The movements of limb segments and joints during locomotion in African and Asian elephants

The elephant hath joints, but none for courtesy. His legs are legs for necessity, not for flexure.

Ulysses in Act II, Scene iii(Shakespeare, 1609)

Elephants run straight-legged, thigh lined up with shank and upper arm with lower arm, so their legs look rather like mobile Doric columns.

p. 214 in (Bakker, 1986)

As the above quotes exemplify, humans have long recognized the distinctive columnar (straight-legged) limb posture of elephants. This recognition has generated classical misconceptions, such as elephants having no joints, no knees or four knees [e.g. pp. 101-109 in(Tennent, 1999)]. Ridiculous as those fallacies may seem to contemporary scientists, elephant posture and gait remain misunderstood, partly because of their strange anatomy and partly because of little rigorous measurement of elephant locomotion. Hence,potentially misleading oversimplifications persist, even in recent comparative/functional studies (e.g. Bakker, 1986; Paul, 1998; Paul and Christiansen, 2000),and have become integrated into textbook and popular media accounts. Elephants are unusual among terrestrial animals not only in their enormous size [up to 7000 kg in adult African elephants(Christiansen, 2004; Wood, 1972)] and apomorphically long limbs (Alexander et al., 1979a) but also in their limited speed range [∼7 m s^–1 maximum (Hutchinson et al., 2003)], continuous changes of kinematic patterns with increasing speed (Hutchinson et al.,2006) and smooth, relatively low-speed transition to bouncing or`running' hindlimb mechanics (Ren and Hutchinson, 2008).

Earlier studies (Gambaryan,1974; Hildebrand and Hurley,1985; Marey and Pagès,1887) provided basic descriptions of elephant segment and joint motions that are widely cited and useful; however, these were largely qualitative, were based on small sample sizes, and utilized ambiguous or technically limited methodology [e.g. 24 Hz video in(Hildebrand and Hurley, 1985);unknown elephant speeds in most studies]. Our initial studies(Hutchinson et al., 2003)showed that elephants shift from vaulting to bouncing hip motion, from slow to fast speeds; our later studies (Hutchinson et al., 2006) observed that hindlimb flexion seemed to increase concurrently, suggesting a shift from vaulting to bouncing limb mechanics(Ren and Hutchinson, 2008) as previously predicted. This limb flexion has not yet been quantitatively measured or related directly to speed changes but does indicate marked differences in joint motion at least between the forelimbs and hindlimbs. The differences between fore- and hind-foot posture and dynamics in elephants also relate to altered loading and scaling of the bones and tendons(Miller et al., 2008).

Our previous analysis of stride parameters(Hutchinson et al., 2006)demonstrated that elephants change speed by increasing stride frequency, more than stride length, up to a dimensionless speed[û=v/(hg), where û is dimensionless speed, v is velocity, h is hip height, and g is acceleration due to gravity] of 1.0. Beyond this speed, stride frequency approaches its maximum and stride length contributes relatively more to speed increase. Correspondingly, stance time decreases most steeply with speed (continuing beyond û∼1.5), with swing time reaching its plateau at û∼1.0; concurrently, duty factor decreases sharply and then levels off. From the perspective of motion within the limbs, it is thus expected that, as elephants increase speed, they mainly increase joint/segment angular velocities (required for larger stride frequencies) until running quickly (û>1.0) when they rely more on greater joint rotations (larger ranges of motion, perhaps including greater limb flexion) to generate the longer strides observed.

In the present study, we analyze the coordination patterns of the limb segments and joint movements during steady-state locomotion in Asian(Elephas maximus Linnaeus 1758) and African (Loxodonta africana Blumenbach 1797) elephants. As noted above, elephant limbs are the archetype for columnar, graviportal animals [large, relatively slow, with long proximal and short distal limb segments(Gregory, 1912)] and hence are of comparative interest, particularly for deciphering the relationships between body size and locomotor form and function. Therefore, our major aim is to determine how elephant limb motions compare with those of other mammalian species – are elephants always relatively restricted in their joint/segment ranges of motion, having less mobile joints than other animals?Are their limb motions fundamentally distinct from all other animals',especially cursorially specialized forms, as they often have been characterised (e.g. Bakker,1986; Gregory,1912; Paul, 1998; Paul and Christiansen, 2000)?We sought to carefully examine how useful and accurate the term `columnar' is when applied to elephants.

Thus, we pose two fundamental questions here, related to the aims above. Firstly, what are the limb segment and joint angular and angular velocity changes across a normal walking stride in elephants, and how do motions differ within and between limbs? Particularly, just how columnar are elephants (i.e. what are their segmental and joint angles during locomotion)? Secondly, how do elephant limb motions change with speed, from slow walking to fast running;i.e. does their `columnarity' change with speed (are their legs always legs for necessity, not for flexure)? At all speeds, are all joints similarly columnar and of low flexibility/mobility or is there intra-/inter-limb diversity in joint flexibility(Gambaryan, 1974; Hildebrand, 1984; Hildebrand and Hurley, 1985)?We test the null hypothesis that joints all use a similar fraction of their maximal range of motion (i.e. that is allowed by joint surfaces and ligaments)by comparing maximal in vivo (fast locomotion) vs in vitro(cadaver manipulation) joint range of motion and discuss alternative hypotheses.

We used motion analysis with 15 elephants covering a sevenfold body mass range to quantitatively answer these questions. Accurate baseline joint and segment kinematic data are vital for further biomechanical analyses, e.g.`internal work' [movements of segments relative to the body's center of mass(Hildebrand and Hurley,1985)], joint powers (e.g. Dutto et al., 2006), or inverse dynamics analysis of muscle/bone stresses (e.g. Alexander et al., 1979b; Biewener, 1989; Biewener, 1990) of locomotion. We expected that there would be no major size/species differences in elephant kinematics (as in Hutchinson et al.,2006; Ren and Hutchinson,2008) but here search for any previously overlooked differences within limbs, as earlier studies have focused on whole-body or whole-limb kinematics. Another subsidiary goal of our analysis was to quantify how`normal' elephant limbs move in order to establish a comparative dataset for identifying foot, joint or other limb pathologies, which are a major concern for elephant keepers (Csuti et al.,2001; Egger et al.,2008).

Table 1 lists the animals we worked with and the zoos/parks where they were held. For Asian elephants, we used two juveniles (⩽5 years old; 521 and 688 kg body mass), two sub-adults (1740 and 2072 kg) and four adults (⩾20 years old;3149–3684 kg body mass). For African elephants, we used one juvenile(930 kg), three sub-adults (2550–3230 kg) and three adults(3100–3512 kg). Ages were known to trainers ±1 year (or better for juveniles), and body masses were obtained using truck scales (±5 kg) or a custom-made force platform apparatus (for Thailand elephants;constructed by Arsalis Inc., Louvain-la-Neuve, Belgium; 7000 kg max. load, 16 1 m×1 m plates). However, for the three adult African elephants mass was unknown so it was estimated from published mass–shoulder height equations (Laws et al., 1975; Christiansen, 2004). Hip and shoulder heights were measured from the ground to the approximate hip joint center or to the top of the scapula (Fig. 1) respectively, with flexible measuring tape (±1 cm) when the animal was standing still. All studies were approved by The Royal Veterinary College's animal welfare and ethics board.

Elephants were led by their handlers, using positive reinforcement such as food rewards and vocal commands, with the goal of maintaining a steady speed across a straight distance of ∼15 m. They also had at least 5 m before and after this distance to accelerate and decelerate to a steady speed, which,from previous experience, we knew to be sufficient(Hutchinson et al., 2006). Trainers randomly varied the speed from slow walking to fast running across trials and allowed ample rest and food between trials to prevent fatigue. Experiments were cancelled if animals showed musculoskeletal pathology,fatigue or any other artifacts that would cause discomfort or adversely affect our measurements. Handlers sought to build speed up to the near-maximal speed that the animal could achieve, which as usual among captive elephants was below the top speeds observed in sleeker, more active elephants [e.g. in Thailand 6.8 m s^–1(Hutchinson et al., 2003; Hutchinson et al., 2006)]. Data collection was conducted outdoors (during cloudy/twilight periods to reduce sunlight interference with our infrared motion capture) except at the Colchester Zoo site, when data were collected inside an elephant barn. All animals were moving over very firm (concrete, asphalt, packed dirt or force platform) and level substrates.

Infrared-reflective tape (Scotchlite 8850; 3M, Manchester, UK) covering styrofoam hemispheres (7 cm diameter for all elephants, except the juveniles,for which 3.5 cm diameters were used) were attached to the skin with double-sided carpet tape, over palpable landmarks. Fig. 1 explains these landmarks and positions. The ears (particularly in African elephants) hid the shoulder marker in some trials so data on the upper arm segment and elbow joint angle are scarcer. Due to time constraints (sunlight, animal and trainer availability, and manageability) the number of markers we could use was limited. This was exacerbated by the tendency of elephants to intentionally or accidentally dislodge or destroy markers. We considered using multiple-marker clusters to rigorously quantify 3D limb motions (e.g. Cappozo et al., 2005; Rubenson et al., 2007) but this was judged to be impossible under the constrained conditions.

A synchronized six-camera Qualisys (Gothenburg, Sweden) MCU 500 system (240 Hz) was used to record elephant limb marker motions, digitally triggered at the start of each trial. The system was calibrated before and after trials to a 3-D measurement accuracy of ∼1 mm. Total capture volume varied with ambient light and other conditions but was generally ∼12 m×3 m×4 m. Animal forward velocity for each stride was measured by calculating the averages of the hip and shoulder marker velocities. We defined steady-state trials as those in which the absolute difference between the forward velocities at two consecutive heel strikes was less than 20% of the average forward velocity. Trials with greater or smaller values of acceleration/deceleration were discarded. Froude numbers[Fr=v²/(hg)] and dimensionless speed (û=Fr^0.5) were calculated to normalize speeds (e.g. Alexander and Jayes, 1983) for comparison between elephants of different sizes and with previous stride parameter data (Hutchinson et al.,2006).

To estimate maximal joint ranges of motion, we conducted in vitrostudies with fresh cadaveric limb material (joint capsules and ligaments intact, skin and muscles removed) of one juvenile Asian elephant (830 kg body mass; 3 years old at death) that had no significant musculoskeletal pathologies. We used the same motion capture system described above but with the cameras in a ring around the specimen, and 2.5 cm diameter markers attached on bony landmarks and anatomical reference points (total of at least five markers per segment) to calculate the sagittal plane joint motions(detailed below) of the hip, shoulder, knee and elbow joints. We captured a static pose emulating standing posture (for calibration of distances between markers), then manually flexed and extended each joint, one at a time, through its maximal range of motion for five trials per joint. Measurements on an additional adult elephant cadaver were performed but we were unable to safely apply sufficiently large loads to cover a plausibly large range of motion. For comparisons with other species, we conducted the same in vitromeasurements with the forelimbs and hindlimbs of one Dutch Warmblood horse(adult, previously healthy, 500 kg body mass) using the same markers as Back et al. (Back et al., 1995a; Back et al., 1995b) and collated literature data for cats, dogs and humans (see Discussion).

All motion analysis 3-D coordinate data were first filtered using a low-pass, zero-lag Butterworth digital filter [fourth order, cut-off frequency 8 Hz (Winter et al., 1974)]. We calculated the sagittal plane (approximated as the plane parallel to the mean direction of motion in each trial) motions of the upper arm, forearm,forefoot (manus), thigh, shank and hindfoot (pes) segments and the elbow,wrist, knee and ankle joints. Segmental angles were `external' angles measured with respect to the vertical. Joint angles were the `internal' angles between two articulated segments. As there were no repeatable landmarks on the scapula or pelvis that we trusted to have minimal skin motion, we did not measure shoulder or hip joint angles, although our upper arm and thigh segmental angles are roughly comparable to these. More detailed analyses of 3-D kinematics and skin motion for these two joints and the scapula segment [a critical component of mammalian limb motion(Fischer and Blickhan, 2006; Fischer et al., 2002)] are still needed. Qualitative estimates of segment abduction and adduction can be made using our data (as the motion capture is inherently 3-D; see Discussion for qualitative descriptions of these motions) but here we focus primarily on sagittal plane motions as these are clearly the dominant component of elephant limb motion. Angular velocities of joints and segments were calculated using a first-order finite differentiation method(Pezzack et al., 1977).

We divided trials into their component strides by identifying the stance and swing phases for each limb. Limb touch-down was defined as when the vertical position (extracted from our motion capture data) of the fore- or hindfoot carpal or tarsal marker reached its minimum. Limb lift-off was defined as when the fore or hind limb middle toe marker(Fig. 1) reached its lowest position (Hutchinson et al.,2006) (Fig. 2). The resulting duty factors matched those at comparable speeds from video data(Hutchinson et al., 2006),validating this approach and avoiding a reliance on lower-resolution video footfall identification.

Although we depict angular motions and velocities for all studied elephant segments and joints across whole strides, for statistical comparisons we chose reference events during the stride to compare among elephants. For stance phase, we used touch-down, mid-stance (50% of stance time) and lift-off events as reference events. It is more difficult to quantify reference events in the swing phase but we selected minimal and maximal angle (or angular velocity)during the swing phase to emphasize the full range of motion used; in the present study we simply refer to these as minimal swing and maximal swing. Finally, the maximal value of each parameter minus the minimal value for the entire stride was the range of motion (ROM) for angles, and range of angular velocity (RAV) for angular velocities. These two parameters capture the widest excursions or rotational speed variations of the joints and hence are of biomechanical and functional significance although, like minimal and maximal swing, they are not always necessarily anchored to the same point in each stride.

As suggested by our marker placement repeatability assessment (see Results), we identified (post hoc) moderate offsets in some angle measures vs stride time (i.e. % gait cycle) that were probably caused by inaccurate marker placements, although most of the angle measures were repeatable. In these cases, to minimize the bias these offsets would bring into our statistical analyses, the whole angular displacement curves for a stride were shifted so that the mid-stance angles matched the mean mid-stance angle for all elephants. As the angular velocity is insensitive to this marker placement offset, this error does not affect those measurements. Similar relative offset errors are presumably present in most other studies of animal limb motion but are seldom discussed or investigated.

Our in vitro cadaveric studies calculated sagittal plane joint motions more rigorously as they used multiple markers attached directly to the skeleton. To quantify the total ROM of each joint we simply used the 3-D coordinates of each joint marker to quantify the sagittal plane joint angles in maximal flexion and extension.

One might expect that the positioning of skin-mounted motion capture markers would be hard to reproduce on multiple animals or experiments with the same animal. Therefore, we conducted a basic initial analysis of how consistently we were positioning the skin markers. The same investigator(J.R.H.) placed all 10 markers on two African elephant subjects (B and C in Table 1). The elephants did four trials of normal walking at the same speed, then the markers were removed and replaced with a new set. This was repeated 10 times for subject B and five times for subject C. We calculated the mid-stance segment (for upper arm and thigh) or joint angles as above and analyzed the results statistically as below.

Soft tissue artifacts (caused by the skin/muscles moving with respect to the underlying bones) are also certainly a problem for studies of elephant joint motion, perhaps more so than in smaller animals. Absolute error in estimating skeletal joint centers using skin markers is large, and the mobile,thick skin of elephants may also cause large relative errors. Invasive bone pin measurements (Reinschmidt et al.,1997; van Weeren et al.,1988; van Weeren et al.,1990) are impossible, and elephants are too large for cineradiographic imaging studies of joint motion (e.g. Cappozzo et al., 1996; Filipe et al., 2006; Gatesy, 1999). However,studies of human and horse skin marker accuracy show that errors in calculating flexion and extension angles are relatively minor, especially for distal joints (Back et al.,1995a; Back et al.,1995b; Leardini et al.,2005; Reinschmidt et al.,1997; van Weeren et al.,1988; van Weeren et al.,1990). Therefore, we assume that our flexion/extension measurements are reasonably accurate, pending more exhaustive in vitro and in vivo analyses.

All statistical analyses were conducted using SPSS 15.0 software (SPSS,Inc., Chicago, IL, USA). The effects of locomotor speed, species and body mass on angles and angular velocities were analyzed using analysis of variance(ANOVA) with repeated measurements via a linear mixed model approach by taking into account of the intra- and inter-subject variability. The different speed ranges, elephant species and body mass ranges were the fixed effects, and elephants were random effects. Differences between each pair were tested using Fisher's least significant difference (LSD) multiple comparison based on the least-squared means. This approach was chosen to maximize the amount of usable data, as opposed to regression techniques.

Our marker replacement repeatability test involved an independent simple t-test for each segment or joint at mid-stance (between elephant differences), a one-way ANOVA to test for the effect of trial number, and a one-sample Kolmogorov–Smirnov test for normal distribution of segment or joint angles between marker sets. The effect of speed was removed viaa Pearson's two-tailed t-test for correlation between speed and mid-stance angle. A linear curve fit equation was then used to remove speed effects if a speed–angle correlation was present. For normally distributed angles we used a two-way ANOVA to test the influence of marker set on angle (non-normally distributed angles were omitted). Statistical significance was considered as P<0.05.

In total we collected 167 trials and 288 strides of data for our 15 elephants, with a roughly eightfold mean forward velocity range of 0.62–4.92 m s^–1. Our in vitro analysis provided 18 valid trials of maximal joint ROM for the juvenile elephant (only three valid trials for the wrist) and 20 valid trials for the horse (horse data are presented in the Discussion). Where particular values for angles or angular velocities are shown below, mean values are used; the Tables (Tables 2, 3, 4; supplementary materialTables S1–S7) show the standard errors and N values.

Subjects B and C had mean (±s.d.) walking speeds of 1.08±0.17 m s^–1 and 1.52±0.36 m s^–1,respectively, ranging from 0.68 to 1.49 and 0.59 to 2.15 m s^–1. As the ears hid some skin markers, mid-stance upper arm and elbow joint measurements were only available for subject B (N=18 and 12, respectively). For the wrist, thigh, knee and ankle we obtained 88/52,76/57, 63/57 and 66/49 valid strides of data for the two subjects.

As the two subjects showed statistically significant differences(P<0.05), they were treated separately. No effect of trial number was found (P>0.05). The mid-stance angle data were all normally distributed except for the thigh and wrist from subject B (which were not subsequently analyzed). Speed only had a significant effect on subject B's knee joint angle and subject C's thigh segment angle (P<0.01), as the speed range was narrow. Except for these latter two angles, which showed a significant difference between marker sets (P<0.05), and the two excluded for non-normally distributed data, the remaining six angles showed a repeatable pattern at mid-stance (P>0.05).

Post hoc examination of the significantly different or non-normally distributed angles (and outliers) showed that, in most cases,markers had been replaced in positions that were slightly offset from the normal position, offsetting the entire segment/joint angle vs stride time curves upward or downward ∼5–10 deg. (cf. Figs 2, 3, 4); if manually shifted back to lie over the mean values (see Materials and methods), these differences disappeared. These results indicated that the placement of the skin markers was repeatable when conducted by the same experienced investigator and also that we needed to correct for offset angle vs stride time curves.

At a comfortable walking speed (Fr∼0.10), elephant limb segment and joint motions throughout the stride were generally quite smooth(Fig 2 and Fig 3). At mid-stance, the forearm, forefoot and thigh segments were all relatively vertical (within 4 11 deg.), whereas the upper arm, shank and hindfoot segments were less vertically inclined (–19, –23 and 38 deg. to vertical, respectively). Correspondingly, the elbow, wrist and knee joints were fairly extended at mid-stance (157 deg., 186 deg. and 152 deg.) but the ankle joint was more flexed (117 deg.). Touch-down and lift-off angles varied by <20 deg. from these values.

During the stance phase of the forelimb(Table 2; Fig. 2), the upper arm was retracted throughout stance, along with the forearm (which sometimes showed increasing segment angles very late in stance) and forefoot. The elbow and wrist joints both extended slightly, remaining almost static (but with hints of a shift from early flexion to extension in some strides), and then flexed late in stance (Fig. 3). Similarly, decreasing segmental angles in stance [shifting to negative (i.e. behind vertical) angular values at lift-off] prevailed for the hindlimb. The thigh was protracted slightly before lift-off, the shank showed a smooth rotation toward negative values throughout stance, whereas the hindfoot angle decreased steeply in late stance. The knee joint flexed throughout stance(most steeply in late stance but with a flexion–extension–flexion sequence in some strides) and the ankle joint flexed past mid-stance, with some extension very early in stance in some strides, then extended in the last third of stance (Fig. 3).

In earliest swing, segment angles continued to decrease (except for the thigh), then slightly later reached their minimum angles(Fig. 2), although more proximal segment angles tended to decrease little, or no further, from their lift-off values (0–3 deg.; Table 2). Segmental maximal swing angles occurred just before touch-down in the forelimb (angles decreasing gradually before touch-down) but closer to mid-swing in the hindlimb. Therefore, the segmental angles began decreasing from late swing through touch-down, rather than initiating this decrease in early stance. However, the presence of this late swing `retraction' was more variable for the upper arm and shank, especially at slower speeds. Elbow and wrist joint flexion during swing (Fig. 3; Table 2)exceeded the values for the knee and ankle (mean flexion of 20 deg. and 24 deg. from lift-off to minimal swing vs 12deg. and 4deg.,respectively). The elbow and wrist joints flexed and then extended steeply,beginning to shift back toward flexion in late swing. The knee joint flexed in early swing, then extended for most of swing with a brief flexion before touch-down. The ankle joint was unusual in that it remained almost static(near touch-down angle, with more gradual flexion in some strides) for the last half of swing after an early swing extension–flexion shift(Fig. 3).

The greatest ROM in the forelimb (Table 2) was for the forefoot segment and wrist joint (90 deg. and 66 deg.), with smaller values for more proximal segments and joints(36–52deg.). This is expected as the rotations of proximal segments contribute to the rotation of distal segments. In the hindlimb, the pattern was similar; the hindfoot segment was the most mobile (76 deg.), followed by the shank (55 deg.) and thigh (29 deg.), and the knee joint was slightly more mobile (42 deg. ROM) than the ankle (30 deg.). Overall, the upper arm segment was less vertical and had ∼50% larger ROM than the thigh segment, during stance phase and across a whole stride; some of this presumably relates to scapular motion.

As the elephants increased their speed across an almost eightfold speed range, from the slowest speeds we recorded (0.62 m s^–1; Fr=0.026) to the fastest (4.92 m s^–1; Fr=1.66), their segment and joint motions mostly changed continuously. Relatively small increases of joint and segment rotation(Fig. 4) and large changes of angular velocity (Fig. 5;discussed further below) relate to increased stride length and especially frequency [i.e. decreases of stance and swing time(Hutchinson et al., 2006)]. Movies 1 and 2 in supplementary material show representative motion capture data in real time for added comparison. Many segments and joints did not show significant changes of their angles with speed even from slow walking to faster running. Shifts between joint flexion and extension during stance became more obvious in many trials at higher speeds (cf. Figs 3 and 4; elbow, knee and ankle joint angles) but otherwise the sequence and timing of segment and joint motion did not markedly change.

In the present study, for brevity, we describe the significant changes from the slowest (û<0.25) to fastest (û>1.0)speeds (citing mean values from Figs 6, 7, 8, 9; supplementary materialTables S1–S4), but these changes became evident at different speeds within this range for each segment/joint and event. Non-significant trends(∼5 deg. changes) existed for other cases, not outlined here (cf. Figs 6, 7, 8, 9).

Forelimb segmental angles changed most markedly with speed (Figs 4 and 6; supplementary material Table S1) for the upper arm segment at mid-stance (–15 deg.), the forearm segment at minimal (–7 deg.) and maximal (+8 deg.) swing, and the forefoot segment angle at lift-off (+10–15 deg.), minimal (–13 deg.) and maximal (+21 deg.) swing. Joint angles reflected these changes(Fig. 6; supplementary materialTable S2). At speeds past the presumed gait transition point[(Ren and Hutchinson, 2008) û>0.50; speed range E–G in Fig. 6], notice that the trend for mid-stance angles in particular became markedly steeper, indicating increased limb flexion, especially for the upper arm and elbow.

In the hindlimb (Figs 4 and 7; supplementary material Table S1), the thigh segment angle showed only moderate changes (7–8 deg.),the shank angle decreased at mid-stance (–13 deg.) and minimal swing(–5deg.), and the hindfoot angle only changed in swing phase: –16 deg. for minimal swing and +14 deg. for maximal swing. Overall, the knee joint exhibited marginally larger increases toward flexion, and greater ROM, than the elbow, whereas the wrist shifted to become strikingly even more flexed during swing than the ankle joint, consistently with more than twice the ROM. By contrast, during stance, the ankle angle (changing from 116 deg. to 108 deg.) at mid-stance became even more flexed than the wrist angle(∼186–189 deg.). Again, at speeds past the presumed gait transition point (û>0.50; speed range E–G in Fig. 7), we observed steeper trends for thigh segment, knee joint and ankle joint mid-stance angle changes with speed; the hindlimb was becoming appreciably more flexed.

Joint and proximal segment angular velocities changed sharply with increasing speed (Figs5, 8, 9; supplementary materialTables S3 and S4). Some noisy fluctuations are present but the data do show the shifts of segment or joint angular velocities from positive to negative values, especially during stance phase (e.g. elbow, knee and ankle joints). The largest relative increases (as a multiple of values at û<0.25 vs û>1.0) of angular velocity were during stance, often around 7–9× (but 203× for shank touch-down), compared with ∼3× increases for swing-phase angular velocity and RAV. These changes concur with rapid decreases of stance (and swing) time in faster-moving elephants(Hutchinson et al., 2006). Thigh segment lift-off angular velocity showed the only shift of sign, from a mean value of 16 deg s^–1 at the slowest speed to –17 deg s^–1 at the fastest speed(Fig. 9).

Unsurprisingly, the largest absolute increases of angular velocity were for distal segments (supplementary material Table S3), especially RAV. Maximal swing velocity increases (positive values) were comparable for upper arm and thigh and for forearm and shank, but the increase in the forefoot was >50%larger than the increase in the hindfoot. There was a similar trend for velocity decrease – the largest decreases were for distal segments, but with comparable values among serially homologous segments (<–100 proximal, <–200 middle, >–300 deg. s^–1distal). We measured very similar trends for the joints(Figs8 and 9; supplementary material Table S4). Few, if any, limb segment/joint angular velocity values seemed to plateau at faster speeds (Figs 8 and 9; supplementary materialTables S3 and S4). As stride frequency and swing time reach their maxima and minima at Fr>1.0 (Hutchinson et al., 2006), this is unsurprising; elephants at the top locomotor speeds measured in the present study(Fig. 5; speed range G in Figs 8 and 9) should have reached close to their peak angular velocities. At the fastest speeds, wrist joint angular velocity ranged from –772 to +773 deg. s^–1 whereas the ankle ranged from –180 to +390 deg. s^–1; the elbow and knee velocity ranges were more similar at –258 and +319 deg. s^–1 and –223 and +328 deg. s^–1,respectively. Hence, overall, the maximal wrist RAV remained at least twice the RAV values of the other joints.

Maximal ROM values were 127, 115, 122 and 67 deg. for the elbow, wrist,knee and ankle for the elephant (identical qualitative patterns were also observed in the adult elephant). We estimate that, during high-speed locomotion, the more proximal joints used 31–40% of their available ROM whereas the more distal joints used 55–77%(Table 3).

Elephants did not significantly change their limb segment or joint angles across the sevenfold size range we observed (P>0.05). There were slight statistical differences among sizes (supplementary material Table S5),particularly <1000kg vs >3000kg, for the angles of the forefoot segment at maximal swing, thigh segment at touch-down, shank segment at mid-stance and lift-off and knee joint at minimal swing. Yet only the forefoot, thigh, shank and knee joint's minimal swing angles had consistent trends (slightly more extended joints in larger elephants) across the whole size range, and even these differences were slight. Total ROM also did not change significantly with size for any segments or joints (supplementary material Table S5).

Segment and joint angular velocities decreased markedly with increasing elephant size (Table 4), as expected from measured size-related differences in stride frequencies(Hutchinson et al., 2006). These reductions (most evident between <1000 kg and >3000 kg animals)occurred at different points in the stride for different segments and joints. Values for 1000–3000kg and >3000kg animals differed only marginally.

For the forelimb, we measured angular velocity decreases with size (toward zero values; supplementary material Table S5) for the upper arm at mid-stance and its RAV, the forearm at mid-stance, minimal and maximal swing and RAV; and the forefoot at maximal swing. No forelimb joints showed size-related decreases. For the hindlimb, angular velocity decreases were more widespread,occurring for the femur at mid-stance, maximal swing and RAV; the shank at all events except touchdown, and the hindfoot at mid-stance. In contrast to the forelimb, the knee joint showed large decreases for lift-off, minimal and maximal swing and RAV, although the ankle joint merely reduced its mid-swing angular velocity. Notably, touch-down angular velocity never showed a statistical size-related difference or clear trend for any segment or joint.

As with general footfall patterns, we found some slight statistical differences between limb segment and joint angles and angular velocities during normal walking in African and Asian elephants (supplementary materialTables S6 and S7). We detected a few statistically significant differences for the angular velocities of two segments and one joint: the forearm segment at minimal swing, forefoot segment at minimal swing and RAV, and knee joint at minimal swing (supplementary material Table S7). The mean differences (African minus Asian angular velocity values) were –25 deg. s^–1(25% of African value), 99 deg. s^–1 (26%), 116 deg. s ^–1 (15%) and –39 deg. s ^–1 (31%),respectively.

In this section, we scrutinize how well the stereotype of a columnar posture applies to elephants (i.e. how vertical are their limbs?), examine how much of their maximal range of motion elephant joints use during running (and relate these values to estimates for other species), compare and integrate our results with those of previous studies, discuss whether elephants show appreciable size or species differences in limb motions and, finally, consider how similar or different elephant limb motion is to published data for other species.

Considering other studies of footfall patterns(Hutchinson et al., 2006) and evidence for bouncing gaits at higher speeds(Hutchinson et al., 2003; Ren and Hutchinson, 2008), our results are changing how elephants are viewed: no longer simply the straight-limbed, inflexible juggernauts of classical literature. The present study shows that elephant limbs are more than just columnar legs for necessity, not for flexure. Flexion increases gradually with speed(Fig. 10), so the posture of an elephant at top speed is somewhat different from a slow-walking elephant– there is no single columnar posture adopted at all speeds. A fully columnar limb would incur large, potentially damaging, transient impact forces and jarring, expensive center of mass motions due to its infinite stiffness(Fischer and Blickhan,2006).

Few joints or segments are very columnar during stance (let alone swing);the limbs appear vertical but the underlying skeleton is only partly so(Fig. 10). In particular,during stance, the upper arm, shank and hindfoot segments remain at >20 deg. angles to the vertical, even during slow walking. Only the wrist joint behaves as a relatively static (i.e. with little motion) structure during stance; others maintain angles of <160 deg. and exhibit stronger flexion or extension motions. Furthermore, there are marked differences between limbs and joints (Gambaryan, 1974; Hildebrand, 1984; Hildebrand and Hurley, 1985);for example, in swing phase the wrist and knee joints move through moderate ROM arcs (89deg. and 49deg., respectively, vs <40 deg. for other joints/segments).

Our study refutes the notion that elephants have `inflexible' or `rigid'ankles (Gambaryan, 1974; Hildebrand, 1984; Hildebrand and Hurley, 1985; Paul, 1998). The ankle ROM(mean 37deg. vs 89deg.) and peak angular velocities (mean–180/+390degs^–1vs–772/+773degs^–1 in ankle vs wrist) are less than half those of the wrist [not less than one-fifth as in Hildebrand(Hildebrand, 1984)] even at Fr>1 but the movement is appreciable and not purely passive (but see Gambaryan, 1974). For example, ∼27deg. of ankle dorsiflexion occurs during swing, which is likely to be actively controlled in order to achieve ground clearance. As the ankle dorsiflexes and rebounds 15–20deg. during stance in running, and extensive elastic tissues cross the ankle joint(Gambaryan, 1974), there is the potential for elastic energy storage – it is probably incorrect to characterize elephants as having ankles that are not spring-like(Paul, 1998). Although the wrist uses a large ROM during swing phase, its stance phase motion is actually less spring-like than that of the ankle. Unlike plantigrade primates(Pike and Alexander, 2002) or digitigrade felids (Day and Jayne,2007), elephants do not hold their ankles (or knees in the additional case of felids) relatively static throughout the stride; the ankle is a dynamic structure. However, our in vitro study (see below) of elephant joint ROM shows that elephant ankles have low mobility relative to cats, dogs and horses (but not humans), which may simply correlate with their increased plantigrady, a speculation that deserves testing with data from other species.

A brief mention of the patterns of the segment/joint abduction and adduction we observed during locomotion in elephants is warranted here as,despite their size and graviportal, fairly upright limb structure, they clearly do use appreciable non-sagittal limb motions (see also Schwerda, 2003) that are obfuscated by labels like `columnar'. Although our markers were positioned lateral to joint centers and hence would generally lead to quantitative overestimates of abduction that are unreliable, we can safely infer qualitative patterns of motion orthogonal to flexion/extension motions that can apply to all speeds, sizes and species observed. Elephants smoothly adducted their upper arm and thigh from mid-swing through late-stance phase,then abducted. The elbow tended to be fairly static in adduction during stance, then abducted and adducted in swing, whereas the knee showed a similar motion to the upper arm and thigh but with markedly large swing-phase abduction [note that the knee joint's helical axis passively contributes to this motion (Weissengruber et al.,2006)]. The wrist remained quite static (more so than the elbow)in slight abduction during stance (much like its stasis in extension) and then quickly abducted, then adducted during swing. The ankle adducted throughout stance then abducted in late swing after being static in early swing. Overall,the magnitudes of swing phase abduction in the hindlimb tended to be markedly larger than those of the forelimb. Like Schwerda(Schwerda, 2003), we infer that elephants achieve foot-ground clearance during swing largely viaflexion of the wrist (which is much greater than ankle flexion) and abduction of the whole hindlimb (especially hip and knee). Thus, elephant limbs are often not as parasagittal as might be assumed.

We have also found that the `columar, graviportal vs crouched,cursorial' dichotomy also breaks down somewhat when other mammalian species,large and small, cursorial and not, are compared with elephants (see further below). Surprisingly, the columnar, graviportal limbs of elephants and the flexed, cursorial limbs of horses are posed rather similarly at comparable speeds, excepting differences in foot posture(Dutto et al., 2006; Marey and Pagès, 1887),a similarity that many functional studies have overlooked (see below). We feel that the differences between cursorial and graviportal limb structure and function have often been overstated – both are common in larger land animals and both tend to involve more straightened limbs as a size-related consequence (Biewener, 1989),along with other features (Coombs,1978).

Our results for elephant and joint ROM(Table 3) reject the null hypothesis that all joints use a similar fraction of their maximal ROM, as the amount of maximal ROM actually used in running (Fr>1) varies from 31 to 77%. Alternatively, perhaps more distal joints (wrists and ankles) of elephant limbs use a larger fraction of their maximal range of motion than more proximal joints (elbows and knees). This could be because, as in many animals, more distal joints of elephants use a wider absolute range of motion,presumably related to their lower segmental inertia(Gambaryan, 1974; Hildebrand, 1984; Hildebrand and Hurley, 1985; Marey and Pagès, 1887). This hypothesis is tentatively supported(Table 3).

A second alternative hypothesis is that, for reasons of safety, perhaps larger animals such as elephants stay far from their limits of joint motion(i.e. show positive allometry of the maximal ROM vs utilized ROM ratio). Few published data on maximal joint ROM in vivo and in vitro exist for other mammalian species that would draw elephants into such a broader context, but Table 3 shows comparative data for cats, dogs, humans, horses and elephants (∼4–4000 kg body mass). These data do not fit the ideal criteria of being drawn from the same individuals/breeds using identical methods (except for the elephant and horse methodology) and therefore demand careful interpretation. We infer that the proximal–distal decline of joint ROM found for elephants is not ubiquitous for all species but at least applies to elephants, horses and humans. Yet interestingly, for all species,the elbow and knee joints show more narrowly bounded (31–50% and 32–45%, respectively) percent usages of ROM, so the null hypothesis of there being no difference among joints may roughly apply to some homologous joints. There is a general trend for maximum possible joint ROM to decline with size, except for the ankle joint, which is similar in humans and elephants and strikingly different from other taxa including horses(Table 3). However, no clear scaling trend is evident for the percentage of maximal ROM used among homologous joints. Hence, the second alternative hypothesis is not supported.

The method used in the present study was limited in that we did not apply massive elephantine loads to the cadaveric material, which would provide an extra amount of flexion and extension. However, we felt that we were reaching reasonable approximations of maximal ROM as the joint ligaments and capsules seemed to be approaching their limits of failure. It is likely that elephants employ larger joint ROM during non-locomotor activities such as lying down, so the behavioral (not to mention mechanical, such as tissue stress and strain)context of ROM usage in animals remains a fertile ground for exploration, and the ROM of the scapula and shoulder/hip joints deserve investigation. We hope that this preliminary investigation of joint ROM inspires researchers to investigate this phenomenon in other species, which may reveal general principles of joint design and control.

Our limb motion data (using our mean values for Fr>1.0) concur with those from previous studies of Asian(Gambaryan, 1974; Marey and Pagès, 1887)and African (Alexander et al.,1979b; Hildebrand and Hurley,1985) elephant limb motions during running. However, the lack of data on marker placement and other methods, speed, size or other parameters makes comparison difficult; differences of 10–15 deg. are expected and evident among studies. The closest match among all studies is for thigh segment motion.

Overall, the results from the present study compare least well with Hildebrand and Hurley's study (Hildebrand and Hurley, 1985) and better with others (cited above). The former study (see also Hildebrand,1984) showed a less vertical upper arm segment and less extended wrist, knee and ankle joints, often with disagreement of 30–50 deg. with measurements observed in other studies. Joint center estimation surely contributed to some differences, especially for the toe `marker' this was positioned more laterally at midfoot rather than cranially on digit 3.

Two studies (Gambaryan,1974; Hildebrand and Hurley,1985) found much higher wrist ROM compared with our mean values(152 deg. and 104 deg., respectively, vs 89 deg.; the second value was observed in some of our faster individuals). Gambaryan's value was clearly a miscalculation [cf. fig. 113 and table 11 in Gambaryan(Gambaryan, 1974); total ROM in the former is ∼85deg.]. Our angles tended to be the most flexed of those observed, especially at mid-stance, although the figured angles of Marey and Pagès (speed unknown) and Alexander et al. (Fr>1.0) are generally similar (Alexander et al.,1979b; Marey and Pagès,1887). Aside from the differences already noted, ROM is generally larger in Gambaryan's study (we only found a much larger ROM in swing vs stance phase for the elbow, wrist and knee) but is otherwise roughly in agreement among studies, as are the typical patterns of flexion and extension.

We concur with Gambaryan that the more proximal segments of elephants(upper arm and thigh) switch between flexion and extension (or vice versa) twice per stride (using angular displacement to identify switches;Figs 2, 3, 4), whereas more distal joints typically switch four times (`biphasic' motion)(Gambaryan, 1974). A biomechanical or control-based explanation for these patterns remains elusive,and unfortunately angular velocity data are too noisy(Fig. 5) to provide deeper insight. In the present study, we have presented the first data on segment/joint angular velocities for elephants, although Hildebrand and Hurley used unspecified values (for an animal traveling at an unsubstantiated speed of 10 m s^–1) to calculate mechanical energies of the limb segments (Hildebrand and Hurley,1985). Our finding for the wrist joint's rapid flexion and extension (>720 deg. s^–1) is exceptional but other joints(even proximal segments) showed in our data peak rotations of >200 deg. s^–1.

Like footfall patterns (Hutchinson et al., 2006) and center of mass mechanics(Ren and Hutchinson, 2008),elephant limb motion changes almost continuously with speed. Differences are evident at the extremes (Hutchinson et al., 2003), but those extremes lie on a continuum. Our data show that the major changes of elephant limb motion with increasing speed are temporal (i.e. angular velocities; Figs 5, 8, 9). Likewise the slight increases of joint angular motions with speed we have measured would generate the observed stride length increases with speed(Hutchinson et al., 2006). The elongate limbs of elephants (Alexander et al., 1979a) allow even small increases of rotational arcs to contribute substantially to increasing stride length and thus speed. For example, proximal segments will still contribute the most to increasing step length – estimated stance phase scapular motion for walking elephants is 15±5 deg., contributing 55% of step length(Fischer and Blickhan, 2006; Schwerda, 2003); thigh motion is 23±1 deg. (our data), contributing up to 82% of step length(Fischer and Blickhan, 2006; Schwerda, 2003). However,measurements of these proximal segment and joint motions will still require advanced methodology that carefully takes into account the larger relative skin motions that are expected to occur proximally(Back et al., 1995a; Back et al., 1995b; Leardini et al., 2005; Reinschmidt et al., 1997; van Weeren et al., 1988; van Weeren et al., 1990). Rather than present flawed kinematic data for these motions, we prefer to accept the limitations of this study caused by excluding them and await more accurate measurements.

The observed increase of limb flexion (especially at mid-stance,particularly past û=0.50; Figs 6 and 7) with speed is consistent with the hypothesis that elephants shift to bouncing gaits(Hutchinson et al., 2003; Ren and Hutchinson, 2008) and are, in a sense, `Groucho running'(McMahon et al., 1987). The hindlimbs (generally more flexed than the forelimbs) have already been inferred to involve some bouncing at moderate speeds(Ren and Hutchinson, 2008). Yet, as even the forelimbs became more flexed at the fastest speeds we observed (Fr>1.0), this leaves open the possibility that there are bouncing forelimb mechanics at such speeds. Fig. 10 and supplementary material Movies 1 and 2 summarize the moderate changes of limb motion with speed. In particular, a flattening of the hip (and shoulder) arc of motion during stance is evident (Fig. 10), although this motion is less concave in the trial shown than described for other elephants (Hutchinson et al., 2003; Hutchinson et al., 2006).

Although our fastest speed data (4.92 m s^–1; Fr=1.66) are not as speedy as the near-maximal documented velocities for athletic elephants (6.8 m s^–1; Fr>2.5)(Hutchinson et al., 2006), our data (e.g. Figs 6, 7, 8, 9) could be extrapolated to estimate kinematics at greater speeds, with the caveat that at these speeds stride frequency is probably already at its maximum, and hence increased joint angular excursions, rather than velocities, should play a larger role in speed increase (Hutchinson et al.,2006).

We found no major differences between the motions of smaller and larger elephants, except for the lower angular velocities reached by many segments and joints in larger elephants (Table 4), and so conclude that there are no biologically significant size-related differences in elephant limb kinematics. This concurs with intraspecific data for other animals (e.g. Pennycuick, 1975), unlike broad interspecific scaling trends for other species(Biewener, 1989; Biewener, 1990; but see Day and Jayne, 2007). Likewise, as the differences between African and Asian elephants are so relatively small (supplementary material Tables S6 and S7), we conclude that no profound biological differences exist for their locomotor dynamics(Hutchinson et al., 2006; Ren and Hutchinson, 2008).

Our conclusions should apply well to other members of the elephantid crown group such as mammoths, at least where limb proportions(Pike and Alexander, 2002) and other aspects of locomotor morphology overlap with extant elephants (e.g. Christiansen, 2007). Even small dwarf elephants may not have differed in posture from extant elephants,although there is tantalizing anatomical evidence that this may not be the case (Roth, 1992). Yet,because some elephantids reached masses of >10,000kg(Christiansen, 2004),biomechanical constraints might have imposed more severe limits on limb angles and ROM [see Hutchinson et al. (Hutchinson et al., 2006) for examples of intraspecific locomotor scaling].

How different are elephant limb motions from bipedal, smaller, less long-legged or more cursorial animals? As humans have a similar hindlimb design to elephants (Weissengruber et al.,2006) (e.g. long femur and short tibia, large functionally plantigrade foot) despite their bipedalism, it is interesting to compare their limb motions. These were previously described as quite similar, except for the damping, compressive and more digitigrade feet of elephants and slightly greater limb flexion of humans (Marey and Pagès, 1887). Otherwise, the patterns compare well(Fig. 11). Elephants also exhibit similar total limb protraction and retraction angles to humans[∼22 deg. (Novacheck,1998; Schwerda,2003; Seyfarth et al.,2003)]. The main differences we find are the smoother motions[attributed by Gambaryan (Gambaryan,1974) to fascial sheets] and smaller ROM of elephant limbs. Even the foot motions of elephants and humans are similar (especially in stance),despite some anatomical differences, although the more horizontally oriented feet of humans indicate some differences, at least in relative joint moments.

Elephant stance phase segmental and joint ranges of motion are also surprisingly similar to those observed in trotting horses [3–4 m s^–1 (Back et al.,1995a; Back et al.,1995b; Dutto et al.,2006)], although toe joint motions in elephants remain unknown[cf. Figs 2, 3, 4, 10 and figs 3 and 4 in Dutto et al.(Dutto et al., 2006)]. Elephants also have more flexed ankles and more extended wrist joints than horses. This fundamental similarity was recognized long ago(Marey and Pagès, 1887)but has since been largely forgotten by comparative analyses. Knee flexion in elephants exceeds that in trotting horses. Horses can thus be only marginally less columnar than elephants and even more columnar for some joints (e.g. ankle, knee). Our in vitro analysis also shows similar maximal joint ROM for the elbow and knee in horses and elephants, among other similarities(Table 3). This evidence has been overlooked by many previous qualitative studies of functional anatomy and the cursorial–graviportal continuum (e.g. Bakker, 1986; Gregory, 1912; Gambaryan, 1974; Hildebrand, 1984; Paul, 1998; Paul and Christiansen,2000).

In many ways, limb motion in elephants is typical of walking, and even running, in smaller quadrupedal mammals. As widely recognized, elephants generally adopt straighter limbs but their limbs still use poses and ROM that are similar, or identical, to those of smaller animals, not just humans and horses. The ROM of elephant limbs (particularly in swing phase but also in stance) overlaps the ROM used even by many small mammals, although the ROM of elephants can be smaller than some values in much smaller cursorial taxa (e.g. Day and Jayne, 2007). For example, in the stance phase of walking, elephants and many other mammals retract their thigh segment or extend their hip joint across an arc of 20–40 deg. and flex the knee through ∼25–50 deg., with similar values for the forelimb, although elephants flex their elbows and ankles through smaller arcs during stance (9 deg. and 12 deg. vs 30–40 deg.) (Table 2; Figs 3 and 4)(Fischer et al., 2002; Pike and Alexander, 2002). The rather static stance-phase patterns of the elbow and especially wrist joints of elephants are also observed in trotting horses [wrist(Back et al., 1995a)], dogs[elbow (De Camp et al., 1993)]and, at least, walking felids [wrist in particular(Day and Jayne, 2007)]. As such stasis is less evident in smaller mammals(Fischer et al., 2002) it is tempting to speculate that it relates to a more vertical limb orientation,cursoriality–graviportality and body size.

Like many other mammals, elephants use late swing-phase limb retraction at all speeds (Day and Jayne,2007; Fischer et al.,2002), unlike humans who only use it during running. This allows limb protraction to be modulated at touch-down in response to locomotor perturbations, contributing to stability(Seyfarth et al., 2003). Hildebrand and Hurley contended that elephants do not exhibit segmental retraction after lift-off or just before touch-down(Hildebrand and Hurley, 1985),but these patterns indeed were evident in our elephants, even at slower speeds[except where noted in the Results; also see figs 115 and 116 in Gambaryan(Gambaryan, 1974)].

Elephants change their limb motions moderately with speed, unlike many smaller mammals (Fischer et al.,2002). As in other moderately-large mammals(Gambaryan, 1974), elephants use somewhat less biphasic distal joint motion (flexion-extension switches;see above) during stance [cf. fig. 5 in Pike and Alexander (Pike and Alexander, 2002) for Perissodactyla and Artiodactyla; Day and Jayne (Day and Jayne, 2007)for felids] than in smaller mammals (e.g. Fischer et al., 2002). The simpler flexion and then ∼50 deg. extension of the knee during swing most resembles that observed in some Carnivora[(Day and Jayne, 2007) see fig. 5 in Pike and Alexander(Pike and Alexander,2002)].

We have compiled a large dataset of 288 strides from 15 elephants of both major extant species, covering a sevenfold size range and an eightfold speed range. We hope that our analysis of skin-marker placement, and caution about skin motion errors (e.g. scapula, shoulder and hip motion), stimulates further progress for other comparative studies, which have lagged behind progress on human and horse skin motion artefacts (e.g. Back et al., 1995a; Back et al., 1995b; Cappozzo et al., 1996; Filipe et al., 2006; Fischer et al., 2002; Leardini et al., 2005; Reinschmidt et al., 1997; van Weeren et al., 1988; van Weeren et al., 1990; but see Gatesy, 1999; Rubenson et al., 2007). Here we have shown that elephant limb motions: (1) do not simply involve a vertical(or parasagittal) columnar posture [`mobile Doric columns'; p. 214 in Bakker(Bakker, 1986)] – limb motion changes gradually with speed, and some joints are quite flexed during stance, showing potential for elastic energy storage even in the purportedly inflexible ankle; (2) exhibit appreciable differences within and between limbs– the wrist has roughly double the range of motion and peak angular velocities of the ankle, yet the wrist is quite static during stance whereas the knee is the most mobile joint in the hindlimb; (3) have a general proximal distal increase in how much of maximal ROM is used at faster speeds (as in, at least, humans and horses); (4) contribute to speed changes mainly viaangular velocity, which can be quite large (>720 deg s<sup>1</sup> in flexion and extension for the wrist), although an increased ROM occurs for some segments and joints; (5) reduce their angular velocity as size increases but otherwise do not change; (6) are essentially identical for African and Asian species despite some anatomical differences; and finally (7) are more similar to those of smaller mammals than has previously been acknowledged. Elephant limbs have a more limited ROM for some segments/joints and are, of course, more straight-legged on average – but barely so relative to walking humans or especially to trotting horses. Elephant limb motions fall on a continuum that does not dichotomize neatly into `flexed, cursorial' and`columnar, graviportal' categories. To a certain extent, the term columnar obscures more information about elephant locomotion than it conveys and, as such, is sometimes not a useful term in light of modern understanding of locomotor dynamics. The limb motions of running horses are mostly only trivially less columnar than those of elephants or are actually more columnar for some distal joints. These data demonstrate that limb configuration and running ability [top speeds <20 m s^–1 in horses, ∼7 m s^–1 in elephants(Hutchinson et al., 2006)] are not as tightly associated as sometimes assumed (e.g. Bakker, 1986; Paul, 1998; Paul and Christiansen, 2000). The data provided are useful not only in the comparative context emphasized here, but also for future studies of locomotor mechanics and as baseline data for clinical gait analysis of elephants.

LIST OF ABBREVIATIONS

 
• Fr

  Froude number

 
• h

  hip height

 
• g

  acceleration due to gravity

 
• RAV

  range of angular velocity

 
• ROM

  range of motion

 
• v

  velocity

 
• û

  dimensionless speed (Fr^0.5)

For their expert assistance with elephants we thank Anthony Tropeano and staff (Colchester Zoo, UK), Andrew Plum and staff (West Midlands Safari Park,UK), Lee Sambrook and staff (Whipsnade Wild Animal Park, UK), Thüringer Zoopark Ehrfuhrt (Germany) staff, and Richard Lair and the staff of the Thai Elephant Conservation Centre (Thailand) and Forest Industry Organization. We thank Karin Jespers for her assistance with Qualisys data collection in the UK, as well as Daniel Seng (Qualisys, Inc.) and Thanasit Ujjin (United Sports Trading Pvt, Ltd.) for assistance in Thailand. Advice on statistical analyses was kindly provided by Renate Weller and Zhangrui Cheng. J.R.H. thanks the BBSRC for New Investigator research grant number BB/C516844/1 awarded in 2005,and the Department of Veterinary Basic Sciences (The Royal Veterinary College)for financial support. Hearty thanks for constructive input on this work are due to Steve Gatesy and three anonymous reviewers. Aid with conducting the Thailand data collection was provided by Norman Heglund, Patrick Willem,Giovanni Cavagna, Joakim Genin and others.