for and picked up the object in whatever manner they chose. The target objects were plastic containers that were grasped using a 5-finger grip. A measure of participantsÕ strength was also obtained by having them perform an isometric pull on a handle connected to a strain gauge. This strength measure enabled us to scale the target objectÕs weight (expressed in terms of force) in terms of each participantsÕ strength. Thus, we obtained intrinsic measures of each objectÕs weight and distance for each participant. When the reach modes used are plotted in a space defined by intrinsic measures of weight and distance, we expect to see a common slope for men and women.

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2. Method 2.1. Participants Six men and six women undergraduates participated in this experiment as part of a course requirement. The mean total standing height was 179 cm for the men and 164 cm for the women. All participants were right handed as indicated by their handedness preference for writing and throwing. They were treated in accordance with the ethical standards of the American Psychological Association. 2.2. Equipment Participants sat on a Roc-n-Soc LSG drum throne (Waynesville, NC) with a 5-point base, a screw-type height adjustment mechanism adjustable from 44 to 61 cm, a padded ‘‘motorcycle saddle’’ style seat, and a small backrest. There were no armrests. This chair was chosen because the saddle-shaped seat pan did not unduly restrict participants from standing up if they felt this action was necessary in order to reach an object. The chair was set in front of a motorized workstation whose worksurface height (measured from the floor) was adjustable in the range of 74–117 cm. A video camera recorded the actions from the participantÕs right side. A reflective, 3-cm spherical marker was attached to each participantÕs right shoulder (acromion). Another marker was mounted on a small horizontal rod that was then attached to the left shoulder. These markers facilitated the process of classifying reaches when coders viewed the videotapes. Participants reached for five different 8.89 · 8.89 · 3.81-cm plastic containers that were filled with various materials such that the following masses were obtained: 80, 430, 920, 1648 and 3640 g. The corresponding measures of force are: 0.80, 4.31, 9.22, 16.51 and 36.48 N. ParticipantÕs strength was measured using the force transducer module of a PHY-400 Physiometer (Premed, Oslo, Norway) controlled by a battery operated microcomputer with a 10 channel A/D converter. The force transducer (Maywood Instruments, Ltd, Basingstoke, England) had a range of 1–100 kg. One side of the force transducer was attached to a metal chain that was connected to a wooden board that the participants stood on. The other side of the transducer was attached to a handle that participants pulled on using their right hand. The length of the chain could be adjusted so that participants could grasp the handle when standing upright with their right arm at their side. 2.3. Procedure Participants were told that we were interested in how our perception of the world guides our actions. In this particular experiment, we were interested in how the distance of objects affects the way in which people go about reaching for them. After

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explaining to participants about their rights as a subject in this experiment and receiving their permission to be videotaped, the following anthropometric measurements were made: total standing height, standing eyeheight, seated shoulder height, popliteal height, total arm length (to tip of the thumb) and lower arm length. These measures permitted us to set the seatpan height to 105% of each personÕs popliteal height and the table height to a level that was halfway between seatpan height and shoulder height. The horizontal distance of the center of the chairÕs backrest to the table edge was set to 75% of the total arm length. After positioning the chair and table, we determined the participantÕs absolute critical boundary for a seated reach. The participant was handed an empty container and instructed to place it on the table surface as far as possible in the plane of their right shoulder. The participant was told to remain seated and not to stand up or slide forward. The experimenter then moved the container 2-cm farther away and asked the participant to pick up the object (again without standing or sliding forward). This continued until we determined the farthest distance that the participant could pick up the object. This distance became the participantÕs absolute critical boundary and was used to determine the other distances at which the containers would be placed. Participants were then instructed that a container would be placed at various distances in front of them. Their task was to ‘‘reach for the object in whatever manner you find most comfortable or natural’’. They were told to use their right hand to grasp the object and use a five-finger grip in which the thumb and fingers were placed on the sides of the object. The containers were placed at 10 distances, 0.50, 0.60, 0.070, 0.75, 0.80, 0.85, 0.90, 0.95, 1.00, 1.10, measured in units of each participantÕs absolute critical boundary for a seated reach. The object was placed in front of the participant in the plane of his or her right shoulder. Each participant performed 10 reaches for each combination of weight and distance, thus reaching for a total of 500 trials. The trials were blocked by weight of the object. The five weights were presented in a different random order for each participant. Prior to beginning with a new weight, participants were permitted to heft the object. We permitted participants to take short breaks as they saw fit. The entire testing session lasted about 90 min. The reach actions were videotaped so that the reach actions used on each trial could be classified into one of the three reach actions noted above. Strength measure. After the reach actions were completed, we obtained a measure of each participantÕs strength by having them perform an isometric pull using the Physiometer. The apparatus was placed on the floor. Participants were told to stand on the board such that they could grasp the handle comfortably with their right arm hanging straight down at their side. The length of the chain to which the handle and force transducer was attached was adjusted so that the handle could be grasped without the participant having to bend at the waist or knees. When the equipment was adjusted, the experimenter instructed participants to pull as hard as they could on the handle for roughly 1 s. The peak force measured by the load cell was recorded by the microcomputer. Participants performed this pull five times. The highest recording was taken as the participantÕs strength measure.

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2.4. Analysis of the videotapes and determination of the preferred reach mode Each videotape was reviewed by two judges who independently classified each reach as either an arm-and-shoulder, arm-and-torso, or standing reach. For those reaches for which the raters disagreed (<3% of the trials), they discussed the reasons for their decisions and attempted to arrive at an agreement. On those occasions where the raters could not agree (<0.1%), a third member of the team was consulted. Criteria for classifying reaches. The judges categorized each reach action into one of three categories: arm-and-shoulder reach, arm-and-torso reach and standing reach. There were no cases where a participant used an arm-only reach. This is a consequence of the reach distances that we chose. An arm-and-shoulder reach involves a rotation of the torso around the spine. This was evident when the actorÕs right shoulder was extended forward and the marker placed behind the left shoulder moved backward. To be counted as an arm-and-shoulder reach, the actor had to maintain contact with the backrest of the chair throughout the course of the reach. An arm-and-torso reach consisted of any reach in which the participant leaned forward such that (a) both shoulders moved forward and (b) all or part of the participantÕs back lost contact with the backrest. Often the judges could see the chairÕs backrest move forward as the actor leaned toward the target. Finally, any reach in which the participantÕs thighs and legs lost contact with the seat pan was classified as a standing reach. Standing reaches included both partial standing reaches in which the actorÕs legs remained bent throughout the course of the reach as well as fullstanding reaches in which the actorÕs legs were nearly straight, i.e., the ‘‘knees were locked’’. We did not distinguish between full and partial standing reaches because we expected from previous work (Gardner et al., 2001) that there would be very few fullstanding reaches at the distances used in this study. Thus, we are focusing on two critical reach boundaries: the transition between arm-and-shoulder and arm-andtorso reaches and the transition between arm-and-torso and standing reaches. Determination of preferred reach mode. For each participant, the preferred reach mode for each of the 50 reach distance/target weight combinations was established as the reach mode used on at least 80% of the trials. Across the 12 participants, there were only 16 distance/weight combinations (out of 600 total) for which the most frequently used reach mode was used less than 80% of the time (all of those were 70%). To simplify our analysis, we classified those distance/weight combinations on the basis of the most frequently used reach mode.

3. Results and discussion The relative contributions of object distance and weight for predicting the reach mode were evaluated using both the statistical method of discriminant analysis and the qualitative method of dimensional analysis from physical biology. First, we examined object distance and weight each expressed in units extrinsic to the actor, i.e., meters and Newtons respectively. A second group of analyses maintained the extrinsic measure of weight, while substituting an intrinsic measure of distance,

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i.e., scaled with respect to each actorÕs maximum-seated reach (absolute critical boundary). In our third set of analyses both distance and weight were expressed in units intrinsic to each actor, with weight being expressed in terms of a measure of each actorÕs strength. As part of each set of discriminant analyses, separate analyses were conducted on the data for each individual, the composite data for all participants of a given sex (i.e., the data for all men were combined into a single analysis and the same was done for womenÕs data) and the combined data for both sexes. Our discriminant analyses employed the cross-validation method using the leaveone-out option in SPSS. The percentages of correct classifications allowed us to determine the accuracy with which group membership could be predicted using a classification function. In this procedure functions are calculated from all cases ruling out one case and then classifying the ruled out case. This method repeats the same process N (number cases) times such that all cases have been left out once and classified based on the function developed by N
1 cases. The correct percentages obtained from this cross-validation method are slightly lower than obtained simply by counting the misclassified cases. At the same time, it is more conservative and provides a reasonable estimation of how well the classification functions derived on all N cases will predict for a new sample. The overall WilksÕ lambdas calculated for each of the discriminant analyses reported were significant, p < 0.01, indicating that the predictors effectively differentiated among the three reach modes. 3.1. Analyses based on extrinsic measures of reach distance and object weight Two discriminant analyses were conducted on the data for each individual participant. One discriminant analysis used extrinsic measures of reach distance and object weight as predictor variables and reach mode (arm-and-shoulder, arm-and-torso, standing reach) as the discriminant variable. The second analysis used the natural logarithms (ln) of extrinsic measures of reach distance and object weight as predictor variables. Another pair of discriminant analyses was performed on the composite data for each sex. A final discriminant analysis combined the data for both sexes. Individual analyses. Table 1 (column 2) shows the percentage of correct predictions for each of the 12 participants. For both discriminant analyses (untransformed and logarithmic transformed measures), the reach mode for each weight–distance combination could be predicted with a mean accuracy that was less than 85% for women and 83% for men. The level of accuracy did not exceed 90% for any participant. (Because the logarithmically transformed data predicted a slightly higher percentage of reach modes used, the remaining analyses were performed on those data.) Composite analyses for each sex. We conducted a pair of discriminant analyses – the first using the combined data for men and another using the combined data for the women. Table 1 shows that the percentages of correct predictions of reach mode used for the men and women were 68% and 73%, respectively. These mean percentages for each sex were decidedly lower than those for individual participants, reflect-

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Table 1 Summary of discriminant analyses performed on the natural logarithms of extrinsic measures of object weight (W) and distance (D) (columns 2 and 3), extrinsic measures of weight and intrinsic measures of distance (columns 4 and 5) and intrinsic measure of object weight and distance (columns 6 and 7) Subject no.

W (extrinsic), D (extrinsic)

W (extrinsic), D (intrinsic)

W (intrinsic), D (intrinsic)

Ln W, Ln D

Slope

Ln W, Ln D

Slope

Ln (W/S), Ln D

Slope

Women 1 2 3 4 5 6 Composite

80 84 74 90 82 82 68


23
24
29
27
29
30
27

94 90 92 94 90 94 96


27
23
23
27
32
29
26

94 90 92 94 90 94 96


34
28
30
34
46
35
34

Men 7 8 9 10 11 12 Composite

88 84 84 86 78 74 73


35
39
38
45
31
40
38

96 92 92 94 90 86 94


31
39
37
61
25
36
35

96 92 92 94 90 86 94


39
51
48
94
32
48
46

For each analysis the left column shows the percentage of correct predictions of reach mode for each subject and the combined data (composite) for each sex. The slope refers to lines that divide the ln distance–ln weight space into regions corresponding to the three reach modes.

ing the variability introduced by the different metric distances for each participant. From the separate discriminant analyses for men and women (Table 1, column 3), we determined the equation for the line that best separated one reach mode from another by deriving coefficients for ln reach distance and ln weight. In each discriminant analysis the slopes of the two lines separating the three reach modes were negative and nearly identical in magnitude, i.e., the lines were nearly parallel. However, there were different slopes for the men and women: The means for the men and women were
38 and
27, respectively, t(10) = 3.58, p < 0.01. Overall, these findings mirror those reported by Cesari and Newell (1999) in their analysis of grip configuration. We did not, however, construct a graphical representation of these data similar to Cesari and NewellÕs (1999) fig. 2 because the distances used in this study were intrinsic to each participantÕs maximum-seated reach and the resulting picture would depict an uninterpretable cloud of points representing different reach modes superimposed on top of one another. Combined data for men and women. A final discriminant analysis was performed on the combined data for men and women. The resultant function predicted less than 53% of the reach modes used, indicating that a single discriminant function did a poor job in predicting the reach modes used for both men and women.

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We can observe from our discriminant analyses that our extrinsic measures of object distance and weight did not provide an adequate basis for predicting the reach mode used. This finding stands in contrast to Cesari and NewellÕs (1999) analysis of cube length and mass in extrinsic units; they found such extrinsic measures predicted close to 90% of the grip configurations used. The relatively poor predictive power revealed in this analysis of reaching may be related to variability in relevant aspects of the actorsÕ body scale. For prehension, Cesari and Newell identified a single dimension, hand size, as relevant to grip transitions. However, for the transition between seated and standing reaching, several body dimensions are involved, including arm length and seated shoulder height (the distance between the seat pan and the shoulder, which determines how far forward a person can lean). These dimensions are only very loosely correlated (Pheasant, 1986). As a result, at a given distance, different actors may use different reach modes depending on their particular body dimensions. We now examine whether this variability can be minimized by intrinsically scaling reach distance in terms of each participantÕs maximum-seated reach. 3.2. Analyses using an intrinsic measure of reach distance and an extrinsic measure of object weight Individual analyses. These discriminant analyses used an extrinsic measure of weight and the intrinsic measure of reach distance. They were performed on each participantÕs data to determine the contributions of weight and reach distance for predicting reach mode: The first discriminant analysis used reach distance and object weight as predictor variables and reach mode (arm-and-shoulder, arm-and-torso, standing reach) as the discriminant variable. The second analysis used the natural logarithms (ln) of reach distance and object weight as predictor variables. Because the analysis using the logarithms of weight and length resulted in slightly higher levels of accuracy, especially for the women, the remaining data analyses will use the natural logarithms of weight and length. This decision is consistent with Cesari and NewellÕs (1999) prehension results as well as typical scaling functions for human performance (e.g., McMahon & Bonner, 1983). Table 1 (column 4) shows the percentage of correct predictions for each of the 12 participants. The discriminant analyses showed that the reach mode for each object weight–distance combination could be predicted with a level of accuracy that exceeded 90% for 11 of the 12 participants. Composite analyses for each sex. Discriminant analyses were also conducted on the combined data for each sex using the natural logarithm of object distance and weight. The composite measure in Table 1 (column 4) shows that the percentage of correct predictions for each sex exceeded 94%. A t-test comparing the individual slopes for men (Mean =
35) and women (Mean =
26) (Table 1, column 5) approached the 0.05 level of significance, t(10) = 2.15, p = 0.06. Thus, there is still reason to believe that the slopes for men and women are different. Separate discriminant analyses were also conducted in which the ln distance was considered separately from the ln weight in order to evaluate their relative contributions to determining reach mode. The ln of distance predicted close to 88% of the

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reach modes for both men and women. In contrast ln weight accounted for 56% of the reach modes for women and 50% for men. Object distance, then, appears to be a more important determinant of reach mode than object weight. Combined data for men and women. A final discriminant analysis was conducted on the combined data for men and women. The resulting function predicted 88% of the reach modes used by the 12 participants. The common slope was
31. These findings indicate that a single discriminant function could make accurate predictions of the reach modes used by both men and women. The result is noteworthy because the percentage of correct predictions for both men and women was higher than the percentages reported by Cesari and Newell (1999) for their individual participants. Fig. 2a and b show plots of the natural logarithm of reach distance (abscissa) with respect to the natural logarithm of object weight (ordinate) for men and women.

Men 4.0 ln Weight

3.0 2.0 1.0 0.0 -1.0 3.7

3.9

4.1

4.3

4.5

4.7

Arm-and-Torso

Standing

4.9

ln Distance Arm-and-Shoulder

(a)

Women 4.0 ln Weight

3.0 2.0 1.0 0.0 -1.0 3.7

3.9

4.1

4.3

4.5

4.7

4.9

ln Distance

(b)

Arm-and-Shoulder

Arm-and-Torso

Standing

Fig. 2. The preferred macroscopic reach mode for each combination of reach distance and object weight. Reach distance is expressed in intrinsic units of the percentage of the absolute critical boundary for seated (arm-and-torso) reaches. Object weight is expressed in extrinsic units of force, Newtons. Both axes show the natural logarithms of these measures. Parallel lines obtained from a discriminant analysis were fit to demarcate regions in which each reach mode was preferred. Fig. 2a (top) and 2b (bottom) show the data obtained for men (slope =
37) and women (slope =
26) respectively.

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Reach distance is expressed in intrinsic units corresponding to the maximum-seated reach distance. Object weight is expressed in extrinsic units of Newtons. The symbol representing each distance–weight combination indicates the reach mode used on the majority of trials. For all but four weight–distance combinations this reach mode was used on at least 80% of the trials. We used the slopes generated by our discriminant analysis on the composite data to fit separate transition lines for men and women that demarcated the boundaries between the three reach modes. The discriminant analysis revealed that the transition lines had nearly identical negative slopes. As a result, we felt justified in constraining the slopes of the transition lines to be parallel as Cesari and Newell had done. The slope of the transition line between arm-and-torso and standing reaches appeared more constrained than the line between arm-and-shoulder and arm-andtorso reaches; for this reason, we fit the latter transition line to match the slope of the boundary between arm-and-torso and standing reaches (cf. Cesari & Newell, 1999). Dimensional analysis. Using the composite slopes for men and women obtained from the discriminant analyses, we were able to write a pair of equations describing the lines obtained in Fig. 2a and b for men :

ln W ¼ b0
35 ln D

for women :

compare to Eq: (1);

ln W ¼ b0
26 ln D

compare to Eq: (2);

ð6Þ ð7Þ

where b0 refers to the y-intercept, D to reach distance and W to the weight of the target object. Because each of the lines had a common slope, we could then define constants for men (Km = (b0/35)) and women (Kw = (b0/26)) such that K m ¼ ln D þ ðln W =35Þ compare to Eq: (3);

ð8Þ

K f ¼ ln D þ ðln W =26Þ

ð9Þ

compare to Eq: (4):

Given that reach distance was measured using an intrinsic scale, at least part of the difference in the slopes between men and women might be the result of strength differences between men and women. Fig. 3a and b show the reach mode used as a function of K for men and women. As with Cesari and NewellÕs grip data (cf. their fig. 4), Fig. 3 shows that for both men and women, critical values of K mark the transitions between reach modes. Fig. 4 indicates that for each transition between reach modes, the critical values of K at the transition were nearly identical for men and women (cf. Cesari and NewellÕs Fig. 6). The difference in K between the individual men and women did not approach the 0.05 level of significance for either transition, F(1, 10) = 2.35, p > .3. Also, the two transitions were marked by different values of K. (A statistical test was unnecessary because there was no overlap in the distributions.) K, then, represents an invariant relationship between distance and weight that determines the reach mode used across diverse participants. We are still left with a difference in the slopes between the men and women (Fig. 2a and b). At least part of these differences may reflect the relative strength of men

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Men

Reach Mode

Standing Arm-and-Torso

Arm-and-Shoulder

3.0

3.5

(a)

4.0

4.5

5.0

4.5

5.0

K = ln D + ((ln W) / 35)) Women

Reach Mode

Standing Arm-and-Torso

Arm-and-Shoulder

3.0

3.5

4.0 K = ln D + ((ln W) / 26)

(b)

Fig. 3. Preferred reach modes as a function of K (Eqs. (8) and (9)) for men (a, top) and women (b, bottom). (cf. Cesari and NewellÕs fig. 4.)

K= ln D+ ((lnW)/h)

5.0

Men Women

4.5

4.0

3.5

3.0 Arm-and-Shoulder to Arm-and-Torso

Arm-and-Torso to Standing

Reach Transition

Fig. 4. The value of K at each transition between reach modes for men and women. The error bars delimit the 95% confidence interval for each value of K. (cf. Cesari and NewellÕs fig. 5.)

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and women. For women, the transition between reach actions occurred at lower weights than for men. Because Fig. 2 depicts the weight of the target object in units extrinsic to the actors, i.e. Newtons, differences in the transition slopes for men and women might be reduced if for each person, the objectÕs weight was rescaled with respect to a measure of his or her strength. 3.3. Analyses using intrinsic measures of distance and strength The strength measure was determined as the highest reading obtained from the force transducer on the five trials. The mean (and standard deviation) strength measure for the women, 111 N (7 N), was 58% of that for the men, 189 N (6 N). Other studies (Holloway, 1994; Laubach, 1976) have reported strength measures for women that are roughly 55–65% of those for men. We used the single highest reading as a measure of each participantÕs strength, rather than an average of the five trials, because most participantsÕ first ‘‘pull’’ or two was decidedly lower than the remaining ‘‘pulls’’. Had we chosen an average of, say, the last three ‘‘pulls’’, we would have obtained slightly lower means, 103 and 184 N for the women and men respectively; however, the ratio of the mean strength measures for women and men would have been 0.56, which was close to the ratio of 0.58 reported using the maximum pull. Thus, we are confidence that the intrinsically rescaled measures of object weight was not affected by our decision to use the maximum pull, rather than some average. There was a large within-subject variation in the five trials used to determine each participantÕs strength measure. Several participants remarked that it took them a few trials to become comfortable making the required movement. For this reason, we decided not to rescale the object weight with respective each individualÕs strength. Rather, we took the average strength for each sex and used that strength measure to rescale each object weight for that sex. (Doing so also made it possible to present the results on two graphs, one for each sex.) Dividing the objectÕs weight by the mean strength for that sex created the intrinsic measure of weight. Because both component measures are in units of Newtons, the resultant intrinsic measure of strength is dimensionless, just like the measure of object distance we have been using. Individual analyses. We conducted a series of discriminant analyses comparable to those performed on the intrinsic measure of weight and intrinsic measure of distance. Table 1 (column 6) shows that for each participant, the discriminant function was able to predict more than 90% of the reach modes used for 11 of the 12 participants, with an average of 92%. Composite analyses for each sex. The separate discriminant analyses conducted on the composite data for men and women predicted 94% and 96%, respectively, of the reach modes used. The slopes of the discriminant functions for the composite data for men and women were
46 and
34, respectively. A t-test conducted on the individual slopes for men and women did not reach the 0.05 level of significance, t(10) = 1.87, p = 0.09. Fig. 5a and b depict the resulting discriminant functions for men and women when both object weight and distance are scaled intrinsically. The slope differences between men and women shown in Fig. 5a and b must be interepreted cautiously: On the one hand, the difference in slopes did not reach the

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Men -1.0

ln(W/S)

-2.0 -3.0 -4.0 -5.0 -6.0 3.7

3.9

4.1

4.3

4.5

4.7

4.9

ln Distance (a)

Arm-and-Shoulder

Arm-and-Torso

Standing

Women -1.0

ln (W/S)

-2.0 -3.0 -4.0 -5.0 -6.0 3.7

3.9

4.1

4.3

4.5

4.7

4.9

ln Distance (b)

Arm-and-Shoulder

Arm-and-Torso

Standing

Fig. 5. The preferred macroscopic reach mode for each combination of reach distance and object weight. Reach distance is expressed intrinsically in terms of the absolute critical boundary for seated (arm-andtorso) reaches. Object weight, however, is also expressed in intrinsic units of the mean strength for men (a, top) and women (b, bottom). Both axes show the natural logarithms of these measures. Parallel lines obtained from the discriminant analysis were drawn to demarcate regions in which each reach mode was preferred. Figures a (top) and b (bottom) show the data obtained for men (slope =
46) and women (slope =
34), respectively.

0.05 level of significance. Also, the observed differences in the absolute magnitude of the slopes are not particularly striking because a slight change in either transition line might have resulted in identical slopes. Still, we are inclined to believe that the slopes are not identical because of the likelihood that the reach mode used could be affected by determinants other than object weight and distance. In surveying the overall differences between men and women, we note that women tended to change reach modes at closer distances and at lower weights. While strength differences probably affected the locations of the transitions between reach modes, our experience over the course of 10 years of reaching research with men and women indicates that there may be subtle differences in their responses to the instructions to ‘‘reach in whatever manner you find most comfortable or natural’’. Women tend to avoid extreme

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movements (arm extension, lean) by changing to another reach mode; this strategy allows them to avoid postures that might be uncomfortable or awkward. Men, on the other hand, tend to try to minimize their overall body movement. They often avoid introducing other parts of the body until it is absolutely necessary. This strategy increases the likelihood of making extreme movements. Factors other than distance, object weight and strength may also be determinants of reach mode. Joint flexibility and how far someone can lean forward, for instance, likely affect critical boundaries. In addition, our measure of participantsÕ strength was not ideal for assessing strength because different muscles were involved in performing our strength measure and in picking up an object from a seated posture. Each of these factors might contribute to an explanation for why the slopes for men and women were not identical. Combined data for men and women. In spite of these problems, our strength measure contributed to a single discriminant model that was able to predict in excess of 91% of the reach modes used, with a common slope of
36. Fig. 6 shows a plot the discriminant functions for these combined data on a single graph. The slopes for the lines marking the boundaries between reach modes were obtained from the discriminant analysis. The fact that a single graph could be produced with a common slope for the transition lines indicates that this space reveals geometric and dynamic relationships that are common to men and women. Fig. 6 captures how an objectÕs distance and weight constrain the reach action used across both men and women. In effect, Fig. 6 depicts an affordance space that describes constraints on the macro-

Men and Women -1.0

ln (W/S)

-2.0 -3.0 -4.0 -5.0 -6.0 3.8

4.0

4.2

4.4

4.6

4.8

ln Distance Men Arm-and-shoulder Men Standing Women Arm-and-Torso

Men Arm-and-Torso Women Arm-and-Shoulder Women Standing

Fig. 6. The preferred macroscopic reach mode for each reach distance–object–weight combination for both men (filled symbols) and women (unfilled symbols). Reach distance is expressed intrinsically in terms of the absolute critical boundary for seated (arm-and-torso) reaches. Object weight is also expressed in intrinsic units of the mean strength for men and women. Both axes show the natural logarithms of these measures. Parallel lines (slope =
35) obtained from the discriminant analysis were drawn to demarcate regions in which each reach mode was preferred.

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803

Men

K= log D + (log (W/S) / 36)

Women 4.5

4.0

3.5

3.0 Arm-and-Shoulder to Arm-and-Torso

Arm-and-Torso to Standing

Reach Transition

Fig. 7. The value of K at each transition between reach modes for men and women. The error bars delimit the 95% confidence interval for each value of K. The transitions occur at similar values of K for men and women.

scopic reach action that people will likely use when more than one reach action is afforded. Because the slopes of the transition lines from the rescaled data are quite similar, we tentatively offer a general equation of the transition lines (in Fig. 6) separating the reach modes that is roughly applicable to both men and women lnðW =SÞ ¼ b0
36 ln D:

ð10Þ

Similarly, K ¼ ln D þ ½lnðW =SÞ=36:

ð11Þ

Eqs. (10) and (11) are similar to Eqs. (1), (2) and (5) obtained by Cesari and Newell (1999, 2000). However, unlike Cesari and NewellÕs equations, Eq. (11) does not contain a term for the reacherÕs body (e.g., arm length) comparable to hand size in prehension. The reason Eq. (11) does not need such a term is that throughout our investigation of reaching, we have scaled reach distance using an intrinsic measure of each actorÕs maximum-seated reach (also Gardner et al., 2001). We can use Eq. (11) to calculate a value of K for each distance–weight combination. Fig. 7 shows that the transitions between reach modes again occur at common values of K for both men and women, F(1, 10) = 1.78, p > 0.4. In addition, the two transitions each occur at different values of K. (A statistical test was unnecessary because there was no overlap in the distributions.) 4. General discussion A number of previous studies of affordances have identified invariant relationships between the actorÕs body scale and metric properties of the environment needed

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to support the actorÕs capabilities (e.g., Carello et al., 1989; Mark & Vogele, 1987; Newell et al., 1989). However, the critical boundaries for various action capabilities are also constrained by biodynamic influences (Konczak et al., 1992; Warren, 1984). The act of stair climbing, for example, is constrained not only by the actorÕs leg length (Warren, 1984; also Mark & Vogele, 1987), but also his or her strength and flexibility (Cesari, Formenti, & Olivato, 2003; Konczak et al., 1992), characteristics on which men and women differ and that change with age and physical conditioning. Similarly, reaching and prehension are constrained not only by the distance or size of the goal object, but also by its dynamic properties (weight) as well as the actorÕs strength. The challenge facing investigators of affordances is to develop methods that can capture the relationship between these geometric and biodynamic constraints on the actorÕs capabilities. The current investigation has shown that Cesari and NewellÕs methodology can be adapted to investigate visually guided reaching. We are confident that other goal-directed actions can be examined as well. The similarity of Eqs. (10) and (11) from our investigation of reaching to Eqs. (1)–(5) taken from Cesari and NewellÕs study of prehension provides further encouragement as to the generality of their method. Thus, we believe that Cesari and NewellÕs use of dimensional analysis provides a means for capturing both biodynamic and geometric constraints on affordances and the capabilities of prospective actors. The graphical plots of grip configurations and reach modes (Figs. 2, 5, and 6) reveal important characteristics of affordances, specifically the underlying lawfulness of their geometric and biodynamic determinants. Each graph reveals relationships between size or distance and mass or weight that are invariant across a diverse group of people. These relationships are integral determinants of the macroscopic form of the action. Figs. 5 and 6 advance Cesari and NewellÕs methodology. By rescaling the objectÕs weight in terms of actorsÕ strength, we created a graphical plot of our reach data that has a pair of dimensionless axes; that is, the units of distance and weight are scaled with respect to the actorÕs body scale and strength. The finding that a single discriminant function (Fig. 6) can predict in excess of 90% of the reach modes used indicates that we have created a space that is applicable to both men and women. The significance of Fig. 6 lies in that it depicts relationships between the actorÕs strength and the objectÕs distance and weight that govern the actor-environment relationship inherent to affordance of reaching. The transition lines do not establish absolute critical boundaries for specific reach modes because participants were able to reach in whatever manner they chose. (The same is true for Cesari and NewellÕs prehension data because their participants were free to use whatever grip they wanted.) We learn about what macroscopic reach actions people use when more than one such action is afforded. Thus, Cesari and NewellÕs methodology provides a tool for identifying the constraints that determine the macroscopic actions that a diverse group of people will use under a variety of circumstances. Finally, this method has applications to problems in ergonomics involving the construction of reach envelopes that might be used to establish workplace standards for creating safe and efficient working areas (Dainoff, Mark, & Gardner, 1999). The concept of normal working area refers to an optimal work zone. Geometric models of

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the normal working area have been derived from analyses of theoretical arm-hand movements (e.g., Farley, 1955; Squires, 1959; Wang, Das, & Sengupta, 1999). Because these movements were highly contrived and restrictive, it is unclear how the resulting boundaries relate to conditions under which there are no restrictions on how people are to reach. The approach guiding the current investigation transforms the working area problem from an overly simplified geometric problem to one involving dynamic and geometric determinants. Our use of Cesari and NewellÕs methodology establishes a paradigm for collecting and analyzing data to construct performance-based workspace regions in which people are able to reach comfortably and efficiently (Choi, Mark, Dainoff, & Harvey, 2003).

Acknowledgments This research was supported by a grant to LSM by the Miami University Committee for Faculty Research. Eric Cicak, Mary Fay, Brent Scott, and Mary Beth Scott assisted in the collection of these data. The authors express their appreciation to two anonymous reviewers for their comments. Correspondences should be directed to Leonard S. Mark, [email protected].

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