Effects of growth and speed on hindlimb joint angular displacement patterns in vervet monkeys (Cercopithecus aethiops).код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 81:441449 (1990) Effects of Growth and Speed on Hindlimb Joint Angular Displacement Patterns in Vervet Monkeys (Cercopithecus aethiops) JOEL A. VILENSKY AND EVA GANKIEWICZ Department of Anatomy, Indiana University School of Medicine, Fort Wayne, Indiana 46805-1499 KEY WORDS Primates, Locomotion, Ontogeny, Hip, Knee, Ankle ABSTRACT Hip, knee, and ankle joint displacement patterns are compared across both age and speed for five immature vervet monkeys sampled approximately every 6 months over a 3 year period. The analysis indicated that, as a group, the animals displayed no consistent changes in joint patterns as they grew. However, individual animals showed consistent patterns. There were also no consistent effects of size across animals at the walk-gallop transition. This is contrary to McMahon’s prediction (J. Appl. Physiol. 39:619427, 1975) based upon his elastic-similarity model of animal scaling. With increasing speed, when symmetrical gaits were used, all of the animals tended t o show a decrease in the relative positions of the hip, knee, and ankle maximum values. Furthermore, across the walk-gallop transition, the animals tended to show a decrease in the range of ankle and knee movements. Previous analyses of the effects of increas- monkeys sampled every 6 months over aping speed andlor size on joint angular dis- proximately a 3 year period at the identical placement patterns in primates are ex- speeds. The purpose of the study was to tremely limited. Vilensky and Wilson (1986) determine if there were consistent changes found some consistent changes in hip and in these patterns both across time (i.e., with ankle joint patterns with increasing speed in increases in body mass) and across speed. one vervet monkey. Reynolds (1987) re- Clearly, by using a longitudinal approach for ported that hindlimb angular excursions de- this study, problems caused by intersubject creased with increasing s eed for a variety of variability are controlled. primates. Vilensky et a! (1988) found no MATERIALS AND METHODS consistent effects of body mass on hindlimb angular excursions in vervet monkeys. HowThe raw material for this paper consisted ever, they did find some tendency for the of the same 100 frame& films used in our excursions to increase across slower speeds companion paper (Vilensky et al., 1990). and decrease a t the walk-gallop transition, These films displayed the animals locomotafter which there was an increase with in- ing on a treadmill at the following speeds: creasing s eed. McMahon (1984) reported 0.62, 0.89, 1.17, 1.44, 1.72, 1.99, 2.28, 2.58, for four di erent-sized mammals (none pri- and 2.81 d s . From the “good” strides for mates) that hindlimb excursions at the trot- each trial (see Vilensky et al., 19891, we gallop transition equaled 74.4mas~-~.’~.chose one stride to digitize. Thus, for each Thus the larger animals had smaller angular animal, the following numbers of strides excursions at this transition. This was in were digitized: A l , 38; A2,52; A3,40; A4,44; good agreement with his model that predicts A5,43 (see Table 1 in Vilensky et al., 1990). angles at this transition scale proportionally The specific stride chosen from each trial to (McMahon, 1975). was one that had a cycle duration equal or For this report we have analyzed in detail closest to the mean cycle duration for all of the hip, knee, and ankle joint angular displacement patterns in five immature vervet Received March 27,1989; accepted August 31,1989. 1 @ 1990 WILEY-LISS, INC 442 J.A. VILENSKY AND E. GANKIEWICZ the strides of that trial. Table 1 in Vilensky et al. (1990) details the ages and masses of the animals at each filming. Here, we will only present the ranges for each animal: A1 (female), 1.17-3.17 years, 1.27-2.22 kg; A2 (female), 1.0-3.5 years, 1.31-2.5 kg; A3 (female), 0.83-2.83 years, 1.14-2.27 kg; A4 (female), 0.5-2.83 years, 0.64-1.73 kg; and A5 (male), 0.33-2.33 years, 0.73-2.00 kg. It is noteworthy that the youngest animal filmed was 4 months of age. Because by 2 months of age vervets have the ability to perform both symmetrical and asymmetrical gaits in an adult-like fashion (Vilensky and Gankiewicz, 19891, we do not discuss our findings with regard to the relative neuromuscular maturity of the animals. That is, we consider “size” to be the only variable within individuals at the same speeds. Once a stride was chosen for analysis, the individual film frames were rear-projected onto a digitizing tablet that enabled an experienced technician to estimate visually the locations of the followingjoint centers (right limb) for each frame of the stride: metatarsophalangeal, ankle, knee, hip, shoulder, elbow, wrist, and metacarpophalangeal. Specifically, using a cursor, the technician inputed the estimated locations of these joint centers into the computer. Subsequently, the computer determined the ankle, knee, hip, shoulder, elbow, and wrist joint angle values (illustrated in Fig. 1) for each frame of film. For this report, we will only describe the results based upon the hindlimb angles. The forelimb data will be reported in a forthcoming paper. Once determined, the raw angular values were smoothed using low pass digital filtering (Winter et al., 1974; Winter, 1979) with cut-off frequencies rangingfrom 6 to 8. Next, we determined the followingfive parameters from each of the smoothed curves for each joint: minimum angle, relative position of minimum angle (i.e., the time of occurrence in terms of percentage of cycle), maximum angle, relative position of maximum angle, and range. It is important to note that for some animals at some speeds we changed the location of the minimum or maximum angle for the knee or ankle so that it was in agreement with most of the other trials. That is, as evident from Figure 2, during a complete locomotor cycle the knee and ankle have two minima and maxima. For our purposes (and usually the case), the “true” minimum occurred for both joints during the second half of the cycle, and the “true” maximum oc- Fig. 1. Drawing of one of the animals illustrating the joint angles computed. A Ankle; B: knee; C: hip (to horizontal);D: shoulder (to horizontal);E: elbow; F: wrist. 443 EFFECTS OF GROWTH AND SPEED ON JOINT ANGLES gaits as well as for the transition. S ecifically, for each animal, we analyze (i.e., computed correlation coefficients) across ages only those speeds for which we had at least three symmetrical or asymmetrical gait trials. Similarly, across speeds we analyzed only those ages for which we had at least three trials of either type of locomotion (see Table 1 in Vilensky et al., 1990). However, there was an additional restriction on the asymmetrical strides. We used only strides that had the same leading limb (regardless of gallop type; i.e., transverse or rotary). This was done because during galloping the leading and trailing limbs have been shown to exhibit different angular relationships (Cohen, 1979; Vilensky et al., 1988). Finally, we analyzed the relationship between angular excursions and mass at the walk-gallop transition and the changes in angular patterns at this transition. In accord with our companion paper, and because of the voluminous amount of information produced by this study, we will discuss our findings for all of the animals but present in detail only the results for animal No. 5 (A5). B 35 40 145T 25 KNEE 50 100 /"\ W 75 65 75 0 25 50 75 100 RESULTS PERCEKT OF CYCE Fig. 2. Plots of the smoothed hip, knee, and ankle displacement patterns for A5 at 1.17 m/s at five different ages (and mass values). curred at around 50%of the cycle. However, occasionally the actual minimum occurred during the first half of the cycle or the maximum a t the beginning or end. We changed these so that we were comparing similar turning points for each cycle. We also did not use the position of the hip minimum value for any calculations, because the hip minimum was very closely associated with the beginning of the stride (i.e., limb touchdown). Because we found previously in vervets a discontinuity in hindlimb angular excursion at the walk-gallop transition, and because back motion significantly contributes to locomotor effort during galloping (Hurov, 19871, we will present separate discussions of the data for symmetrical and asymmetrical Symmetrical gaits Figure 2 depicts plots of the displacement patterns of the hip, knee, and ankle angles of A5 across all ages at 1.17 d s . At this speed the animal used only symmetrical gaits. The figure shows that the positions of the minimum and maximum ankle angles tended to increase with size, whereas the actual values did not chan e consistently. However, the maximum an le value was at its lowest at the second youngest age. For the knee, the minimum value, position of the minimum value, and position of the maximum angle tended to increase with size. Also, again, the maximum was lowest at the second youngest age. None of the hip parameters showed any tendency to change in a consistent manner with a e, and, in contrast to the ankle and knee, t e hip maximum was highest at the youngest age. To describe better the relationship between age and angular parameters a i 1.17 m/s as well at other symmetrical ait speeds, Table 1 presents correlation coe ficients for A5 between the listed angular parameters and body mass at each of the different speeds for which we had sufficient data. The only relatively consistent trend among the speeds is for the maximum ankle position to in- a a B 444 J.A. VILENSKY AND E. GANKIEWICZ TABLE 1. Linear correlation ualues for A5 for listed angular parameters Vs. body mass at each speed (symmetrical gaits)' 'lo- HIP <' 100-7 90 Speed (m/s) Parameter Min Ankle Pos Min Ankle Max Ankle Pos Max Ankle Range Ankle Min Knee Pos Min Knee Max Knee Pos Max Knee Range Knee Min Hip Max Hip Pos Max Hip Range Hip 0.62 0.89 1.17 1.44 0.92 0.30 -0.52 0.89 -0.84 0.49 -0.43 0.70 -0.24 -0.65 0.16 -0.73 -0.11 -0.63 0.84 -0.01 -0.16 0.92 -0.72 0.88 0.01 -0.81 0.59 -0.98 0.26 -0.93 0.67 -0.70 0.14 0.91 0.54 0.84 0.53 0.93 0.81 0.40 0.88 -0.48 0.21 -0.14 0.60 -0.31 -0.22 0.63 0.79 0.59 0.58 0.42 0.75 0.62 0.31 0.21 -0.16 0.58 0.54 0.74 - -. /,: >.., ._ .82 m/s 3 0 m/s . 1.17m/s-. ):. 70.60-7 __-' 40 30 0 25 50 75 100 0 25 50 75 100 'There were five ages available for the computations at 0.62,0.89, and 1.17 m/s and four at 1.44 m/s. increase with mass. Similar tables for the other animals indicated the following:' 1) The only somewhat consistent trend shown by A1 was for the minimum ankle angle to decrease with mass; 2) A2 showed a tendency for the maximum ankle and knee positions and the minimum knee value to increase with mass; 3) A3 showed a tendency for the minimum hip value to increase with mass and, accordingly, for the hip range to decrease; and 4)A4 showed tendencies for the ankle, knee, and hip ranges to decrease with mass, and for the minimum knee position also to decrease with mass. Figure 3 depicts the angular displacement patterns of the hip, knee, and ankle joints of A5 at 1.33 years (1.54 kg) across all symmetrical gait speeds. The figure indicates that the ositions of the maximum ankle and hip anges and the hip minimum value decreased with increased speed. Additionally, the ankle and hip maxima reached their lowest values at the slowest speed (0.62d s ) . Table 2 depicts the correlation coefficients for A5 between the available speeds (symmetrical gaits only) and each of the listed parameters at each age (and associated mass). Two strong trends are apparent. As noted for 1.33years in Figure 3, the positions of the maximum ankle and hip angles decreased with speed for all ages. At 0.33,0.83 and 1.83 years, the position of the maximum 160 150i ANKLE \ .I ..u.. 140 1 20 ._: 80 70 0 25 50 PERCENT OF CYCLE 75 1 oc Fig. 3. Plots of the smoothed hip, knee, and ankle displacement patterns for A5 at an age of 1.33years (1.54 kg) across all speeds during which symmetrical gaits were used. f 'It should be noted that the trends listed for A1 to A4, as forA5, were determined subjectivelybased on the consistent appearance of relatively high and similarly signed (i.e., + or -1 r values. Because of the low sample sizes, we did not considerit worthwhile to base our results on only statistically significant values. knee angle also followed this trend. There was also a notable tendency for the hip maximum and range to increase with speed. Evaluation of similar tables for the other animals indicated the following: 1) In Al, minimum ankle angle tended to increase with speed; the positions of the maximum ankle, knee, and hip angles decreased with speed; and the minimum knee position also tended to decrease with speed. 2) In A2,the positions of the minimum ankle and knee angles generally decreased with speed; the maximum ankle angle, ankle range, maximum knee angle, and knee range tended to increase with speed; and the positions of 445 EFFECTS OF GROWTH AND SPEED ON JOINT ANGLES TABLE 2. Linear correlation values for A5 for the listed angylar parameters Vs. speed (symmetrical gaits only) Parameter Min Ankle Pos Min Ankle Max Ankle Pos Max Ankle Range Ankle Min Knee Pos Min Knee Max Knee Pos Max Knee Range Knee Min Hip Max Hiu Pos Ma; Hip Range Hip 0.33 (0.73) 0.83 (1.32) Years of age (mass in kg) 1.33 (1.54) 1.83 (1.77) 2.33 (2.00) 0.98 -0.60 0.65 -0.92 -0.51 -0.67 -0.87 -0.99 -0.99 0.18 -0.75 0.87 -0.96 0.86 0.59 -0.91 0.53 -0.97 0.49 -0.91 -0.64 -0.03 -0.99 0.57 0.36 0.35 -0.97 0.11 0.48 -0.60 0.64 -0.95 0.36 -0.77 -0.32 -0.21 0.38 0.20 -0.93 0.57 -0.99 0.86 0.53 -0.85 0.81 -0.96 0.50 -0.09 -0.90 0.89 -0.85 0.81 0.32 0.91 -0.98 0.78 -0.92 -0.25 0.89 - -0.96 0.91 -0.68 -0.34 -0.45 -0.26 0.87 0.23 0.93 -0.87 0.81 'There were five speeds available for the computationsat ages 0.83 and 2.33 years, six for 1.83 years, four for 1.33 years, and three for 0.33 years (Vilensky et al., 1989). TABLE 3. Linear correlation values for A5 for the listed angular parameters Vs. body mass at each speed (asymmetrical gaits)' Parameter Min Ankle Min Ankle Max Ankle Pos Max Ankle Range Ankle Min Knee Pos Min Knee Max Knee Pos Max Knee Range Knee Min Hip Max Hip Pos Max Hip Range Hip 1.72 Speed (m/s) 1.99 2.28 2.58 -0.67 0.26 o,99 o,48 0.95 0.78 0.90 0.01 0.98 0.67 0.29 0.93 0.54 0.95 0.92 0.99 0.67 0.76 0.58 -0.70 0.55 0.63 -0.80 0.99 -0.31 0.78 -0.67 0.65 0.31 o,84 0.99 -0.37 0.88 0.75 0.44 0.89 0.93 0.47 0.26 0.89 0.16 0.90 2.81 -0.87 0.11 o.51 0,51 0.94 0.80 0 -0.39 1.0 0.63 0.63 0.90 0.86 0.80 -0.01 0.91 0.87 0.78 -0.76 -0.44 -0.98 0.73 0.86 0.96 0.87 0.25 0.97 0.46 'There were five ages available for the computations at 2.81 m/s, four for 1.99 and 2.28 m/s. and three for 1.72 and 2.58 m/s. the maximum ankle, knee, and hip angles tended to decrease with speed. 3) In A3, maximum ankle angle and knee range tended to increase with speed; minimum knee position and hip minimum tended to decrease with speed; and the positions of the ankle, knee, and hip maximum values strongly decreased with speed. 4) In A4, the only consistent trends evident for this animal were for the positions of the maximum ankle and hip angles to decrease with speed. Asymmetrical gaits The displacement curves for the hip, knee, and ankle angles during galloping did not differ grossly in pattern from those during walking, and thus no examples are given. Table 3 presents the correlation coefficients for A5 across age in a similar manner as in Table 1, but for asymmetrical gaits. The table indicates that the maximum ankle, knee, and hip angles generally increased across increasing mass. The ankle range also tended to increase, as did the minimum knee and the positions of the maximum and minimum knee angles. Similar tables for the other animals showed no consistent trends (A1 galloped only on one date, so no analyses were available for her). Table 4 depicts the correlation coefficients for A5 in a similar manner as in Table 2, but for asymmetrical gaits. The table shows a tendency for the maximum ankle position to decrease with speed and for the maximum hip value and range to increase with speed. Similar tables for the other animals revealed the following: 1) The only clear trend evident for A2 was that the position of the maximum ankle value decreased with speed; 2) A3 showed a tendency for minimum hip angle t o increase with speed; and 3) for A4, the positions of the maximum ankle, knee, and hip values decreased with speed, the positions of the minimum ankle and knee angles also decreased with speed, and the hip and knee ranges tended to increase with speed. Walk-gallop transition Figure 4 depicts a log-log plot of the hip, knee, and ankle ranges at the walk-gallo transition (lowest galloping speed) for eac animal for each date for which it galloped vs. mass. Additionally, regression lines and associated r values are depicted for each animal. Furthermore, the line representing the equation computed by McMahon (1984) for hindlimb excursion at this transition (based on a variety of mammals) is plotted on the K 446 J.A. VILENSKY AND E. GANKIEWICZ TABLE 4. Linear correlation values for A5 for the listed angular parameters Vs. speed at each age (asymmetrical paits onhi' Parameter Min Ankle Pos Min Ankle Max Ankle Pos Max Ankle Range Ankle Min Knee Pos Min Knee Max Knee Pos Max Knee Range Knee Min Hip Max Hip Pos Max Hip Range Hip 0.33 (0.73) 0.83 (1.32) Years of age (mass in kg) 1.33 (1.54) 1.83 (1.77) 2.33 (2.00) -0.01 0.32 0.48 -0.66 0.81 -0.99 -0.91 -0.66 -0.99 0.86 -0.98 -0.74 -0.99 0.67 0.49 0.55 0.94 -0.89 0.24 0.44 0.18 0.95 -0.62 -0.44 0.10 0.99 0.18 0.69 0.38 -0.71 -0.19 -0.91 -0.42 -0.04 -0.55 0.59 -0.29 0.41 0.32 0.90 -0.42 0.79 0.20 -0.50 0.41 -0.89 0.14 0.16 -0.58 0.70 0.08 0.81 -0.38 0.94 -0.66 0.89 0.88 0.52 0.35 -0.77 -0.94 0.99 -0.94 0.99 -0.77 0.96 -0.35 0.99 -0.99 0.98 'There were qix speeds available for t h e computations a t age 1.33 years, five for 1.83 years, four for0.83 years, a n d three for0.33 and 2.33 years (Vilensky et al., 1989). hip range graph (see Discussion). Clearly, for all three joints the relationship between mass and walk-gallop transition value was usually poor within animals ke., low r values). Furthermore, the regression lines are highly inconsistent among the animals. Table 5 depicts the differences in the noted angular parameter between the highest walking (running) speed and lowest galloping speed for A5. A negative value implies a decrease from the walking to the galloping speed. For the hip, there were no notable differences. For the knee and ankle, there appeared to be consistent (except for age 1.33 years) decreases in range with the transition to galloping. For the ankle, this was associated with a larger minimum ankle value (i.e., less ankle dorsiflexion). Tables similar to Table 5 €orthe other animals indicated the following: 1)Knee and ankle minimum values increased in A2, and, accordingly, the ranges decreased. 2) The hip maximum and range decreased in A3, and the knee and ankle minimum increased, and the ranges showed some tendency to decrease. 3) In A4, the hip minimum increased, and the ankle maximum and range decreased. DISCUSSION Angular parameters and size The presented data indicate that vervet monkeys, as a oup, do not use consistent changes in h i n g m b joint angular parameters to adjust for the changes in their size with ontogeny during either symmetrical or asymmetrical gaits. Nevertheless, particular animals did show highly consistentpatterns. Although it is possible that the in- dividual patterns we recorded occurred spuriously, the high r values and the consistency across speeds makes this seem unlikely. In contrast to the present report, as far as we can determine, no prior studies of either animal or human locomotion has ever examined ontogenetic changes in joint movements at identical speeds. Thus these data are not directly comparable with those from any other study. However, one previous study investigated joint angle changes at identical speeds in different-sized children (i.e., a cross-sectional study; Vilensky et al., 1987). The authors reported good relationships with stature for hip minimum, knee minimum, and knee maximum angular values. Two studies have reported a remarkable likeness in joint angular excursions in adults and children (Foley et al., 1979; Sutherland et al., 1980), but in neither of these studies was speed controlled. Angular parameters and speed In contrast to the lack of similar relationships across increasing size, the five animals showed some similarities across speed while using symmetrical gaits. The animals exhibited almost uniformly a tendency for the positions of the maximum hip, knee, and ankle values to decrease with speed. For example, for A5 at 0.83 years, the maximum hip position occurred at 61% of the cycle at 0.62 d s but at 43% of the cycle at 1.72 d s . Individual animals exhibited other tendencies as well, but these were not consistent among them. Across the higher speeds, which required 447 EFFECTS OF GROWTH AND SPEED ON JOINT ANGLES A1 A A2-.. = AA 43---' ' T 1.5 As-I 1.04 I r=.96. ..' *A . ' 1.44 -0.20 -0.10 0.00 0.10 0.20 0.30 0.40 I 0.50 LOG MASS (kg) Fig. 4. Log-log plots and regression lines of hip, knee, and ankle angular ranges at the walk- allop transition vs. mass. The solid line on the hip grapgh corresponds to the equation presented by McMahon (19841, which is based on a variety of different sized mammals (see text). asymmetrical gaits, the pattern of changes in angular parameters associated with increases in speed was inconsistent. However, A4 showed, in accord with the symmetrical gaits, a decrease in the positions of the hip, knee, and ankle maximum values. The fact that the relative positions of the maximum hip, knee, and ankle values decrease with speed during symmetrical gaits is not surprising, as these peaks tend to occur late during stance phase, which also decreases with increases in speed (Vilensky et al., 1990). Thus the change in the location of these peaks probably does not represent any fundamental change in limb mechanics associated with increased speed. Reports detailing the effects of speed on joint angular displacement patterns in both humans and animals are quite contradictory, although hip joint amplitude appears clearly to increase during human walking and running (Vilensky, 1987). For animals, the prevailing view seems to be, at least for hip movements, that there are no dramatic changes with speed (Grillner, 1975). For example, Halbertsma (1983) stated that, above 1 d s , changes in joint angles in cats with increases in speed are slight. Our data for A5 presented in Figure 3 suggest this to be true also for vervet monkeys. That is, the hip and ankle maxima at 0.62 m / s were notably less than those at the higher speeds. This was generally also true for the other animals (including the knee maximum at midcycle). Reynolds (1987) reported that the hindlimb angular excursions of two chimpanzees, a spider monkey, and a lemur decreased with increasing speed. Clearly, this finding is not supported by the current study (at least TABLE 5. Differences in the noted parameters (in degrees) for A5 between the values at the lowest galloping speed and the highest walking (runningj speed at each age Years of age (mass in kg) Parameter Ankle Min Max Range Knee Min Max Range Hip Min Max Ranae 0.33 (0.73) 0.83 (1.32) 1.33 (1.54) 1.83 (1.77) 2.33 (2.00) 19 1 -18 7 -11 -18 -8 0 8 5 -13 -18 18 -6 -24 16 1 -15 -5 -19 -14 -2 1 -1 1 -12 -4 8 4 -4 -4 5 -9 -5 2 -3 4 6 3 -2 -5 8 -12 2 4 2 448 J.A. VILENSKY AN11 E. GANKIEWICZ relative to hip range) nor was it supported by seemingly consistent ways to account for the our cross-sectional study (Vilensky et al., changes in body size associated with growth. This clearly shows tremendous flexibility 1988). and/or variability in the neural programs Walk-gallop transition that control locomotor behavior. This study also examined the effects of As noted previously, McMahon (1975) proposed, based upon his elastic similarity speed on hindlimb joint movements. Furmodel of animal scaling, that angular excur- thermore, the study involved sampling the sions at the trot-gallop transition should same animals serially over time at the same scale proportionally to masspo.125.He empir- speeds. This process should have minimized ically determined that hindlimb excursions the possibility of spurious observations beat this transition are equal to 74.4ma~s-~-l’ing reported as the norm. Our analysis indi(McMahon, 1984). The data presented in cated that the most consistent changes with Figure 4 do not indicate that, at least within increased speed are decreases in the maxianimals, joint excursions at the walk-gallop mum positions of the hip, knee, and ankle transition decrease regularly with increases joints. These changes are undoubtedly assoin size. Furthermore, although we did not ciated with the decrease in stance duration measure hindlimb excursion for this report, associated with increases in speed. Finally, it is important to emphasize that, this parameter should be similar to hip range. Thus the hip excursion plot in Figure despite our many samplings of the animals 4 depicts the line corresponding to McMa- for this study, we only examined one “t phon’s empirically derived equation. It is ap- ical” stride for each animal at each spee at parent that this equation did not predict each age. It would seem important now to quantify the variability in these patterns at accurately the vervet transition values. In contrast to the present report, for our set speeds on a single date. Additionally, it cross-sectional study (Vilensky et al., 1988) seems important to investigate the possible we did measure hindlimb excursions in interrelations between joint displacement vervet monkeys. Again, however, we could patterns (i.e,, are greater hip excursions asfind no evidence that larger animals have sociated with smaller knee excursions, and smaller angular excursions at the walk- so forth?) Such projects are necessary to gallop transition, although the actual range understand more fully the biomechanics and of predicted values was not too far removed neural control mechanisms underlying prifrom actual values. Lastly, it is noteworthy mate locomotion. that Alexander (1985) detailed both theoretACKNOWLEDGMENTS ical and empirical problems associated with the theory of elastic similarity. We are grateful to Mr. G. Duncan and Ms. In our cross-sectional study, we reported P. Wilson for assistance during filming, to that hindlimb angular excursions tended to Ms. J. Kettelkamp for digitizing the films, to decrease across the walk-gallop transition. Dr. M. Cartmill and three anonymous reThe present, more detailed analysis shows a viewers for constructive comments on the fairly regular tendency for the range of knee original version of this paper, and to Ms. D. and ankle movements to decrease. This is Jackson for typing the many drafts of the often caused by an increase in the respective manuscript. Funds for this study were supminimum values of those joints (i.e,, less plied by the Indiana University School of flexion). It seems reasonable to suggest that Medicine. the increased back motion associated with LITERATURE CITED galloping may be associated with the reduction in flexion observed for the knee and Alexander RM (1985) Body support, scaling and allometry. In M Hildebrand, DM Bramble, KF Liem, and DB ankle joints (Hurov, 1985,1987). B CONCLUSIONS This study is the first report on the effects of growth on the joint angular displacement values of a specific group of immature individuals at set speeds. We have demonstrated that across individuals there are no consistent changes. However, each individual may modify its angular parameters in certain Wake (eds.): Functional Vertebrate Morphology. Cambridge, MA: Belknap, pp, 26-37. 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