Journal of Experimental Psychology: Human Perception and Performance 1991, Vol. 17. No. 2, 315-322 Copyright 1991 by the American Psychological Association, Inc. 0096-1523/91/$3.00 Grasping Tau G. J. P. Savelsbergh H. T. A. Whiting Faculty of H u m a n Movement Sciences, Free University Amsterdam, The Netherlands University of York, Heslington, York, England R. J. Bootsma Faculty of Human Movement Sciences, Free University, Amsterdam, The Netherlands In the present study a direct manipulation of the optical expansion pattern was carded out. What happens to the timing of the grasp movements involved in catching a ball when optical expansion information is not veridically provided? By using 2 luminescent balls of constant size and a luminescent ball that could change its diameter during flight, it was possible to manipulate the rate of optical expansion directly. The results of 2 experiments (binocular vision in Experiment l and monocular vision in Experiment 2) showed that the time of the maximal closing velocity of the hand--which conforms to the prediction if Ss use retinal expansion information--was later for the deflating ball than for the balls of constant size. Adjustments to the aperture of the hand in response to the different ball sizes, especially the adjustment of the hand to the deflating ball (even though Ss were not aware that the ball was deflating during its approach), point to a finely attuned perception-action coupling. Schiff, Caviness, and Gibson (1962) demonstrated that an optically expanding shadow on a white screen resulted in defensive reactions in diverse species of animals (apes, crabs, and chickens; see also Schiff, 1965). Later, Bower, Broughton, and Moore (1970) reported similar effects in 10-day-old babies when a solid object was made to approach them, giving rise to optical expansion--the "looming" effect. Schiff and Detweiler (1979) extended the scope of these earlier studies by using a filmed, animated approach of a black form. Subjects were told that at a particular stage of its trajectory the approaching object would disappear. Subjects were required to indicate (by pressing a button) when they thought the object would have reached them had it continued on the same trajectory. Several background manipulations were introduced to provide enhanced distance or distance-change information. None of the background manipulations used was found to influence the accuracy of judgments in relation to the two-dimensional blank terrain. On the basis of these findings, Schiffand Detweiler (1979) concluded that observers can and do use two-dimensional time-to-contact information to estimate impact time. With respect to the latter study, however, it has to be stressed that the task given to subjects was that of a perceptual judgment alone, because they were not required to carry out actions more complex than pressing a button. In addition, because of the early curtailment of the projection, no information on the last 2 s of the moving object's trajectory was available to subjects. To set the stage for our experiments, it is necessary to comment further on two important issues stemming from the experiment of Schiff and Detweiler (1979). First, we discuss the use of a button-pressing response. Obtaining accurate information about visual timing on the basis of button-pressing responses was recently questioned by Bootsma (1988, 1989). In his study, subjects were required (a) to strike with a table tennis bat and a squash ball dropped along a fixed path, (b) to release an artificial arm to hit a similar ball, and (c) to press a button when the ball reached the point of contact. All three actions were carded out under similar optic flow patterns. The results indicated that the variability of the moment of initiation was considerably larger under the button-pressing condition than under the artificialarm condition, which again was larger than that under the natural-arm condition. The more the required action was separated from a natural perception-action coupling, the less precise the timing response was found to be; this finding is corroborated by the results of McLeod, McLaughlin, and Nimmo-Smith (1986). Second, we discuss the absence of information in the last 2 s of approach of an expanding optical form (also the case in the McLeod & Ross, 1983, study). Such information might be very important in those tasks such as catching a ball in which subjects have to carry out an action to actually intercept an approaching object. This is confirmed in Alderson, D. L. Sully, and H. G. Sully's (1974) analysis of ball catching, in which the grasp phase of the catching action (a timing problem) occurs some 40 ms prior to contact. In the same vein, an even more valid paradigm (in the sense that more than one velocity was studied) was provided by Lee, Young, Reddish, Lough, and Clayton (1983) in their investigation of visual timing in hitting an accelerating ball. The experimental design (a falling football that had to be punched away) was such that to perform the subactions involved (e.g., extension of knee and elbow) information occurring in approximately the last 250 ms of ball flight had to be used. The results were consistent with subjects' use of visual information occurring in the last 50-135 ms. Experiment 1 is motivated both by the limitations of the aforementioned experiments and the necessity to clarify fur- Correspondence concerning this article should be addressed to G. J. P. Savelsbergh, Faculteit der Bewegingswetenschappen, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands. 315 316 G.J.P. SAVELSBERGH, H. T. A. WHITING, AND R. J. BOOTSMA ther the confounding explanations for the explanatory value of direct versus indirect theories of perception. In a similar type of study, albeit one that used a computer simulation methodology, Todd (198 l) demonstrated that subjects could reliably discriminate arrival times of objects of different sizes starting from different positions with different velocities directly on the basis of two-dimensional information. At about the same time that Schiff was extending his work (Schiff & Detweiler, 1979) on optical expansion, Lee (1976, 1980) demonstrated that the inverse of the relative dilation rate of an approaching object--an optical variable that he denoted by tau--constituted a first-order two-dimensional source of information that specified the time to contact. In the ensuing years, Lee and his co-workers sought to confirm the efficacy of the time-to-contact variable in a series of diverse and elegant studies. Thus, Lee and Reddish (1981) showed how such a variable might be used to explain the timing of diving gannets' folding their wings. Lee, Lishman, and Thomson (1982) followed up this study by demonstrating the efficacy of a similar control parameter in regulating gait during the run-up phase of the long jump, whereas Warren showed the role of this optical variable in the visual control of step length during running over irregular terrain (Warren, Young, & Lee, 1986). Lee et al. (1983) reported on the sequencing of behavior involved in jumping up to punch a falling ball, which provided further evidence for the explanatory power of the optical variable tau. More recently, Bootsma (1988; Bootsma & van Wieringen, 1990) invoked a similar explanation in the control of directed striking of a table tennis ball, and Sidaway and his co-workers (Sidaway, McNitt-Gray, & Davis, 1989) demonstrated that preparatory muscle activation prior to impact landing from different heights is triggered at a specific tau margin. For the regulation of gait in horses' jumping of obstacles, Laurent, Dinh Phung, and Ripoll (1989) demonstrated that the retinal expansion pattern of the obstacle is used by the riders. The studies addressed here provide a catalog of evidence in support of the explanatory power of a direct-perception explanation of control of timing in a variety of ecologically appropriate skills. They constitute a challenge to classical information-processing explanations, which suggest that such actions as those reported here are driven by "a complex predictive system which takes into account any available information about the ball's current position, velocity, acceleration, rate of change of acceleration and so on" (Lee & Young, 1985). Such a complex system, as Lee and Young suggest, would entail unnecessary delays in using the information as well as oversensitivity to noise and is thus unlikely to have evolved. A better system, they suggest, is robust rather than overly refined and takes advantage of the most reliable and rapidly available information--to them the inverse of the relative rate of optical expansion. Although the logic of Lee and Young's argument is fairy convincing and the evidence they produce is rather compelling, it has to be pointed out that no one has directly manipulated the optical expansion pattern while evaluating the consequences in terms of the delayed/accelerated initiation of patterns of action. Computer simulation (Todd, 1981) and discrimination studies (e.g., Schiff& Detweiler, 1979) are not sufficient to evaluate the proposed continuous coupling of perception and action in, for example, the task of catching (Lee & Young, 1985). By the same token, demonstrating that the timing of movement sequences is compatible with the use of the optical variable tau (Lee & Reddish, 1981; Lee et al., 1983) is not sufficient to prove that the relative rate of dilation is responsible for such timing, because the expansion pattern has never been experimentally manipulated. Though we agree that the circumstantial evidence resulting from the aforementioned studies is convincing, the direct demonstration of Lee's proposed perception-action coupling in catching is still awaited; Experiment 1 set out to accomplish this. More specifically, it attempts to provide an answer to the following question: What happens to the timing of the grasp movements involved in catching an approaching ball when optical expansion information is not veridically provided? In an attempt to answer this question, we used a paradigm that, with a repeated measures design, compares the behavior of subjects who were required to catch three types of approaching balls (a small ball, a larger ball, and a ball that decreased in size as it approached). ~ If subjects do indeed gear their catching actions to time-to-contact information derived from the relative expansion pattern of the ball, two important predictions can be made. First, the adjustments of the hand aperture ought to be tuned accurately to the changing ball size (including the deflating ball). Second, the time of appearance of the fingers' maximal closing velocity ought to be later for the deflating ball than for the other two ball sizes. Experiment 1 Method Subjects Subjects were 10 undergraduate women 19-26 years of age who reported normal or corrected-to-normal vision and who were naive to the purpose of the experiment. Subjects were paid for their participation. Apparatus Three balls with different diameters were used as catching objects. Two of these were relatively foam-plastic balls 5.5 cm and 7.5 cm in diameter, respectively, that were enclosed in a tight-fitting balloon painted with luminous paint. A third ball could be made to change its diameter from 7.5 cm to 5.5 cm during flight. This was achieved by using a luminous balloon that enclosed another relatively rigid foam-plastic ball 5.5 cm in diameter. This ball could be inflated to a 7.5-cm diameter prior to release and allowed to deflate during its trajectory until it formed a tight "skin" around the enclosed ball at the moment it arrived at a subject's hand. For each trial, one of these luminescent balls was fastened to the end of an aluminum pendulum 3.92 m in length that was hinged to a point on the ceiling of the laboratory. When raised from its resting ' The idea of using an inflating or shrinking ball in time-to contact research was put forth by Beck (1986). GRASPING TAU position, the pendulum could be held in its new position by an electromagnet. The horizontal distance between the magnet and a subject's hand was 2.48 m, which resulted in a speed of 2.4 m/s. A subject sat in a chair with her right arm secured to a black metal armrest, which left the catching hand free. The armrest was fixed to the table and could be adjusted to the length of the lower arm (see Figure 1). A multi-infrared light-emitting diode (LED) control unit (Den Brinker, Krol, & Zevering, 1985) consisting of an Apple II+ microcomputer coupled to a Selcom 413-3 camera was available for data registration. With this system, we could register the position of four infrared light sources (LEDs) fixed to the lower end of the pendulum, the first thumb phalanx, and the first finger phalanx of the right hand. The position signal was sampled with a frequency of 200 Hz. To control the viewing period, subjects wore liquid crystal spectacles,2 which could be made to change from opaque to clear by an electric signal generated as the pendulum was released by the electromagnet. The rise and decay times for the crystals were less than 4 ms. The spectacles remained clear for a period of 2 s and became opaque again following a signal generated at the moment the ball reached a subject's hand. The experiment was carried out in a totally dark room. Optical Expansion of the Deflating Balloon To establish that the deflating balloon resulted in a pattern of optical expansion different from a ball of constant physical size, we recorded ball flights by means of a video camera with the lens situated at eye level. Analysis of the two-dimensional expansion pattern on the monitor screen was carried out with a video position analyzer (VPA 1000) that allowed the diameter of the ball to be measured frame by frame (40 ms) during its approach. The expansion patterns of the deflating ball (B) and a ball of constant size (A) are shown in Figure 2. This analysis confirms that the deflating ball would result in a different optical expansion pattern than would a ball of constant physical size. Procedure To familiarize subjects with the equipment, the experimenter released the pendulum five times. This was followed by 50 experimental trials in the totally dark room. Between each trial the room 317 1200 A 1000 800 ' ¢0 •~ 600 - IZ I~. X nl 400 - 200 ' 0 = -1500 -1000 , -500 0 "rime betore contact (ms) Figure 2. The relative expansion pattern (on a video screen) of a ball of constant size (A) and the deflating ball (B). light went on to "load" the luminescent paint. During this time the spectacles remained opaque. The two rigid balls were each used 20 times and the deflating ball was used 10 times in an order randomized over trials. Subjects wore white-noise headphones to prevent anticipation resulting from any sound from the deflating ball(oon). Data Analys& The position data were filtered with a recursive second-order Butterworth filter with a cutoff frequency of 8 Hz. The filter was applied twice to negate the phase shift. Dependent Variables We used two criteria in selecting the dependent variables for analysis of the grasping action. First was the need to check whether the manipulation of ball size (large and small) conformed with predictions made on the basis of grasping studies (Jeannerod, 1981, 1984; Marteniuk, Mackenzie, & Leavitt, 1990; Von Hofsten & Ronnqvist, 1988). For this purpose, the following dependent variables were chosen: maximal aperture of the hand, moment of occurrence of the maximal aperture in time, movement time of the grasping component, aperture of the hand at the moment of catch, and maximal closing velocity of the hand. The second criterion was the need to select variables that might be sensitive to changes brought about by the deflating ball and hence to provide information relevant to the predictions made at the end of the introduction. The following dependent variables were selected for this purpose: time of appearance of the maximal closing velocity and the size of the aperture of the hand. Description of Dependent Variables Figure 1. The position of the LEDs on the hand and on the pendulum and attachment of the balls to the pendulum. (The horizontal distance between the hinge of the pendulum and a subject's hand was 1.12 m; the hand was fixated in an armrest. A subject's head was virtually in line with the catching hand and the approaching ball.) Time of initiation of the grasp. This variable denotes the time between the release of the pendulum by the magnet (spectacles become clear) and the initiation of the grasp (defined as the moment of maximal opening of the hand). Movement time. This variable denotes the elapsed time between the initiation of the grasp and the moment of ball-hand contact (catch). 2 We are grateful to the National Aerospace Laboratory NLR, Amsterdam, for the loan of the liquid crystal spectacles. 318 G.J.P. SAVELSBERGH, H. T. A. WHITING, AND R. J. BOOTSMA Table 1 Means and Standard Deviations for the Dependent Variables (Experiment 1) Ball Dependent variable Time of initiation of the grasp SD Movement time SD Time of eatch SD Maximal dosing velocity SD Large Small Deflating 1,575 68 1,580 65 1,585 67 140 51 154 48 153 51 1,716 39 1,738 36 1,739 36 -37 18 -48 15 -50 16 Time of maximal closing velocity -41 -42 -36 10 11 14 Note. Values for maximal closing velocity are in centimeters per second. All other values are in milliseconds. The large ball was 7.5 cm in diameter; the small ball was 5.5 cm in diameter. The deflating ball changed from 7.5 to 5.5 cm in diameter. The significant difference in the "time of catch" is because the large ball, by virtue of its greater diameter, reached the hand earlier than the small ball. Minus signs indicate that the appearance of the time of maximal closing velocity is before ball-hand contact. vs. deflating) analysis of variance (ANOVA) carried out for the means and standard deviations of each of the dependent variables, with a repeated measures design on the last variable. We found a significant main effect for the means of the ball-size variable for the following dependent variables: time of catch, F(2, 18) = 24.94, p < .001; maximal closing velocity, F(2, 18) = 12.46, p < .001. A 6% significance level occurred in movement time, F(2, 18) = 3.24, p = .06, and time of maximal closing velocity, F(2, 18) = 3.25, p = .06. For the standard deviation, only the time of maximal closing velocity reached a 5% significance level, F(2, 18) --- 3.50, p = .05. With respect to the hand aperture, we found a significant effect at the moment of initiation, F(2, 18) = 21.15, p < .001; maximal closing velocity, F(2, 18) = 26.73, p < .001; and time of catch, F(2, 18) -- 22.19, p < .001. We found no significant effects for the standard deviations. Post hoc Newman-Keuls analyses indicated a number of significant differences. SD Maximal closing velocity. This variable denotes the maximal closing velocity of the hand. Time of appearance of maximal closing velocity. (Maximal) aperture of the hand. This variable denotes the (maximal) distance between the LEDs on the thumb phalanx and the finger phalanx. Results The results are reported in Tables 1 and 2 together with the results of a separate three-variable (ball size: large vs. small Table 2 Means and Standard Deviations of Hand Aperture at Different Times Ball Hand aperture time Initiation SD Maximal closing velocity SD Time of eatch Large 8.84 0.71 Small 8.33 0.74 Deflating 8.80 0.71 7.38 0.80 6.30 0.68 6.60 0.76 6.22 4.68 5.00 1.1 1.0 1.1 Note. All values are in centimeters. The large ball was 7.5 cm in diameter; the small ball was 5.5 cm in diameter. The deflating ball changed from 7.5 to 5.5 cm in diameter. SD Differences Between Large and Small Balls We found no significant differences between the intraindividual standard deviations on any of the variables. Significant differences were apparent between the mean scores of the large ball and the small ball for several dependent variables. The small ball showed a smaller maximal hand aperture, a longer movement time, a smaller hand opening at the time of catch, and a higher maximal closing velocity than the large ball (all p < .05). The larger hand aperture for the large ball was in accordance with a number of recent findings in the literature on reaching and grasping movements (e.g., see Jeannerod, 1981; Von Hofsten & Ronnqvist, 1988). As in Von Hofsten and Ronnqvist's (1988) experiment, the difference in hand aperture for the small and large balls was much less than the difference in size of the two balls. The shorter movement time for the large ball is a reflection of the shorter closing distance the fingers needed to cover for the large ball than for the small ball. Similarly, the significantly higher maximal closing velocity for the small ball confirms the logical predictions. The higher velocity and longer movement time for the small ball are complementary consequences of the greater distance the fingers have to travel to catch the small ball. The differences in hand opening at the moment of catch and at the moment of maximal closing velocity reflect differences in the size of the balls and confirm other reported findings of adjustments to hand movement in relation to the particular size of objects (Jeannerod, 1981; Von Hofsten & Ronnqvist, 1988). The fact that the hand aperture is larger than needed indicates a strategy proposed by Wing, Turton, and Fraser (1986; see also Wallace, Weeks, & Kelso, 1990): Adults opened their hand more when a fast reach rather than a slow reach was carried out to a static object. The results meet the expectations stemming from the findings in the literature. They give confidence that there was nothing untoward in the paradigm we used, and at the same time they provide the baselines for the deviations to be reported when a deflating ball is used. GRASPING TAU Differences Between the Deflating Ball and Balls of Constant Size Significant differences were found between the deflating ball and the large ball on the mean scores of several dependent variables. In relation to the data obtained for the large ball, the deflating-ball condition resulted in a longer movement time, a smaller hand aperture at the moment of catch, a higher maximal closing velocity, and a later appearance of the maximal closing velocity (all ps < .05). In accordance with the discussion of the results of the differences between the large and the small ball, these findings confirm that the deflating ball is treated as a ball that is smaller than the large ballminformation that is not available until it is actually under way. A perceptually noticeable difference in its rate of optical expansion leads to an adjustment in the action pattern. The longer movement time and higher maximal closing velocity reflect (as was the case with the small ball) the longer distance that is involved in catching the deflating ball. We found no statistically significant differences in hand-aperture size between the deflating ball and the small ball at the moment of catch. On other dependent variables, however, the significant differences found between the deflating ball and the small ball indicate that the two balls were not treated alike during the earlier parts of their trajectories. The maximal hand aperture for the deflating ball was significantly larger than for the small ball and statistically similar to the maximal hand aperture under the large-ball condition. In agreement with Jeannerod's findings (1981, 1984), we found no differences in the time of appearance of the maximal hand aperture. This finding suggests that subjects probably decide early on the aperture size necessary for a successful catch and allow a sufficient tolerance band for the different ball sizes. We found no differences in standard deviations for either of the dependent variables, which indicates that subjects used a consistent strategy in this respect. The most important finding in the context of the predictions made is the later appearance of the time of maximal closing velocity for the deflating ball in comparison to the other balls. The later appearance of this dependent variable indicated that the deflating ball and the consequent less relative retinal expansion (as opposed to an approaching ball of constant physical size) resulted in an adjustment to the timing of the grasp. When the hand apertures (see Table 2) at the time of initiation, at the moment just before the catch, and at the moment of the actual catch are compared, adjustments to accommodate the differing sizes of all three balls is apparent. We found a significant difference between the deflating-ball and the small-ball conditionsmbut not between the deflatingball and the large-ball conditions--at the moment of initiation. We found significant differences between all balls at the moment of maximal closing velocity, and we found a significant difference between the deflating-ball and the large-ball conditionsmbut not between the deflating-ball and the smallball conditions--at the moment of catch. Figure 3a shows the mean maximal aperture over the last 200 ms, confirming this statement. These findings indicate that adjustments to the 319 hand aperture were still being made up to the last moment before ball-hand contact. In this respect the visuomotor delay time is interesting. By plotting the standard deviation of the hand aperture over the last 200 ms, we get an indication of the visuomotor delay times involved. The interesting statistic in this respect is the point of minimal variance. As Figure 3b indicates, a visuomotor delay time of about 100 ms before ball-hand contact seems to be the case for all ball sizes. This result is in agreement with the findings of other researchers (Bootsma & van Wieringen, 1990; Lee et al., 1983). Discussion Although the results provided here confirm our predictions (made in the introduction) on the basis of subjects' use of time-to-contact information directly specified by optical expansion of the ball, this is not categorical proof that subjects do use such information. The nagging doubt remains that the use of two eyes provides other sources of information that might be used equally well (or additionally). For example, in .-. 8 E P ,,.= 7 L 6 "0 C m 5' 4 -22O | -180 i -140 i0 -1 0 i -60 i -20 20 Time before contact (ms) 1.3 A E 0 b 1.2' 1.1 0 O3 "0 e,, 1.0 L S //// ¢"~ 0.9- B J~ 0.8- a 0.70.6 -220 ! -180 i -140 ! -100 i -60 i -20 20 Time before contact (ms) Figure3. (a) Adjustments to the mean aperture of the hand for the large ball (L), the small ball (S), and the deflating ball (B) in the last 200 ms in Experiment I (sampling 200 Hz); (b) the standard deviation for all three ball sizes in the last 200 ms in Experiment 1 (sampling 200 Hz). 320 G.J.P. SAVELSBERGH, H. T. A. WHITING, AND R. J. BOOTSMA a series of experiments Jones and Lee (1981) showed that performance with binocular vision is superior to performance with monocular vision in a variety ofvisuomotor tasks. When vision with two eyes is provided, an image of the bail is projected on both retinas. The distance between these two images increases when the ball approaches and decreases when the ball goes away, thus providing subjects with a potential source of distance information (Regan, 1986). In principle, therefore, it is possible for catchers to compute time to contact on the basis of this distance information and estimated velocity (the velocity in all trials was the same, which could lead to some experience effect). To obviate this alternative indirect explanation, we need to run a second experiment in which this binocular source of information is removed, that is, in which subjects are required to perform monocularly. Under the latter condition, time to contact specified by optical expansion is still available, and thus the same predictions as for the binocular condition of Experiment 1 apply. Table 3 Subjects" Judgments With Respect to the Kind of Ball Used in the ControlAspect of Experiment 2 (n = 5) Trial Subject 1 2 3 4 5 Large ball Large Large Large Large Large Small ball Small Small Small Small Small Deflating ball(oon) Small Small Small Large Small Large ball Large Large Large Large Large Ball(oon) not deflating Large Large Large Large Large were almost totally in agreement (only Subject 4 referred to the deflating ball as large; the other subjects referred to it as small). None of the subjects referred to the peculiar behavior of the deflating ball. When the bail(oon) was not deflating, all subjects recognized it as a large ball, and when it was deflating (with the exception of Subject 4), they recognized it as a small ball. Experiment 2 Time of Appearance of Maximal Closing Velocity The second experiment was a replication of the methodology used in Experiment 1, with the binocular condition being replaced by a monocular condition. Method Subjects Subjects were 5 undergraduate women 19-24 years of age who reported normal or corrected-to-normal vision and who were naive to the purpose of the experiment. None of the subjects participated in the first experiment; they were paid for their participation here. Apparatus, Dependent Variables, Data Collections, Data Analyses, and Procedure These were the same as in Experiment 1. Only one change was made with respect to the liquid crystal spectacles: To control monocular vision, the spectacles were made to change from opaque to clear for one eye by an electrical signal generated as the pendulum was released by the electromagnet. Subjects underwent 50 trials: 25 in which the ball was seen by the left eye only, and 25 in which (10 with the large ball, 10 with the small ball, and 5 with the deflating ball) the ball was seen by the right eye only. We introduced an additional control into this experiment to check the accuracy of subjects' statements (in Experiment l) that they were not aware of the deflating bail. To this end, subjects were asked after the experiment to make visual judgments about the balls without making a catching attempt. Five trials were conducted: large ball, small ball, deflating ball(oon), large ball, and ball(oon) not deflating. Results Visual Judgment About Balls The control aspect of Experiment 2 produced the data presented in Table 3. As can be seen, subjects' judgments The results for this dependent variable are reported in Table 4. Again, we found differences between the deflating ball and the balls of constant size. The time of appearance of the maximal closing velocity for the deflating ball was later than for the small and large bails. A two-variable (eyes: left vs. right) by three-variable (ball sizes: large vs. small vs. deflating ball) ANOVA with repeated measures on the last two variables showed a main effect for ball size, F(2, 8) = 7.47, p < .015. Newman-Keuls post hoc comparisons showed significant differences between the deflating ball and the two other bails but not between the large bail and the small bail (ps < .05). No significant main effects were found for the eyes' variable, and there were no significant interactions. Adjustment of the Hand Aperture Figure 4a shows the hand adjustments for the last 200 ms. As in Experiment 1, we found the fine tuning of the hand aperture to the ball size. Figure 4b shows the differences in hand aperture between the large ball and the deflating ball Table 4 Means and Standard Deviationsfor the Time of Appearance of the Maximal Closing Velocityfor the Left Eye and the Right Eye and for All Ball Sizes Ball Vision Right eye Left eye Total Large -49.9 -42.9 Small -37.7 -41.7 Deflating -25.9 -21.0 -46.4 -39.7 -23.5 24 16 12 Note. Minus signs indicate that the appearance of the maximal closing velocity is before ball-hand contact. SD GRASPING TAU those found in Experiment 1 for the deflating ball (120 ms) and the large ball (125 ms) but different for the small ball (40 ms). In addition the standard deviation decreases closer to ball-hand contact, which was not the case in Experiment 1. In summary, we replicated the findings of Experiment 1 in this experiment, although the differences in the time of appearance of the maximal closing velocity are somewhat exaggerated under the monocular condition. a L E 0 6 B == Q 12. S 5' '10 e"1" 4' General Discussion 3 -220 i ! i i f -180 -140 -100 -60 -20 Time before contact (ms) E 0 0.5 P 0.4' Q. ca C m J¢ ¢.. b B-S xx \\\ //' / 0.3 0.2' L - B ~ Q 0,1 o =_ 0,0 -220 u ! ! u u -180 -140 -100 -60 -20 20 Timebeforecontact(ms) 1.6 E O 1.4 L B Q. '10 p, 321 1.2 ~ 1.0 ~ 0.8 -220 I ~ -180 -1 0 ! u -100 -60 u -20 Time before contact (ms) Figure 4. (a) Adjustments to the mean aperture of the hand for the large ball (L), the small ball (S), and the deflating ball (B) in the last 200 ms in Experiment 2 (sampling 200 Hz); (b) the differences in hand aperture between the large ball and the deflating ball (L - B) and between the deflating ball and the small ball (B - S); (c) the standard deviation for all three ball sizes in the last 200 ms in Experiment 2 (sampling 200 Hz). and between the deflating ball and the small ball. At the beginning of the flight the deflating ball (as might be expected) leads to hand apertures closer to the large ball; in the last 150 ms it leads to apertures closer to the small ball. Figure 4c shows the standard deviation of the hand aperture for the three ball sizes. The points of minimal variance are similar to The findings of the studies presented here, in which the optical variable tau was experimentally manipulated, are consistent with subjects' use of relative expansion information on which to base their catching actions. Subjects adjusted their action to a deflating ball even though they were apparently unaware (by verbal report in Experiment l and visual-judgment report in Experiment 2) of its peculiar behavior. Not only were they successful in catching the deflating ball, but their actions were finely tuned to its size change. Several reasons for the latter fact exist. As a result of the subtle manipulation of the expansion and the low approach velocity of the balls, the available time window was long enough for subjects to make a catch. Relative expansion, albeit less than that from a ball with a constant physical size, was still available (Figure 2). Thus, the artificially manipulated relative expansion (i.e., not synchronized to the ball approach) still provides enough information to facilitate catching within the time constraints (time window) available. The results obtained under the binocular condition of Experiment l are open to explanations other than subjects' using optical expansion information to make their time-to-contact judgments. Nevertheless, the use of a monocular condition in Experiment 2, which led to similar delay times (albeit with a different group of subjects), suggests that binocular information (other than optical expansion information) does not facilitate catching performance under the conditions of the experiments reported here. The use of different ball sizes together with a deflating ball requires that subjects make subtle changes in their grasping actions if they are to achieve success, some of these changes late in the bali's flight. The fact that subjects were able to attune their actions to such perceptual nonveridical changes argues strongly for the steering effect of environmental information rather than some preprogrammed catching action actuated at some particular moment. This finely attuned perception-action coupling manifests itself most clearly in the adjustments of the hand aperture to the deflating ball (see Figures 3a, 4a, and 4b). The subjects do not know and are apparently not aware that the ball is deflating during its approach. (By the time the ball is caught, there are no detectable differences between the deflating ball and the small ball.) Despite this, subjects adjusted their hand actions to meet the changing demands. As Lee and Young (1985) hinted, the timing of the catching action is under continuous visual control such that adjustments to the catching hand are apparent even at a relatively short time interval prior to ball-hand contact. The fact that the standard deviations of hand aperture become smaller when the ball comes nearer to the hand suggests that the visual information 322 G.J.P. SAVELSBERGH, H. T. A. WHITING, AND R. J. BOOTSMA becomes more precise as contact approaches (see also Lee & Young, 1985). From the experiments reported here, however, it is not clear to what stage in the trajectory of the ball that optical expansion information can be used to adjust the hand aperture. 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