Inertial properties of hominoid limb segments


Dr Karin Isler, Anthropologisches Institut und Museum, Universität Zürich-Irchel, Winterthurerstr. 190, 8057 Zürich, Switzerland. T: +41 1635 54 33; F: +41 1635 68 04; E:


Quantitative, accurate data regarding the inertial properties of body segments are of paramount importance when developing musculo-skeletal locomotor models of living animals and, by inference, their ancestors. The limited number of available primate cadavers, and the destructive nature of the post-mortem, result in such data being very rare for primates. This study builds on the work of Crompton et al. (Am. J. Phys. Anthropol. 1996, 99, 547–570) and reports inertial properties of the body segments of gorillas, chimpanzees, orang-utans and gibbons. Segment mass, centre of mass and the radius of gyration of five ape cadavers were measured using a complex-pendulum technique and compared with the results derived from external measurements of segment lengths and diameters on the same animals. With additional data from external measurements of eight more hominoid cadavers, and published data, intergeneric differences between the inertial properties and the distribution of mass between limb segments are analysed and related to the locomotor habits of the species. We found that segment inertial properties show extensive overlap between ape genera as a result of large interindividual variation. Segment mass distribution also overlaps between apes and humans, with the exception of the shank segment. However, owing to a different distribution of mass between the limb segments, the centre of mass of both the arms and the legs is located more distally in apes than in humans, and the natural pendular period of ape forelimbs is larger than that of the hindlimbs. This suggests that, in contrast to the limbs of cursorial mammals and cercopithecoid primates, hominoid limbs are not optimized for efficiency in quadrupedal walking, but rather reflect a compromise between various locomotor modes. Common chimpanzees may have secondarily evolved a more efficient quadrupedal gait.


Locomotion in non-human primates has become an important field of research, and studies can further our understanding of the evolution of locomotor specializations in primates and the origin of human bipedality (reviewed in Ward, 2002; Schmitt, 2003). However, to develop musculoskeletal models of living primates and, by inference, of their ancestors, quantitative data regarding the inertial properties of the body segments as well as morphometric properties of the limb muscles are essential. Such data have been published for quadrupedal monkeys such as Macaca mulatta (Vilensky, 1979; Cheng & Scott, 2000), Papio (Reynolds, 1974; Raichlen, 2004, 2005b) and one Lemur fulvus subject (Wells & DeMenthon, 1987), but are largely unavailable for hominoid primates, i.e. chimpanzees, gorillas, orang-utans and gibbons (Gibbs et al. 2002) because of the rarity of ape cadavers and the destructive nature of the post-mortem. Crompton et al. (1996) have published details of the inertial properties of five great ape cadavers. They measured the body segments of four specimens of Pan troglodytes and a juvenile Pongo pygmaeus with a complex-pendulum technique. However, this is a very small sample from which to draw precise conclusions regarding interspecific differences in segment inertial proportions, which may be applied to fossil material. As a consequence, the major aim of this study was to present a broader data set of segment inertial data that may be used for biomechanical studies such as (inverse) dynamic analyses of hominoid movement, and for musculoskeletal modelling by superimposing body shape on known locomotor performance (Kramer & Eck, 2000; Ward, 2002; Sellers et al. 2004). To this end we present segment inertial data on a further five ape cadavers.

Although access to ape cadavers for dissection is extremely rare, non-invasive external measurements of cadavers may be more frequently possible, e.g. when a specimen is to be preserved for public exhibition. In this case it is still possible to derive inertial properties from external measurements of the length and diameters of body segments before preparation. Crompton et al. (1996) provided a geometric model based on truncated cones with elliptical or circular cross-sections. In this study, the limb segments of the segmented specimens and eight additional intact hominoid primates were measured externally and their inertial properties calculated according to Crompton et al. (1996). Thus, for the first time a comparison of the results obtained by external measurements and the double-pendulum technique is possible, based on the limb segments of five cadavers.

The superfamily Hominoidea comprises humans and the four ape genera, Gorilla (gorillas), Pan (chimpanzees and bonobos), Pongo (orang-utans) and Hylobates (gibbons), which differ from Old-World monkeys (Cercopithecoidea) in several post-cranial features that are related to the apes’ more frequent use of orthograde modes of locomotion such as vertical climbing and arm-hanging (Hunt, 1991). Despite these shared morphological features, extant hominoids differ considerably in their locomotor habits. The Asian hominoids, Pongo and Hylobates, are almost completely arboreal. The large-bodied orang-utans move slowly and cautiously with the majority of their locomotion being torso orthograde clamber and suspension (Sugardjito, 1982; Sugardjito & van Hooff, 1986; Cant, 1987; Thorpe & Crompton, in press), whereas the slender gibbons use rapid arm-swinging (brachiation), jumps and use a considerable amount of bipedal walking (Fleagle, 1976), but which is quite different from human bipedalism (Yamazaki & Ishida, 1984). The African apes (gorillas, chimpanzees and bonobos) are also adept climbers, but they often walk quadrupedally on the ground, in a locomotor mode called knuckle-walking (reviewed in Doran, 1996). In this locomotor mode, the hand contacts the substrate with the dorsum of the second phalanx. All living hominoids including humans exhibit a broad thorax, a stable lumbar region of the vertebral column and the absence of an external tail, but they differ in numerous details of post-cranial morphology (for a recent quantitative comparison of muscle geometry, see Payne et al. 2006a,b). Locomotor habits might also be reflected in the geometric shape of the limbs. Cursorial mammals show a more proximal distribution of limb mass than non-cursorials (Hildebrand, 1985), which may be an adaptation for reducing the energy costs of swinging distally heavy limbs (Lieberman et al. 2003). We would therefore expect the distribution of limb mass to be more proximal in primates that frequently move quadrupedally on the ground or on horizontal branches, whereas primates that are primarily climbing or clambering need stronger gripping muscles leading to a more distal distribution of limb mass. Thus, interspecific differences or similarities in the geometric properties of the limbs may help us to understand the relationship between limb geometry and locomotor profile in extant animals, which in turn will allow greater accuracy in the modelling of extinct species and increase our understanding of the way in which locomotor specializations evolve. The distribution of mass between body segments can further be compared with the results that Zihlman and co-workers obtained with a slightly different dissection technique (Zihlman, 1984; Morbeck & Zihlman, 1988; Zihlman & McFarland, 2000).

Animals of moderate and large body size move their limbs approximately with an energetically optimal swing period, the natural pendular period (NPP), during quadrupedal walking (e.g. Hildebrand, 1985). The NPP of a limb is the duration of time it takes to swing through one complete oscillation if it were swinging as a pure pendulum. At this oscillation period the exchange between potential and kinetic energy is maximal, and the metabolic energy required to maintain swinging is minimal. Although the swing phase of human walking is not a passive movement (Whittlesey et al. 2000), it can be assumed that actual stride periods do not differ largely from the NPP of a limb during casual walking (Hildebrand, 1985). For quadrupedal animals, it is advantageous to have very similar NPPs in the fore- and the hindlimbs, as all four limbs need to swing with the same frequency during quadrupedal walking. This has been previously demonstrated for domestic dogs (Myers & Steudel, 1997) and yellow baboons (Raichlen, 2004). With the data we have collected for ape limbs, the hypothesis of frequency matching can now be tested for hominoids. It would be expected that the NPPs of fore- and hindlimbs should be more similar in the African apes, which often walk quadrupedally, and less similar in the Asian apes owing to their increased levels of forelimb-dominated, arboreal locomotion. For habitual bipeds, the NPPs of the upper and lower limb might equally be expected to match, but Wang et al. (2003) have proposed that in human evolution selection may rather have operated in the genus Homo so as to match NPPs when loads are carried in the hand.

Materials and methods

All animals used in this study died from natural causes or due to accidents. The study material for the segmentation technique comprised the following cadavers (Table 1): two adult male gorillas (Gorilla gorilla gorilla, Gg1 and Gg2), two juvenile orang-utans (Pongo pygmaeus abelii, Po1 and Po2) and an adult female gibbon (Hylobates lar, Hy1). All animals were fresh-frozen and eviscerated prior to receipt.

Table 1.  Primate cadavers
SubjectSpeciesAgeSexWeight (kg)PreservationOrigin§
  • Subjects marked with an asterisk were used for both the external measurement and segmentation techniques. All other subjects were measured externally only.

  • Estimated body weights were determined from external measurements and from comparisons with intact specimens. All individuals are of normal body build, with the exception of Po4 which showed an accumulation of fatty tissue in the trunk and neck.

  • §

    Origins: Bristol = The North of England Zoological Society, UK; Basel = Zoologischer Garten Basel, Switzerland; Zürich = Zoo Zürich, Switzerland; Rapperswil = Knie's Kinderzoo Rapperswil, Switzerland.

Gg1*Gorilla gorilla gorillaadult (30 years)male∼150frozenBristol
Gg2*Gorilla gorilla gorillaadult (40 years)male∼165frozenBasel
Gg3Gorilla gorilla gorillaadult (32 years)male∼125formalinBasel
Gg4Gorilla gorilla gorillaadult (15 years)female ∼90frozenZürich
Pa1Pan troglodytesadultmale ∼40formalinZürich
Po1*Pongo pygmaeus abeliijuvenile (5 years)female  12.5frozenZürich
Po2*Pongo pygmaeus abeliijuvenile (6 years)male ∼18.5frozenZürich
Po3Pongo pygmaeus abeliijuvenile (∼5 years)male ∼13formalinZürich
Po4Pongo pygmaeus pygmaeusadult (36 years)male112formalinZürich
Hy1*Hylobates laradult (16 years)female   4.65frozenRapperswil
Hy2Hylobates laradultmale     ∼5.4formalinRapperswil
Hy3Hylobates laradult (∼7–8 years)female    6.9formalinRapperswil
Hy4Hylobates syndactylusadult (22 years)male   13.1freshZürich

To allow an optimum use of valuable ape cadavers, we collected data on both inertial properties of the limb segments and on muscle geometry and morphology simultaneously, using separate sides of the body for each technique. The latter are reported in Payne et al. 2006a,b). For the present study one side of the body was measured externally using the method detailed below, and then cut into segments, and its inertial properties determined following the method of Crompton et al. (1996). The body was divided into the following eight segments: head, trunk, upper arm, forearm, hand, thigh, shank and foot. Segmentation was performed by careful dissection of thawed specimens, cutting them so that the musculature was divided between adjoining segments in one plane passing through the estimated location of the joint centre. The legs and arms of one gorilla (Gg2) had been cut off prior to receipt, but the cuts seemed to be reasonably close to the section line that would have been chosen by us. After refreezing, the inertial data were determined using a complex-pendulum technique (see Crompton et al. 1996). In this technique, the number of swing cycles completed by a segment-frame assembly about two parallel axes in a given time is counted. The hands and feet were swung in both sagittal and coronal orientation, as well as any other segments with a pronounced non-circular cross-section. As the normal resting configuration of the hands and feet of non-human primates is with flexed fingers or toes, specimens were frozen and measured with flexion of the second interphalangeal joint. However, the inertial properties of the hands and feet depend heavily on the exact position of the fingers and toes, respectively, which prevents a meaningful interspecific comparison. As the trunk and head were severely damaged by post-mortem examinations in all specimens but one gorilla (Gg1), inertial properties of these segments were estimated from external measurements of length and diameters. For this reason, we did not conduct an interspecific comparison of the head and trunk segments.

Additionally, external measurements of the body segments were taken from eight intact hominoid specimens of Gorilla gorilla gorilla, Pan troglodytes, Pongo pygmaeus abelii, Pongo pygmaeus pygmaeus, Hylobates lar and Hylobates syndactylus (Table 1). For each segment, the length and the proximal, middle and distal diameters were recorded. We measured each segment diameter in both coronal and sagittal directions with an accuracy of 0.5 cm in the larger segments and an accuracy of 0.25 cm in the smaller segments. If the two diameters differed by less than this value, the mean value was used and a circular diameter was supposed. Mean values for left and right body sides were calculated for specimens Gg4, Po2, Hy1, Hy4, the upper limbs of Gg2 and Po4 and the lower limbs of Pa1. In the other specimens, only one side of the body was measured. The mass and inertial properties such as the location of the centre of mass and the principal moments of inertia were calculated using the algorithm given in Crompton et al. (1996). The radius of gyration (rg) of a segment is defined as the square root of the principal moment of inertia (pmi) divided by the mass (m) of the segment:


An object with equal mass that is distributed as a point one radius of gyration away from the centre of rotation would have the same rotational inertia as the segment. To normalize moments of inertia with body size, the radius of gyration is expressed as a percentage of segment length (Cheng & Scott, 2000). The mass density was assumed to be 1 for all segments. In reality, the mass and moments of inertia would be about 4–10% higher, being larger in distal segments than in the head or trunk (Crompton et al. 1996). However, as these values are based on only one chimpanzee, they are not applied in our study.

For many individuals, the total body mass prior to evisceration was not known (see Table 1), but was estimated from external measurements of the available body segments and subsequent comparison with specimens with known body weight. In consequence, comparisons between individuals are not conducted relative to body weight, but only relative to the sum of the masses of the four limbs.

The overall shape of a limb is reflected in the period with which it would swing, if suspended from its proximal end. This parameter, the NPP is defined as:


with mi being the moment of inertia of the limb about its proximal end (i.e. hip or shoulder joint), m the mass of the limb and CoM the distance of the centre of mass from the proximal end of the limb. In this study, the NPP was calculated for outstretched limbs. The foot was assumed to be positioned at 90° to the lower leg segment, whereas the position of the hand was continuous with the forearm as in knuckle-walking. Fingers and toes were bent in the proximal interphalangeal joint.

Additionally, the data of one juvenile Pongo pygmaeus (Po5) and four Pan troglodytes (Pa2, Pa3, Pa4 and Pa5) from Crompton et al. (1996) are included in the comparisons. Segment weights of one Pan troglodytes and one Pan paniscus from Zihlman (1984), two Pongo from Morbeck & Zihlman (1988) and four Gorilla gorilla gorilla from Zihlman & McFarland (2000) are also included, where appropriate. Subject data for the these specimens are summarized in Table 2. Intergeneric comparisons were conducted with the non-parametric Kruskal–Wallis test and post-hoc tests (Zar, 1998). All individuals from one genus were pooled for these tests, neglecting possible sexual dimorphism as the sample size is too small to allow even tentative analysis of this factor. To enable a comparison with humans, the inertial data for 100 adult male human cadavers were taken from Zatsiorsky (2002).

Table 2.  Published subject data on hominoid body segments
IndividualSpeciesAgeSexWeight (kg)Source*
Gg5Gorilla gorilla gorillaadult (27 years)female99.5a) female a
Gg6Gorilla gorilla gorillaadult (38 years)female159.1a) female b
Gg7Gorilla gorilla gorillaadult (36 years)male172.7a) male a
Gg8Gorilla gorilla gorillaadult (36 years)male211a) male b
Pa2Pan troglodytesadultfemale33.1b) Pan 1
Pa3Pan troglodytesadultfemale47.1b) Pan 2
Pa4Pan troglodytesinfantmale4b) Pan 3
Pa5Pan troglodytesadultmale57.1b) Pan 4
Pa6Pan troglodytesadultfemale31.5c)
PpPan paniscusadult (24 years)female29.5c)
Po5Pongo pygmaeusjuvenilemale19.8b)
Po6Pongo pygmaeusadult (9 years)female27.8d)
Po7Pongo pygmaeus pygmaeusadult (15–20 years)male102d)


Comparison of methods

The mass, location of the centre of mass and radii of gyration of the body segments of each specimen studied are given in Table 3. Scaled data are shown to enable comparisons between different sized individuals and species. However, a rather low radius of gyration as a percentage of segment length may still result in high internal energy rates if it is combined with a long segment and fast movements.

Table 3.  Inertial properties of hominoid body segments
IndividualLength (m)Mass (kg)CoM (%)*rg x (%)rg y (%)
  • *

    The position of the centre of mass (CoM) is expressed as the distance from the proximal joint centre as a percentage of total segment length. In the case of the feet, trunk and head, the values are defined with reference to the calcaneal tuberosity (foot), the centre of the acetabulum (trunk) and the external occipital protuberance (head).

  • The radii of gyration (rg) in the sagittal (x) and coronal (y) orientation are derived from the principal moments of inertia, i.e. about the centre of mass of the segment.

 Gg10.89433.900 (evisc.) 49.0 27.0 29.0 
 Gg20.770 52.669 52.2 31.2 28.9
 Gg30.680 81.579 48.6 33.0 29.2
 Gg40.650 38.743 49.6 31.7 29.2
 Pa10.430 12.857 47.3 31.1 29.0
 Po10.280 6.787 46.8 32.9 31.4
 Po20.350 9.778 46.0 31.5 29.0
 Po30.330 6.446 49.3 31.0 28.8
 Po40.650 50.781 45.9 33.2 30.4
 Hy10.245 2.603 48.2 31.1 29.4
 Hy20.220 1.484 43.0 30.9 30.1
 Hy30.295 2.573 49.4 29.4 28.5
 Hy40.320 5.712 44.2 31.9 29.9
 Gg10.3708.900 16.2 33.7 33.7 
 Gg20.350 9.717 43.4 29.9 29.9
 Gg30.340 8.394 42.6 29.4 29.4
 Gg40.300 5.502 45.2 30.2 30.2
 Pa10.220 2.675 49.1 29.4 29.4
 Po10.170 0.832 50.0 27.9 27.9
 Po20.195 1.419 50.0 28.2 28.2
 Po30.170 1.613 53.5 31.1 31.1
 Po40.310 15.810 51.2 32.4 32.4
 Hy10.110 0.376 43.7 30.8 30.8
 Hy20.116 0.383 45.9 30.1 30.1
 Hy30.118 0.433 43.9 30.7 30.7
 Hy40.140 1.034 46.8 32.9 32.9
 Gg30.350 3.762 45.1 30.3 30.1
 Gg40.380 4.069 51.3 30.7 30.2
 Pa10.300 1.388 46.9 30.0 30.0
 Po10.2400.675 0.71742.240.726.828.826.828.2
 Po30.220 0.289 46.3 30.6 30.6
 Po40.420 4.803 49.0 29.6 29.5
 Hy20.240 0.118 50.0 29.0 29.0
 Hy30.217 0.231 48.0 28.5 28.4
 Hy40.280 0.348 39.0 29.4 29.3
 Gg30.350 2.266 48.5 29.5 29.0
 Gg40.345 2.248 41.6 29.5 29.2
 Pa10.290 0.865 44.4 29.3 29.3
 Po30.240 0.330 45.7 29.9 29.9
 Po40.430 3.600 48.4 29.0 28.6
 Hy20.280 0.112 44.1 27.9 27.9
 Hy30.275 0.186 46.1 28.8 28.7
 Hy40.315 0.235 46.2 28.1 28.0
 Gg30.185 1.335 51.2 32.7 29.7
 Gg40.180 0.654 52.8 31.2 28.8
 Pa10.200 0.397 52.8 29.0 27.8
 Po30.150 0.256 50.0 29.5 28.3
 Po40.185 1.170 50.4 33.3 30.9
 Hy20.110 0.045 52.0 28.0 27.1
 Hy30.110 0.088 50.3 29.1 27.9
 Hy40.120 0.078 49.3 30.3 29.7
 Gg30.270 3.356 44.6 33.1 30.0
 Gg40.255 4.014 41.0 33.9 32.1
 Pa10.240 1.907 43.8 29.9 29.9
 Po30.150 0.339 46.5 31.5 31.5
 Po40.285 3.846 46.0 32.3 30.9
 Hy20.200 0.130 50.0 29.6 29.5
 Hy30.190 0.223 43.7 28.8 28.6
 Hy40.230 0.504 47.1 30.4 29.8
 Gg30.320 2.554 48.6 29.8 29.4
 Gg40.300 2.301 45.1 30.7 30.2
 Pa10.230  0.847 46.4 29.9 29.9
 Po30.180 0.257 47.8 30.7 30.7
 Po40.315 1.860 50.0 30.1 30.1
 Hy20.210 0.077 50.6 27.6 27.5
 Hy30.185 0.105 44.4 29.1 29.1
 Hy40.215 0.208 45.3 28.6 28.5
 Gg30.235 1.255 48.5 29.3 28.3
 Gg40.200 0.938 49.6 29.0 28.0
 Pa10.220 0.483 46.7 28.2 27.5
 Po30.160 0.254 50.0 29.1 28.8
 Po40.280 1.349 50.0 29.7 29.7
 Hy20.109 0.053 47.5 26.8 25.8
 Hy30.110 0.068 48.4 27.1 25.8
 Hy40.120 0.166 49.9 27.7 25.5

Both complex pendulum measurements as well as estimations from external measurements of segment diameters are reported for five specimens. The segment mass estimated from external measurements was highly correlated with the actual weighed mass of the limb segments (r2 = 0.998, Fig. 1A). The estimated location of the centre of mass was also correlated with the location of the centre of mass measured with the complex-pendulum technique, albeit with a somewhat higher amount of variation (r2 = 0.956, Fig. 1B). The location of the centre of mass of both hands and feet was most often estimated more distally, whereas no systematic bias could be detected in proximal and middle limb segments. In gorilla Gg2, the centre of mass of the upper arm and thigh segments were measured to be at a relatively distal location with the complex-pendulum technique (Table 3). The arms and legs of this individual were cut off during post-mortem examination, and deformation might have occurred. For further comparative analyses, data from complex-pendulum measurements were used for those five specimens, and data from external measurements for the other specimens.

Figure 1.

Least-squares regressions of segment mass (A) and of the location of the centre of mass (B) as obtained by modelling the segments from external measurements compared with measurements with the complex-pendulum technique (specimens g1 = Gg1, g2 = Gg2, h1 = Hy1, p1 = Po1 and p2 = Po2). (A) ln(mass estimated from external measurements) = 1.025 ln(mass determined by double-pendulum) − 0.035, correlation coefficient r2 = 0.996. (B) ln(centre of mass estimated from external measurements) = 0.956 ln(centre of mass determined by double-pendulum) + 0.113, r2 = 0.957. Lines x = y are dashed.

Distribution of mass between segments

The distribution of mass between segments, as a percentage of total limb weight, is reported in Table 4, together with published data. As the values of Zihlman (1984), Morbeck & Zihlman (1988) and Zihlman & McFarland (2000) are very similar to our results, we have pooled all data for a statistical intergeneric comparison between Gorilla, Pan, Pongo and Hylobates. Kruskal–Wallis tests yielded significant differences for forearm, hand and thigh weight relative to total limb weight between the hominoid genera (Table 5). Post-hoc tests revealed that Pan has heavier thighs than Pongo, and lighter forearms and hands, resulting in a heavier forelimb in orang-utans compared with chimpanzees. Furthermore, Pongo has heavier forearms than Gorilla.

Table 4.  Mass of the limb segments as a percentage of total limb weight
Individual*Upper armForearmHandThighShankFootFore-limbsHind-limbs
Homo10.9 6.52.557.217.45.519.980.1
Table 5.  Kruskal–Wallis test of segment mass as a percentage of total limb mass in hominoid genera [n = 26 individuals, k = 4 groups, χ2(0.05, 3) = 7.815] : Post-hoc tests: Q(0.05,4) = 2.639
Upper arm4.2700.234 
Forearm13.3710.004Pongo has heavier forearms than Pan or Gorilla
Hand7.9340.047Pongo has heavier hands than Pan
Thigh13.1780.004Pan has heavier thighs than Pongo
Forelimbs14.3440.003Pongo has heavier forelimbs than Pan
 GorillaPanPongo GorillaPanPongo
 Pan0.203   Pan1.071  
 Pongo3.0453.145  Pongo1.7622.743 
 Hylobates1.5211.6541.028 Hylobates0.6271.4970.842
 Pan1.335   Pan1.850  
 Pongo2.3463.564  Pongo1.9043.634 
 Hylobates0.5871.6761.363 Hylobates0.9612.4660.633

Table 4 shows that in chimpanzees and bonobos, the hindlimbs are always heavier than the forelimbs. In one of the chimpanzees (Pa2, an adult female), the distribution of weight between arms and legs was very close to that shown by the adult female bonobo Pp from Zihlman (1984). In gorillas, the relationship was less clear cut than in the genus Pan, but the hindlimbs are heavier than the forelimbs in most individuals. In orang-utans, the forelimbs are slightly heavier than the hindlimbs in all but two individuals (Po5 and Po6), and the difference is most pronounced in the adult males Po4 and Po7. In gibbons, the forelimbs are also heavier than the hindlimbs, with the notable exception of the siamang Hy4, in which the forelimbs account for only 42.9% of total limb weight.

Segment inertial properties

The mass, centres of mass and radii of gyration of each specimen are given in Table 3. The principal moment of inertia can easily be calculated from these values by multiplying the mass with the square of the radius of gyration. As the inertial properties of the segments of our Pan troglodytes specimen (Pa1) lie in the range of values reported for Pan by Crompton et al. (1996), and as their Pongo (Po5) is similar to our Pongo sample, the two datasets are pooled for the following comparisons. In Fig. 2, the position of the centre of mass relative to segment length is shown for the upper arm, forearm, thigh and shank segments. Müller (1994) reported the location of the centre of mass in the body segments of an adult Hylobates lar, obtained with a balance-board technique. In the forearm, the centre of mass is located more proximally (42%) than in our gibbon specimens, whereas the values for the upper arm (47%), thigh (42%) and shank (45.2%) lie in the range of our values shown in Fig. 2. In Yamazaki (1985), the location of the centre of mass of both thigh and shank are given as 50%, which is very close to the values of our specimen Hy2.

Figure 2.

Boxplot of the position of the centre of mass indicated as a percentage of segment length for upper arm, forearm, thigh and shank segments. Data are pooled from this study and from Crompton et al. (1996). The data for humans are mean values ± one standard deviation from Zatsiorsky (2002).

For comparison, the mean values of the location of the centre of mass in 100 young adult human males (from Zatsiorsky, 2002) are also shown in Fig. 2. If average values are compared, the centre of mass is always located more proximally in humans than in apes. However, in the upper arm, forearm and thigh segments, standard deviations overlap and there is no clear separation between apes and humans. Only the shank segment clearly differs between humans and apes.

Within the non-human hominoids, the values of the location of the centre of mass overlap to a considerable extent, and Kruskal–Wallis tests yielded no significant discrimination between the genera studied here (Table 6). The radius of gyration relative to segment length is not correlated to body size (Cheng & Scott, 2000) and can therefore be used for an interspecific comparison. For this purpose, the mean value of the radii of gyration in sagittal and coronal planes was calculated. The Kruskal–Wallis test yielded a significant difference only for the thigh segment (P = 0.012), Hylobates differing from Pongo. Gibbons have a smaller radius of gyration in the thigh than orang-utans (Table 7).

Table 6.  Kruskal–Wallis test of the position of the centre of mass as a percentage of total limb length in hominoid genera [n = 18 individuals, k = 4 groups, χ2(0.05, 3) = 7.815]
Upper arm2.6140.455
Table 7.  Kruskal–Wallis test of the mean radius of gyration as a percentage of total limb length in hominoid genera [n = 18 individuals, k = 4 groups, χ2(0.05, 3) = 7.815] : Post-hoc tests: Q(0.05,4) = 2.639
Upper arm 4.7750.189 
Forearm 0.6370.888 
Hand 4.1250.248 
Thigh10.5790.014Hylobates has a larger radius of gyration of the thigh than Pongo
Leg 4.4530.217 
Foot 5.0770.166 

The inertia data of the entire forelimb and hindlimb are given in Table 8.Overall, the difference in limb mass between fore- and hindlimbs is not significant (Wilcoxon signed rank test, P = 0.145, Table 9). By contrast, the differences in limb length and the location of the centre of mass are significantly different (both P < 0.001). In hominoids, the NPP of the forelimbs is generally higher than the NPP of the hindlimbs (Wilcoxon signed rank test, P < 0.001, Table 9, see Fig. 3). However, the two values are more similar to each other in chimpanzees than in the other apes.

Table 8.  Inertia data of the forelimb and hindlimb in hominoids
Individual*Mass (kg)Length (cm)CoM (%)MI prox. (kg m2)NPP (s)
  • Forelimb = upper arm, forearm and hand, hindlimb = thigh, shank and foot. In non-human primates, fingers and toes are bent in the second interphalangeal joint. In humans, finger joints are extended. In all individuals, the foot is held at a right angle to the long axis of the leg.

  • *

    Specimens Pa2, Pa3, Pa4, Pa5 and Po5 from Crompton et al. (1996) are included. For comparison, mean values for 100 human males calculated from Zatsiorsky (2002) are shown.

Gg19.596 9.992124.
Homo3.60414.517 68.563.135.826.00.3310.9971.231.30
Table 9.  Wilcoxon signed rank test of the characteristics of the forelimbs vs. the hindlimbs in hominoid genera (n = 18)
Length0.0002Forelimbs are longer
CoM (%)0.0006The centre of mass of the forelimbs is more proximal
NPP0.0002The NPP of the forelimbs is larger
Figure 3.

Natural pendular period of hominoid limbs. Gorillas (diamonds), chimpanzees (filled circles), orang-utans (squares) and gibbons (triangles).



One might expect that the main source of error in the measurement of inertial properties derived from segmented cadavers would be deformation of the segment prior to freezing, and that deformation would be more pronounced for cadavers with bulky segments such as gorillas than for slender animals such as gibbons. We did indeed find a suspiciously distal location of the centre of mass in the proximal limb segments of the male gorilla Gg2, whose limbs had been cut off during post-mortem examination. However, overall, estimation of the centre of mass in this study was not found to be less accurate for bulky segments than for slender segments, and thus deformation prior to re-freezing can be ruled out as a major source of error if sufficient care is applied to conserve the original shape of bulkier segments. For segments with a complex shape such as the hands and feet, the model used here does not describe segment geometry accurately enough to allow a valid estimation of their actual inertial properties, even if the mass can be estimated correctly.

Cadavers of large primates are extremely rare and difficult to obtain. The long lifespan of these animals generally limits available material to that provided by the occasional natural deaths of captive individuals. In addition, the customary post-mortem pathological examination often results in considerable damage, especially to the trunk and head. As a consequence, the moments of inertia of the trunk segment remain almost completely unknown.

As in humans, there are different types of body shape within an ape species, notwithstanding the differences between subspecies or sexual dimorphism. The relatively high interindividual variation in hominoid body form suggests that the results gained from just a few individuals must be treated with caution. However, it is important to publish data, even from single subjects, so that in future a broader worldwide database may be created. The database could also be supplemented with external measurements obtained from living, anaesthetized animals during routine checkups or operations. Even though inertial properties estimated from external measurements may contain some degree of error resulting from different mass densities along the limb axis, according to the distribution of bone, fat and muscle tissue, our results suggest that errors are relatively small compared with the extent of interindividual variation. Nevertheless, for most segments, we maintain that data obtained using the double-pendulum technique are more accurate than those obtained through external measurements alone, especially for hand and foot segments. However, to avoid errors from deformation during the process of segmentation and refreezing, we recommend external measurement of the cadaver in its original, unsegmented shape. In summary, these results suggest that the use of mean values from a broad sample of specimens is most appropriate for accurate dynamic modelling.

On the whole, the mass proportions of hominoid body segments of Zihlman (1984), Morbeck & Zihlman (1988) and Zihlman & McFarland (2000) are very similar to our results, although the dissection technique differs. Morbeck and Zihlman cut the muscles at the attachment sites and measure the entire muscle–tendon unit with the more proximal segment. Thus, their results might be expected to show a slight bias towards a more proximal distribution of mass when compared with our results. However, it seems that this effect is only present in data concerning segment weights relative to total body weight, which is, in any case, a problematic variable. The proportion of limb weight to body weight is highly variable in captive great apes, which often tend to obesity and fat accumulation in the trunk. In consequence, the present study uses only segment weights relative to total limb weight, not total body weight, to enable interspecific comparisons.

Inertial properties of the forelimb

The segment inertial properties of the hominoid forelimb can be compared with those of humans (Zatsiorsky, 2002) and macaques (Vilensky, 1979: Macaca mulatta; Cheng & Scott, 2000: Macaca mulatta and Macaca fascicularis); the data are summarized in Table 10. Compared with that for macaques, the centre of mass of the hominoid upper arm is located slightly more proximally, whereas the centre of mass of the hominoid forearm is generally located more distally. The radii of gyration of both upper arm and forearm segments are smaller in the quadrupedal monkeys than in hominoids. Crompton et al. (1996) found that the centre of gravity in the upper arm and in the forearm was located more distally in apes than in humans. With a considerably larger sample size of the present study, we now see that although the average centre of mass of the forelimb segments is located more distally in apes, ranges and even standard deviations overlap between the two groups. In the forelimb as a whole, however, humans show a more proximal distribution of mass than non-human primates (Table 6), owing to their relatively light forearms and very small hands.

Table 10.  Mean segment inertia data
  Non-human hominoids (Gorilla, Pan, Pongo, Hylobates) n = 18Human males (a)* n = 100Macaca mulatta (b) n = 15Macaca mulatta (c) n = 6Macaca fascicularis (c) n = 6
  • *Source: (a) Zatsiorsky (2002), (b) Vilensky (1979), (c) Cheng & Scott (2000).

  • CoM = centre of mass, rg = radius of gyration, both as a percentage of segment length (mean ± SD).

  • Forelimb = upper arm, forearm and hand, hindlimb = thigh, shank and foot. In non-human primates, fingers and toes are bent in the second interphalangeal joint. In humans, finger joints are extended. In all individuals, the foot is held at 90° to the long axis of the leg.

  • §

    For the thigh segment, adjusted values of de Leva (1996) were used, as they correspond better to our measurement techniques.

Upper armCoM47.8 ± 4.045.0 ± 4.248.0 ± 2.450 ± 7.351 ± 9.8
rg29.2 ± 2.532.8 ± 1.6 24.7 ± 3.924.5 ± 1.5
ForearmCoM46.6 ± 4.942.7 ± 3.342.2 ± 2.844 ± 4.943 ± 7.3
rg28.2 ± 1.429.5 ± 0.9 26.0 ± 2.025.7 ± 1.5
ForelimbCoM43.0 ± 3.235.846.8 ± 3.7  
rg31.6 ± 3.030.3   
ThighCoM45.0 ± 3.841.0 ± 1.6§51.1 ± 3.0  
rg31.3 ± 2.132.9 ± 1.0§   
ShankCoM48.5 ± 2.940.7 ± 2.843.4 ± 1.6  
rg28.6 ± 1.728.1 ± 0.6   
HindlimbCoM46.1 ± 4.426.047.4 ± 2.2  
rg36.4 ± 2.826.2   

According to Preuschoft et al. (1992), the only determinant of shape of the hominoid forelimb is the concentration of a heavy mass of flexor muscles on the forearm to move and to control the fingers for secure handholds. When the whole arm is considered, the centre of mass is located more distally in apes than in humans. This difference is most obvious in orang-utans, while the ranges of chimpanzees and humans overlap. This might reflect the fact that forelimb-suspended locomotion is less important in chimpanzees than in orang-utans. By contrast, in the quadrupedal Macaca mulatta the centre of mass of the forelimb seems to be located even more distally than in hominoids.

For humans, Li & Dangerfield (1993) found that the centre of mass of the upper arm moves in a proximal direction with increasing age. Macaques (Grand, 1977b; Turnquist & Wells, 1994) and baboons (Raichlen, 2005b) show the same pattern of mass distribution changes during ontogeny. By contrast, this is not the case in the orang-utans studied, where it is more distal in the adult male than in the juveniles. As the ratio of available force to body mass is less favourable in larger animals (Taylor et al. 1972), an adult male orang-utan needs much stronger flexor muscles on the forearm to be able to hold its body weight in suspensory posture and locomotion than a juvenile.

Inertial properties of the hindlimb

Theoretical considerations from Preuschoft & Witte (1991) and Preuschoft et al. (1992) indicate that the human hindlimb, like that of a cursorial quadruped, would be expected to have a more proximal location of mass than that of non-human hominoids, because a more proximal location of the centre of mass would reduce the inertial resistance of the human leg to pendular motion. Indeed, this can be observed in the distribution of weight between thigh and shank. The thigh of humans represents a much larger proportion of total hindlimb weight than in apes. Accordingly, the centre of mass of the whole hindlimb is located considerably more proximally than in non-human apes (Table 10). Additionally, the centres of mass of both leg segments are located more distally in apes than in humans, although there is considerable overlap in the thigh segment. Only the geometrical shape of the shank segment is clearly distinct between the two groups, the centre of mass being more proximal in humans than in all other hominoids (Fig. 2).

These findings correspond well with the observation that apes, in general, have longer muscle fascicles and shorter tendons compared with humans (Thorpe et al. 1999; Payne et al. 2006a). Thus, our data confirm the conclusions of Crompton et al. (1996) that ape limbs are not optimized for pendular motion during walking, but rather reflect an adaptation for climbing, which is energetically more demanding than walking. Leaping primates, by contrast, resemble humans in this respect (Günther et al. 1992).

As in the forelimb, the ranges of mass distribution in hindlimbs of non-human hominoids overlap, and interspecific differences are therefore difficult to assess. In a comparative analysis of muscle dimensions (Payne et al. 2006a), it was found that gibbons have relatively shorter muscle bellies and longer tendons than great apes. In the data presented here, however, the location of the centre of mass in the gibbon hindlimb is not more proximal than in great apes, although the radius of gyration of the thigh is significantly smaller than in orang-utans. This could indicate that the mass is distributed more evenly along the limb in gibbons.

From our limited database, it seems that adaptations to specific locomotor preferences may become more pronounced during ontogeny. In the infant chimpanzee, the thigh segment is relatively light in weight compared with adult chimpanzees, and thus the centre of mass of the whole hindlimb is located more distally. Feet and hands of juvenile apes are relatively larger and heavier than in adults, because their survival depends on the ability to grip the fur of their mother (Preuschoft et al. 1992). In addition, juvenile African apes climb and use suspension more often than adults (Doran, 1992, 1997; Hunt, 1992; Remis, 1995). Thus, a secure grip of hands and feet remains important well after the infants start to locomote independently. Gripping muscles are located in the forearm and leg, respectively, and thus the centre of mass is expected to be more distally located in infants and juveniles compared with adults. In turn, quadrupedal gait is expected to be less efficient in infants than in adults. This is confirmed by experimental data showing that infant primates exhibit a less stable gait than adults (Dunbar & Badam, 1998; Wells & Turnquist, 2001). Raichlen (2005a) even showed that in infant baboons, the development of mature gait kinematics and relatively proximal distribution of limb mass coincide. But, in vertical climbing, juvenile apes seem capable of utilizing a stable gait, although they often choose to add some irregularities which appear to be a playful kind of locomotion (Isler & Thorpe, 2003; Thorpe & Crompton, in press). This is not likely to be influenced by their limb mass distribution, but rather by their relatively large strength compared with body size (Cartmill, 1972; Taylor et al. 1972; Cannon & Leighton, 1994; Isler, 2005). To allow a more detailed study of ontogenetic changes, however, and enable us to draw more reliable conclusions on the differences between ape species that differ in locomotor activities, it would be necessary to obtain more data on the inertial properties of juvenile hominoid limbs.

Forelimbs compared with hindlimbs

The distribution of weight between fore- and hindlimbs indicates the relative importance of the respective limbs in locomotion (Grand, 1977a). In African apes, the hindlimbs are almost always heavier than the forelimbs, reflecting the need for very strong hindlimb muscles in locomotion with bent hips and bent knees (vertical climbing, quadrupedal and bipedal walking). Studies on muscle mass, fascicle length, physiological cross-sectional areas and moment arms (Thorpe et al. 1999) show that chimpanzees provide smaller moments at their hindlimb joints for the same muscle stresses than humans, although they actually need higher moments due to the bent position of their joints. Thus, propulsive hindlimb muscles of chimpanzees are less well adapted for force production than those of humans. It is probable that the ranges of weight distribution of chimpanzees and bonobos should overlap. For more reliable conclusions to be made, however, a sample of the different subspecies of chimpanzees and more bonobo individuals should be analysed. Orang-utans have relatively heavy forearms and light thighs compared with the other hominoids. This corresponds well to the very specialized locomotor adaptations of orang-utans, which rely on their forelimbs to a considerable extent (e.g. Cant, 1987; Thorpe & Crompton, 2005, in press). Additionally, orang-utans not only use more extended hip postures during voluntary bipedalism and similar torso-orthograde positional behaviours than do the other great apes, but their musculature has better potential than that of the other non-human apes to exert extensor force at the hip (Payne et al. 2006b). In gibbons, which are highly specialized for rapid, ricochetal brachiation, which contains phases of free-flight between subsequent handholds (e.g. Swartz et al. 1989; Bertram & Chang, 2001), the arms are also mostly heavier than the legs, with the notable exception of the siamang individual Hy4. An adult female Hylobates agilis (M. Günther, unpublished data) was also found to have heavier legs than arms (legs, 54.8%; arms, 45.2% of total limb weight). By contrast, an adult female siamang (dissected by Lynda Brunker, cited in Zihlman, 1984) showed a different distribution of mass in the fore- and hindlimbs than Hy4: its forelimbs weighed 52.6% and the hindlimbs only 47.3% of total limb weight. This large discrepancy is unlikely to be caused by different methods of measurement. It seems that the distribution of weight between fore- and hindlimbs in gibbons and siamangs is highly variable. Interestingly, gibbons are more similar to African apes in this respect than to orang-utans. Although the intermembral index (humerus + radius length divided by femur + tibia length) is even higher in gibbons than in orang-utans, gibbon legs are also relatively long compared with trunk length (Schultz, 1930). Apart from brachiation, hindlimb-dominated locomotor modes such as bipedal walking, vertical climbing and jumping comprise a large part of the daily locomotor repertoire in gibbons (Fleagle, 1976). Bipedal walking with bent hips and bent knees (Yamazaki & Ishida, 1984), as well as jumping (Gunther et al. 1991) both require relatively long legs and strong leg muscles. The biomechanics of gibbon locomotion other than brachiation, however, remains to be fully investigated.

The NPPs of arms and legs are an important factor in the use of fore- and hindlimbs. However, in primates contact of extremities with the substrate is highly variable: digitigrade, semiplantigrade and plantigrade modes are preferred by different species (Schmitt & Larson, 1995), which may considerably alter functional limb length and thus NPP (Preuschoft, 2004). In non-cursorial mammals such as primates, functional limb lengths are more difficult to determine than in cursorial mammals such as ungulates (Gebo, 1992). In domestic dogs (Myers & Steudel, 1997) and yellow baboons (Raichlen, 2004), the NPP was found to be equal for the forelimbs and the hindlimbs. In rhesus monkeys (Macaca mulatta), the NPP of the hindlimbs is larger than that of the forelimbs (Myers & Steudel, 1997; calculated from the data of Vilensky, 1979). In the present study, the NPP of ape forelimbs was found to be always larger than the NPP of the hindlimbs. It is highly likely that the NPP of both fore- and hindlimbs is overestimated in the present study as, during quadrupedal locomotion, the arms and legs are not outstretched throughout a limb cycle, but rather are flexed to varying degrees at the elbow, wrist, knee and ankle. In quadrupedal locomotion of African apes, the knee in particular has a large angular movement (D’Août et al. 2002) and the product moments of inertia and thus the NPP of the leg could be considerably smaller than the values reported here. In this case, actual NPP values for fore- and hindlimb would differ even more. Thus, limbs are not optimized for efficiency in quadrupedal walking, in this respect at least, even in the African apes. As in the hindlimbs of dogs and baboons, the longer forelimbs of apes are counterbalanced by a more proximal concentration of mass in the forelimbs, but not enough to produce equal NPPs in fore- and hindlimbs. As gibbons never walk quadrupedally and orang-utans exhibit pronograde behaviour less frequently than orthograde (Thorpe & Crompton, in press), an equal NPP in all four limbs is unlikely to be of benefit to them. In African apes, quadrupedal knuckle-walking comprises a major component of the daily locomotor repertoire, and as such, they would profit from an equal NPP in fore- and hindlimbs. By contrast, the morphology of African apes reflects a compromise between adaptations to various locomotor modes, whose kinematics may overlap to a large extent (D’Août et al. 2004). This polyvalence could explain why the limbs of African apes are not optimized for pendular motion during quadrupedal walking. However, in the four chimpanzees from the study of Crompton et al. (1996), the NPPs of the forelimbs and hind limbs are almost equal (Table 6). We may tentatively conclude that common chimpanzees are better equipped for an efficient quadrupedalism than gorillas. Data on gorilla locomotion are relatively scarce. However, Thorpe and Crompton's comparison of hominoid posture and locomotion (in press) noted that orang-utans and lowland gorillas exhibited similar positional behaviour profiles. Together these results are a further indication that African apes are by no means functionally equivalent animals of different size.


Differences in limb lengths between apes and humans are well known and play a major role in many scenarios of hominid evolution (Richmond et al. 2002). The results presented here show that, in addition, significant differences between apes and humans exist in the distribution of mass within as well as between limbs. The centre of mass of both the arms and the legs were found to be located more distally in apes than in humans. This was particularly the case for orang-utan forelimbs, which reflects the importance of forelimb suspension in orang-utan locomotion. The NPP of forelimbs was found to be larger than that of the hindlimbs for all ape specimens in our study, with the possible exception of four common chimpanzees in which the difference was rather small. This suggests that hominoid limbs are not optimized for efficiency in quadrupedal walking, but rather reflect a compromise between various locomotor modes. Common chimpanzees, but not gorillas, may have secondarily evolved their limb mass distribution for a more efficient quadrupedalism. This could indicate that the common ancestor of African apes was not a proficient quadruped. Our results further suggest that adaptations to specific locomotor preferences may become more pronounced during ontogeny. Interspecific differences in limb mass distribution may exist, but are partly obscured by a large interindividual variation in all ape species. In conclusion, inertia characteristics of hominoids can and should be used in any biomechanical study of ape locomotion (e.g. Isler, 2005) and especially in models of early hominid locomotion.


We thank the zoos of Zürich, Basel, Bristol and Knie's Kinderzoo, the Naturhistorisches Museum in Basel and the Anthropological Institute and Museum of the University of Zürich for the ape cadavers, and all who helped during dissection, especially Beno Schoch and Marcus Gisi. Research by the Liverpool group was funded by NERC, BBSRC and the Leverhulme Trust.