603
LOCOMOTORY ADAPTATIONS I N MAMMALS
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS. By J. MAYNARDsbWl"l',
Department of Zoology, University College, London and R. J. G. SAVAGE,
Department of Geology, The University, Bristol.
(With 14 text-figures.)
[Read 20 January 1965.1
INTRODUCTION.
Many post-cranial skeletal characters can be analysed as adaptations to different
methods of locomotion. Galen was probably the first to investigate along these
lines, but it was not until the seventeenth century that Wm. Croone 'in England and
J. A. Borelli in Naples made the first extensive studies in the mechanics of locomotion.
Many contributions followed these, but with the acceptance of organic evolution
during the nineteenth century, functional anatomy acquired a new stimulus.
Gregory (1912) described the differences between cursorial and graviportal mammals,
while more recently Slijper (1946) discussed the comparative anatomy of the
mammalian vertebral column and Howell (1944) collected much interesting information both on anatomy and on the gaits of mammals.
I n the present paper it is suggested that much of the variation of mammalian
skeletons can be explained by two mechanical considerations. The first concerns
the mechanical advantage of the muscles (the term 'mechanical advantage' is
defined in tj 2). It is shown that a muscle can be adapted either for a rapid and
weak or for a slow and strong movement of the skeleton. The second consideration
concerns the gait of mammals. The gait adopted by an animal is shown to depend
both on its size and on the speed a t which it is travelling. However, these Factors
alone are insuEcient to explain the gaits of animals. An antelope, a kangaroo
and an ostrich may be approximately the same size, and all travel fast on level
ground, yet one gallops, one leaps and one runs. These differences depend on the
structure and habits of tlieir ancestors. Bipedal mammals, with the exception of
map, normally proceed by a series of leaps, since they have evolved from galloping
mammals in which the hind legs tended to move together. The gallop is a gait not
found among reptiles, in which the hind legs move alternately. Accordingly
bipedal reptiles usually run, as do all birds capable of rapid locomotion on the ground.
The gait decides what modifications of the skeleton are of selective advantage. The
mechanical problems which arise are dealt with in the appendix.
Attention has been confined to running, jumping, digging and swimming
mammals. The choice of examples has largely been determined by the material
available. The main arguments rest on living mammals, whose habits can be
observed, but some fossil mammals are mentioned to illustrate how patterns of
locomotion can be inferred from skeletal characters.
THE PECTORAL
GIRDLE AND FORELIMB.
A striking contrast between two different types of mammalian fore limb can be
obtained by comparing a cursorial and a fossorial mammal. In running, high speeds
achieved, and the limb and girdle must be adapted to move the foot as rapidly
as possible relative t o the body. I n digging, resistance to motion is greater and
speeds are consequently lower: very rapid movement of the foot is impossible,
and the limbs must be adapted to a powerful rather than to a rapid stroke.
Fig. 1 shows the fore limb and scapula of Equus and Dasypus, respectively a
cursorial and a fossorial form. The main muscles flexing the fore arm are the latissi.
mus dorsi and the teres major, with, amongst others, the pectorales and deltoid
assisting. Of these muscles the teres and deltoid originate from the scapula and
insert into the humerus.
41'
604
SMITH AND SAVAGE
The line of action of the m. teres major is shown in fig. 1. If P is the tension or
pull in this muscle and v its rate of contraction, we can calculate the backwards
thrust ( T )produced a t the ground, and the velocity ( V ) imparted t o the foot relative
t o the shoulder girdle. I n fact T = P x l / h and V = V X h/l, where l=moment arm of
the muscle about the fulcrum (A), i.e. the perpendicular distance from the glenoid to
the line of action of the muscle, and h= perpendicular distance from the glenoid t o
the ground.
If the ratio llh is large, the movement will be powerful though slow. If the ratio
is small, it will be fast but weak. Gregory (1912) gave a correct, although unnecessarily complicated account of this relationship. For the limbs shown in fig. 1, the
values of l/h are approximately 1/13for Equw,and 114 for Dasypus. The difference is
of t.he kind which would be expected in view of the habits of these animals.
Fro. 1.-Left
fore limbs of (a) Equue and (b) D a s y p , to show line of eation of m. term major.
The ratio I/h corresponds t o the ' mechanical advantage ' of a lever : that ie, the
ratio of the distance of the applied force from the fulcrum (1) t o the distance of the
load from the fulcrum (h). A large value of l/h is only a n advantage for strong but
slow movements, whereas a small value of l/h is a n advantage for fast movements.
I n Equw the scapula is high and narrow, the bone normally being held with the
long axis nearly vertical. Consequently the teres major and other muscles from the
scapula to the humerus are lengthened, but their moment arms are not increased.
Muscles contract by varying amounts, though generally by about 115 t o 113 of the
extended length. Increase in length of the teres major enables it t o rotate the
humerus through a wider arc. I n Equus a contraction of 115 would rotate the
humerus through 50'. This rotation is achieved with considerable rapidity because
of the short moment arm.
The scapula of Dasypus is held with the spine directed postero-dorsally at about
45" to the horizontal. The spine carries an elongated acromion for the origin of the
deltoid muscle. The infraspinous fossa is extensive, and the blade sweeps down
beyond a secondary spine t o give a relatively large area for the origk of the teres
major. The humerus is ahort and robust. The moment arm of the teres muscle is
605
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS
C
e
FIQ.%-Left soapule of (a) M a r k , (b)Lutra. (c) Delphinue, (d) Potamotharium, ( e ) ZdOphtM,
(f) Phoca.
b
a
d
e
Fro. S.--Luft scapula of (a) Myrmecophnga, (b)Pl~a8colov~ysr.
[c) Talpa, (d) L)a?ypiis, (e) Priodoniea.
606
SMITH AND SAVAGE
increased, though the relative length of the muscle is not greatly altered. A
contraction of the muscle by 1/5 of its length would rotate the humerus through a n
arc of about 30".
This comparison is a help in understanding some of the variations in the form
of the scapula in other mammals now to be considered.
The scapulae of some aquatic and fossorial mammals are shown in figs. 2 and 3;
they can be compared with the scopula of a relatively unspecialized carnivore, Martee.
fig. 2 (a). The two types have many features in common, and it is sometimes difficult
t o distinguish clearly between them, since some species combine both habits. These
scapulae are relatively short, and held more nearly horizontal than vertical. The
width is large compared t o the height, and the shape tends t o approach an asymmetrical crescent. The coracoid and vertebral borders tend to be confluent and the
coraco-vertebral angle is usually indistinct or absent.
C
Fig. 4.-Left
scapula of (a) Fezis CatU8, (b) Lepue,
(0)
Acinonyt, (d) C'hrysocyon.
The more rounded outline of the scapula results in an increased surface area for
the mm. spinati, and frequently secondary spines develop either anterior or posterior
t o the,main spine. Dmypus is exceptional in having both an anterior and a posterior
secondary spine. The development of the main spine and its processes differs
considerably in aquatic and fossorial forms. I n aquatic mammal8 the spine is low,
with very reduced processes. Cctacea have an acromion but no spine ; the process
probably ensures freer abduction of the flipper. Potamotherium, an Oligocene otter,
has processes more reminiscent of a fossorial than an aquatic animal, though otherwise it shows highly aquatic characters.
I n fossorial types the spine is usually high and long, and carries an elongated
acromion process, often extending a great distance beyond the glenoid. Talpa is an
exception in having a long narrow scapula, low spine and small acromion ; moles
canfine much of their work in digging to the lower parts of the limb, and movements
of the humerus are effected mainly by the mm. latissimus dorsi and pectorales, which
do not originate on the scapula.
The backward prolongation and ventral curvature of the blade in fossorial and
aquatic mammals increases the mechanical advantage of the teres muscle, as shown
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS
607
in detail for Dasypus. The mm. subscapularis and spinati act as stabilizers, retaining
the humeral head in the glenoid and opposing the deltoid. The enormous fossorial
rtcromion is understandable when it is remembered that digging is not normally a
direct to-and-fro movement but a scooping action. The manus passes through an
ellipse, enabling the arm to avoid the earth scooped out in the previous movement.
Observation of a n armadillo provided UB with a beautiful example of this action.
Thus the architecture of the shoulder in aquatic mammals is adapted t o produce
powerful flexion of the limb, and in fossorial mammals to produce in addition
powerful abduction and adduction.
FIG.&-Left scapula of (a) Phenacodzls, (b) TragziZzc8,
(e) Boa, (f) Cerzwcr.
( c ) Daina, (dj Equva,
Turning now t o cursorial mammals, the scapulae of some carnivores and a hare
are illustrated in fig. 4, and those of some ungulates in fig. 5 . Phenacodus, a n Eocene
condylarth, was probably a close relative of the stock from which the ungulates
evolved.
These scapulae are elongate, with a narrow neck, a shallow suprascapular notch,
fairly straight coracoid and axillary borders, a blade which gradually widens to a
maximum near the vertebral border, and well-defined coraco-vertebral and vertebroaxillary angles. These features are on the whole more pronounced in the ungulates
and the hare than in the carnivores. The scapular spine in the carnivores is fully
developed though not enlarged, and there are distinct spinal processes. I n the
ungulates the spine is low, often not extending to the vertebral border, the acromion
weak and the metacromion absent. The hare has a slender spine and delicate
metacromion. I n all these scapulae the infraspinous fossa is larger in area than the
supraspinous fossa, and in ungulates the difference becomes very considerable.
Cursorial specializations of the scapula were discussed by Hopwood (1947) in the
leopard (generalized arboreal), the cheetah (cursorial) and the lion (intermediate).
He interpreted the form and the muscle scars of the cheetah scapula as modifications
t o freer movement in a sagittal plane. The angular shape of the scapula in cursorial
mammals is a similar modification, depending on the function of the m. serratus
ventralis. This muscle tends to be divided into two parts, which cooperate to raise
608
SMITH A N D SAVAQE
the thorax, but act as antagonists in the forward and backward movement of the
limb. I n both horse and cow the serratus is divided into cervical and thoracic parts,
inserting medially at the anterior and posterior ends of the vertebral border of the
scapula. I n the horse ‘‘ The cervical part draws the base of the scapula [i.e. the vertebral border] toward the neck, while the thoracic part has the opposite action ; these
effects concur in the backward and forward swing of the leg respectively” (Sisson,
1917). I n fact the mode of action of the two parts of the serratus muscle is rather
more complex than this.
Fig. 6 shows the positions of the scapula and humerus a t the start and finish of a
backward stroke of the leg (inferred from photographs in Muybridge, 1899, series 46).
The approximate positions of the two parts of the serratus muscle are also shown.
It will be seen that the cervical part assists the backward movement of the leg, while
the thoracic part undergoes little change of length. Associated with this fact, the
cervical part is thick and fleshy, whereas the thoracic part is covered on the superficial face by a thick tendinous layer. The subsequent recovery of the scapula during
the forward stroke is effected by the cervical part of the m. trapezius.
BIG.&-Left scapula and humerus of Eqtbzc.8 at the start (full line) and finish (broken line) of a
backward movement of the leg during the gallop, showing the lines of action of tho cervical
and thoracic parts of the m. serratus.
The serratus muscle in cursorial artiodactyls probably resembles that of the cow
in having separate cervical and thoracic parts. Although the mode of action may
not be identical with that in the horse, the division into two parts will enable the
muscle to assist fore and aft movements of the limbs.
I n the dog, Bradley (1948, fig. 75) showed the thoracic part of the m. serratus
passing forward t o insert anteriorly into the scapula. However, we found in three
mongrel terriers that, although there is a continuous area of insertion of the serratus,
the insertion of the four posterior digitations of the muscle is concentrated a t the
vertebro-axillary angle, and that of the anterior three t o four digitations on the
coraco-vertebral angle of the scapula. These two parts of the muscle make up
together about half the total weight. It follows that in dogs there is some specializa-
609
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS
tion of the serratus for assisting the fore and aft movement of the limbs, but it is less
extreme than in the cursorial ungulates.
Summarizing, in cursorial mammals the scapula tends to be high and narrow,
enabling the muscles to produce a large angular movement of the humerus at high
speed. The sharp angles a t the ends of the vertebral border of the scapula are
associated with the functional division of the serratus muscle into two parts which
assist the fore and aft movement of the limbs.
I n graviportal mammals (fig. 7 ) the scapula tends to be both high and broad,
presumably in order to provide sufficient area for the attachment of the serratus
and other shoulder muscles which must support the great weight of the animal.
The blade is frequently expanded posteriorly, the vertebro-axillary angle being
drawn postero-ventrally, thus increasing the mechanical advantage of the teres
muscle. The spine is usually heavy and may have a posteriorly projecting flap in
the mid region, overhanging the infraspinous fossa, as in Rhinoceros and Brontops.
Alternatively the long heavy spine may terminate in a large acromion, as in
Lomodonta and Uintatherium. These features are again seen though less pronounced
in the ' semi-graviportals ', for example Tapirus and Teleocerw.
a
b
C
FIQ.7.-Left scapule of (a)Tapirua, (b)Teleoceraa, ( c ) Rhinoceros, (d) Brontops, ( e ) Uintatktrizrm,
(f) Lozodonta.
An interesting contrast between the distal parts of the fore limbs of different
animals can be obtained by measuring the mechanical advantage of the triceps
muscle. Table I gives the ratio of (i) the length of the olecranon from its tip to the
middle of the sigmoid notch, divided by (ii) the length from the middle of the sigmoid
notch to the tip of the fingers. A large value of this ratio enables the triceps t o
impart a slow but powerful movement to the hand. The ratio is approximately
0.10 in Martes, and among cursorial carnivores drops to 0.08 in Chrysocyon (the
maned ' wolf '). I n cursorial ungulates it ranges up to 0.12 in Equus. The aquatic,
fossorial and graviportal forms show increasingly large ratios, reaching 0.33 in Talpa.
The low value in the elephant (0.12) is understandable if it is remembered that the
elbow joint is only slightly flexed in this animal, and consequently little force is
required to maintain an upright posture.
610
SMITH AKD SAVAGE
TABLEI.-&fECHANICAL
namely
0.08
0.08
0.09
0.10
0.10
0.10
0.1 1
0.1 1
0.1%
0.12
0.15
0.17
0.21
0:Pl
0.26
0.27
0.33
Lepva
Chrysocyon
Vulpes
Felia
Martea
Oryctolagiia
Tragulzr.8
Megaloceros
Eq'IbUs
Elephaa
Lutra
Potamothera'ibm
Orycteropw
Phaacolomys
Rhinoceros
Dasypiba
Talpa
ADVANTAGE
OF TRICEPS
MUSCLE
Length of olecranon process.
Length of fore arm and manus.
I
}
Cursorial carnivores m d lagomorphs
Cursorial ungulates
Aquatic, fossorial and graviportal types
THE GAIT OF MAMMALSAND ASSOCIATED
MODIFICATIONS
OF
THE
VERTEBRAL
COLUMN.
Quadrupedal mammals may achieve high speed on land by means of the leaping
gallop or the horse gallop (Slijper, 1946). These two types of gallop are illustrated
in fig. 8. A gallop pace includes a phase in which all four legs are off the ground
at the same time. I n the leaping gallop (e.g. dog) this ' floating ' phase comprises
a relatively long part of the gallop sequence. There are in fact two such phases of
approximately equal length in a single sequence : (i) the animal launches itself
forwards with its fore legs and lands on its hind legs, and (ii) a second floating phase
a
FIG.8.-Sequence
of phases in the gallop of a horse ( a ) and a greyhound (a) (After Muybridgo,
1899).
when the hind legs leave the ground before the fore legs touch it. I n the horse gallop
the single floating phase is relatively short, the front legs are the last to leave the
ground and the animal lands on its hind legs.
The leaping gallop is practised by some marsupials and insectivores, nearly all
rodents and carnivores, and by suids and tragulids. The equids and larger ruminants
practise the horse gallop ; some species of small deer and antelope show a gait intermediate between the two types. I n general the leaping gallop is characteristic of
611
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS
small mammals, and the horse gallop of larger ones. I n addition to the gallop,
almost all mammals adopt other gaits for moving a t lower speeds. I n the walk
and slow trot, a t least two legs are on the ground a t any instant, and in the rapid
trot there is a brief floating phase in which all four legs are off the ground a t the
same time. Very heavy mammals when travelling fast adopt the ambling gait in
which there is no floating phase ; a t least two of the legs being on the ground a t
any instant. The mechanical reasons for these gaits are discussed in the appendix,
but the conclusions may be summarized here.
An animal travelling on a level surface must do work in two different ways,
namely t o raise its centre of gravity each time it leaps, and to accelerate its legs
with each to-and-fro movement. I n gaits other than galloping, namely walk,
amble and trot, there is little alteration in the height of the centre of gravity, and
almost all the work done is devoted to accelerating the legs. Where the gait consivts
ofa series of long leaps (e.g.jerboa or kangaroo) most of the work is directed to raising
the centre of gravity. Fig. 9 shows how the work done varies with the relative length
of the floating phase of the gait. For an animal of given size travelling a t a given
speed there is an ‘ optimum ’ gait which minimizes the total work done. This can
be achieved by expending relatively more energy either on leaping when travelling
Leaping
Leaping
25
50
75
100
25
50
75
1 0
Ord.: work done. Abs.: floating phase as percentage of a stride.
FIQ.0 . 4 u r v e s showing the contributions of leaping and stepping to the total work done in
running for
A. A large animal at low speed.
B. A large animal at high speed or a small animal at msdium speed.
C. A small animal at high speed.
fast, or on moving the legs to and fro when travelling slowly. This conclusion is
confirmed by the typical mammalian gaits-walking, trotting and galloping.
Further, it can be shown that in larger animals greater energy ehould be expended
in moving the legs and less energy used in raising the centre of gravity. This
explains the series of different gaits, namely the leaping gallop in small mammals,
the horse gallop in large mammals, and the amble in very heavy mammals. From
the photographs in Muybridge (1899) it is estimated that in a greyhound (leaping
gallop) the floating phase occupies 40 t o 50 per cent of a stride, and in a horse
(horse gallop) this phase occupies 20 to 30 per cent of a stride.
The structure of the vertebral column and the spinal musculature will depend on
the type of gait adopted. There is no ‘ typical ’ cursorial mammal ; there are a t
least two different types. Thus when Gray (1944) wrote : “ I n the case of a typical
cursorial mammal the propulsive drive is normally controlled by the muscles of
the limb, whilst the axial musculature of the back cooperates by providing the body
with adequate rigidity ”, he was making a statement which is true of a horse, hut
untrue of a hare or greyhound.
An excellent account .of the anatomy of the vertebral column is given by Slijper
(1946). I n mammals adopting the leaping gallop the backbone is very flexible,
612
SMITH AND SAVAGE
especially for arching in a sagittal plane, and the axial musculature plays an important part in leaping by extending the backbone from its flexure. I n mamma,ls
adopting the horse gallop the backbone is relatively rigid, although the lumbo-sacral
joint may show a certain degree of flexibility, and the axial musculature shows a
marked reduction in the fleshy elements .and a better development of the tendinous
ones ; it i u therefore adapted for resisting tension rather than for active contractions.
THE h L V 1 0 GIRDLE AND HIND LIMB.
The modifications of the pelvic girdle in mammals may best be understood by
considering first the girdle in a mammal (e.g. Martes, fig. 10) with no very specialized
locomotory adaptations.
F I ~10.-Left
.
pelvis and femur of Mar.te.9, showing lines of a d o n of the extensor muscles of
the thigh.
A, acetabulum. Ad, m. adduotor magnus. B, m. biceps. b, moment arm of m. gluteus medius
U, m. grmilis. UZ,m. gluteus medius. m, moment arm of m. biceps. Sm, m. semimembranosus. St, m. semitendinosus.
There are two main groups of muscle extending the femur, and their lines of
action are shown in the figure. The gluteal group (gluteus medius and g. minimus)
originates from much of the lateral surface of the ilium and inserts into the great
trochanter of the femur. The second group forms the ischio-pubic complex,
comprising mm. biceps femoris, semitendinosus, semimembranosus, gracilis and
adductor magnus. These originate from the posterior borders of the ischium and
pubis and insert into the distal end of the femur and the proximal half of the tibia.
SOME LOCOMOTORY ADAPTATIONS IN MAMhULS
613
Although both groups extend the femur, they have an important functional
difference, which can be explained if the moment arms of the muscles about the
acetabulum are considered. I n Martes. the moment arms measured were :
Gluteus medius
0.5 cm. approx.
Biceps femoris
1.5 cm. approx.
It follows that the gluteus medius is adapted for rapid movement, whereas muscles
in the ischio-pubic complex produce powerful but relatively slower movement.
These two muscle groups must cooperate in extending the femur, and it is probable
that the ischio-pubic group is of greater importance a t the beginning of the stroke,
when movement is slow and the resistance to be overcome relatively great, whereas
later, towards the end of the stroke, the gluteals predominate to provide greater speed.
The contrast between these two groups of extensors is more clearly seen by
comparing the pelvic girdles of mammals adapted to different methods of locomotion.
b
FIG.11.-Left
pelvis of (a)Martea-, (b) Lutra, (c) Potamotherium, (d) Phoca.
The extreme aquatic example is Phoca (fig. l l d ) , in which the ilium is short and the
ischio-pubis very long. The gluteal muscles are weakly developed, and the femur
is extended by the muscles of the ischio-pubic group, which have long moment arms,
thus giving more power at the expense of speed. The seal employs lateral movements of the vertebral column in swimming, and sagittal movements only when on
land. Associated with these lateral movements the iliac wing is deflected outwards
t o give attachment to the well-developed ilio-costalis muscles. The sacro-pelvic
angle is small (25"). This is the angle formed by the ventral surface of the sacrum
and a line from the sacro-iliac articulation to the anterior tip of the pubic symphysis.
The sacral articulation is rigid and, because of the small angle, the ischium is elevated
t o the level of the backbone, thus lengthening the ischio-pubic muscles, which,
because of the permanent backward poise of the leg, would otherwise be very short.
The morphology of the pelvic girdles of h t r a and Potamotherium is intermediate
between those of Martes and Phoca ; the four form a series illustrating the increase
of adaptation for power in aquatic locomotion.
The relative lengths of femur, tibia, and pes in four aquatic mammals are
given in Table 11. I n Enhydra and Phoca the great elongation of the pes relative
t o the other segments provides strong skeletal support for a broad paddle-like flipper.
The girdle structure of Equus (fig. 12) is very different from that of Phoca. The
ilium is large and expanded medially, while the ischio-pubis is very short. I n
614
SMITH AND SAVAGE
consequence the gluteal muscles are greatly elongated and the moment arm of the
ischio-pubic muscles much reduced. Hence speed and not strength is emphasized
in thigh extension. The sacro-pelvic angle is large (60") and articulation is not
rigid, so that the stride can be lengthened by rotations of the pelvic girdle a t the
sacral articulation. Thh movement is assisted during the backward stroke of the
leg by the gluteus medius muscle, which has a tongue extending anteriorly on t o
the lumbar vertebrae.
Lumbar
FIG.
12.-Left
pelvie and femur of Equua (abbreviations &B in fig. 10).
A series from the primitive Phenacodus, through the leaping-gallop type Tragulus
t o the climax with Cervus and Equus (fig. 13), shows the progressive changes in proportions of the pelvic girdle in cursorial forms. I n contrast to the aquatic forms
shown in fig. 11, the ilium is lengthened relative t o the ischium and pubis.
The limb proportions of mammals adopting the leaping and horse gallop are
shown in Table 11. I n the horse gallop the major part of the work is done in
accelerating the legs. This work is proportional t o the moment of inertia of the
limb about the acetabulum. Therefore in ungulates adopting the horse gallop
there is a marked tendency t o concentrate the weight of the limb a t the proximal
end. The proximal bones are short and relatively stout, and the distal bones slender
615
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS
and elongated. The muscles in the distal part of the limb are reduced and the
distal elements are moved by long tendons from muscles in the proximal region.
Since in the leaping gallop relatively little energy is needed to accelerate the legs,
there is less need to lighten the distal part of the limb. This may help to explain
the apparent paradox that although some carnivores can overtake the fast ungulates
they do not show such extreme specialization of the limbs.
e
b
Fro. 13.-Left
J
d
pelvis of (a) Equus, (b) Cem~is,( c ) Phenacodu.8, (d) Z’ra~ulue, ( 8 ) Aciraonyx,
(f) Vulpea.
TABLEII.-LENQTHS
OF
FEMUR,
I~BIA
AND PESIN VARIOUS
MAMMALS
(given as percentages of total leg length).
53
Tibia
28.5
34
30
Pes
33
I7
15
Phocrc
Enhydra
Potanwtheriuni
Lutm
I6
21
‘4
30
35-5
27
32
33
48.5
54
44
37
Megaloceroa
Equu.8 (racehorse)
EQplu.8 (pony)
Strepiceroa
30
30
49
28.5
29
28.5
30
31.5
41
41.5
41
40
Martea
32
33.5
34.5
29
35
30.5
30.5
33
35
35
35
35.5
37
36
30
32.5
34
30
25.5
45
22.5
44
41 6
30.5
33.5
37
40.5
Gait
Graviportal
Aquatic
Horse gallop
Arboreal and leeping gallop
Bipedal jumping
Rhinoceroa
Loxodonta
Mastodon
Macropua
Elepha?Uulue
Dipua
Femur
38.5
49
Egclue (racehorse)
(pony)
Strepskeros
Horse gallop
Bipedal jumping
Leaping gallop
Macropw
DipW
LeP
Chrysocyon
OryetOlql8
Tragdwa
Acimyx
Arboreal and leaping gallop Martas
Potumtheriwn
Lutra
Elepb
LOXOOh&3
Rhinoceros
Aquatic
Graviportal
Gait
1
1
1
5
5
3
4
4
55
16.5
81.5
31.5
35.7
1.43
0-06
0.44
2.47
0.48
0.49
2.0
29
72.3
0.22
21-8
69
9.25
0.69
0.59
56
39
32
Femur
area
sq.cm.
A
22.8
138
83
118
27.1
28-7
1
112
188
160
Total
1%
length
cm.
BORES
OF TEE HIND
Number of
functional
elements in
metetarsus
T-4BLE I I I . ~ R O S S - s E C T I O N A LAREAS OF THE
0.75
0.84
1.0
0-68
0-79
0.69
0-67
0.70
1.18
0-61
0.65
0.80
0.68
0.95
0.81
0.89
0.90
1.0
1
1-0
.o
1
1.o
.o
1.o
1.0
s o
1.0
1.o
1
1-0
1-0
1*o
1-0
1.0
Ratio of amas
tibia
and
femur fibula
0.59
0.70
0.77
0-87
0-68
0.81
0.52
0.76
0.41
0-48
0-55
1.04
1.13
0.94
0.98
0.75
Pa
44
21
21
26
33
21
19
24-1
15
8.7
10
10.6
14-0
3-9
6.3
6.6
l2/l0OA
Index of
slenderness
LIMB OF VABIOWS MABlMAIS.
gY
5
kiU
m
SOME LOOOMOTORY ADAPTATIONS IN MAMMALS
617
The limb proportions of three bipedal jumping mammals, Elephctntulus, Dipus
and Macropus, are also given in Table 11. Jumping requires limbs which allow
the maximum movement of the feet in a vertical direction relative to the centre of
gravity (see appendix). This imposes two major differences in the limbs from
those of mammals adopting the horse gallop. First the long pes can be flexed t o
form an acute angle with the tibia, so that when the leg is fully flexed the foot in
close beneath the centre of gravity. Secondly, although in both types there in i l
relative elongation of both distal elements compared with the femur, the tibia in
jumping mammals is relatively longer compared with the pes, and the gastrocnemius
muscle is better developed. The moment arm of this muscle about the tibioastragalar joint is small, while the foot is long, so that the muscle is adapted t o give
a rapid downward movement of the foot.
Howell (1932) pointed out that in jumping mammals there is a progressive
shortening of the iliac as opposed to the ischio-pubic region of the pelvis. This
change is the opposite t o that found in galloping mammals. Now it has been
suggested above that the main function of the gluteus medius muscle in a more
generalized mammal is to impart high speed extension of the limb at the end of the
stroke. I n jumping mammals this rapid final phase of the stroke will be produced
in the main by the well-developed gastrocnemius muscles moving the elongated foot.
If this be so, the main function of the muscles originating on the pelvis is t o produce
a large acceleration at the commencement of the stroke, a role best performed by the
ischio-pubic group with their relatively large moment arm.
Gregory (1912) and Osborn (1929) discussed the modifications of the limbs and
girdles in graviportal mammals. The ilium is broad, with a continuous rugose
edge for the attachment of the oblique abdominal muscles. The legs form straight
pillars with the articular facets in line with the main axis of the bone. There is a
lengthening of the proximal as opposed to the distal elements of the limb (see Table
11). Theue characters are an adaptation to supporting a great weight without
imposing excessive bending stresses on the bones, or requiring the muscles to exert
large tensions when standing. They are however the reverse of the adaptations
described above both for galloping and jumping mammals.
The cross-sectional areas of the bones of the hind limbs of various mammals are
given in Table 111. These areas were measured at the narrowest section of the
bone, and have been calculated from the formula (n/4)a b, where a and b are the
minimum width and breadth. Where more than one bone is involved (tibia and
fibula, or several metatarsals) the area given is the sum of the separate bones. The
length of the limb is the sum of the femur, tibia, and pes ; it is therefore somewhat
greater than the distance from the acetabulum t o the ground. The ratio in the
last column is a measure of the slenderness of the limb, namely Z2/100A,where 1 is
the length of the leg and A the cross-sectional area of the femur.
This table brings out several points of interest. Firstly, the larger the mammal
the stouter (relative to length) the limbs tend to be. This is to be expected from the
fact that weight increases as 13. Secondly, the limb is tapered, the areas of the
tibia and of the pes being usually less than that of the femur. The moment of
inertia of the limb skeleton about the acetabulum can therefore be reduced without
altering the total length of the limb if the relative length of the distal elements is
increased. This taper is most marked in mammals with a single functional element
in the metatarsus, i.e. cursorial ungulates. The relative lightening of the pes in
these mammals is possible because of the greater structural efficiency of a single bone,
which resists bending better than two bones of the same total cross-sectional area.
Hence the importance of the cannon bone in reducing the moment of inertia of the
leg in mammals adopting the horse gallop.
A comparison between the two horses measured is of some interest. The relative
lengths of femur, tibia, and pea are very similar in both. The larger race-horse has
relatively stouter limbs, as is to be expected from its greater size. However, the
JOURN. LINN. ROC.--ZOOLOGY, VOL. XLII.
42
618
SMITH AND SAVAGE
most marked difference lies in the greater taper of the limbs of the race-home as
compared to the pony ; this is precisely what would be expected as an adaptation
to very high speed in a horse.
APPENDIX.
THE MECHANICS O F fifAMMALL4X GAITS.
NnmmaLq are remarkable among tetrapods for the variety of gaits which they
adopt. Different gaits can be regarded as methods of solving the mechanical
problems involved in overcoming the force of gravity in leaping, and in overcoming
Inertia in moving the limbs. I n this appendix the way in which these problems
vary with the size of the animal and with the speed of movement is discussed.
The estimates given below of the work done in running are based on two assumptions, which are almost but not quite true of all tetrapods. The first concerns the
kinetic energy of the legs. In running the legs are moved alternately backwards and
forwards. During, for example, the backward stroke the limb has kinetic energy
relative to the animal’s body. It is assumed that all this energy is degraded into
heat in the antagonistic muscles, and none is converted into potential energy available
for the next forward stroke. The second assumption concerns gaits consisting of a
series of leaps. When an animal lands after a leap it has a downward velocity,
and hence an additional kinetic energy. It is assumed that this energy iFj degraded
into heat in the muscles, and is not available for the next leap.
These two assumptions are not always true. We can sometimes compare a leg
with a pendulum, which will continue to swing for a long time with no input of
energy. I n a man walking, part of the kinetic energy of a leg as i t moves backwards
is converted into potential energy a t the end of the movement, since the foot swings
up off the ground. This potential energy can be reconverted to kinetic energy
during the forward swing of the leg. Such a pendulum action only oeeurs when the
rate of stepping is of the same order as the natural period of oscillation of the leg.
It is best to me the term ‘ walking ’ only for gaits in which this is the case, For a
leg of length I, in geometrically similar animals, the period of oscillation will be
proportional to %4,and the length of stride to 1. It follows that the speed of walking
will be proportional to dl, so that the walking speed will increase with the size of
the animal. When walking an animal is moving with the minimum expenditure of
energy, but the gait is possible only for fairly large animals and at low fipeeds. For
small mammals, and a t high Rpeeds, the assumption made concerning the kinetic
energy of the legs will be true.
In a limited sense leaping can be coinpared to a weight bouncing on top of a
spring, the compressed spring ‘ storing ’ the energy to raise the weight again. This
is the case when part of the shock is taken by elastic tendons. For example, a horse
landing after a leap uses the energy stored in the elastic tendons of the foot for the
next take-off (Camp & Smith, 1942 ; Simpson, 1951).
Although both the pendulum action of the legs and the springiness of tendons
are important in reducing the work done by mammals in certain types of gait, they
are omitted from the treatment given below.
It is reasonable to expect that an animal will adopt a gait which will minimize
the total work done by its muscles a t a given speed. When travelling on a level
siirface, the work done is devoted mainly to accelerating the legs a t each step, and
t o raising the centre of gravity a t each leap. The gait of a mammal may be divided
into two phases, namely a ‘ floating ’ phase during which all four legs are off the
ground, and a ‘ stepping ’ phase during which a t least one leg is on the ground. The
main result of a change in gait is to alter the relative lengths of these two phases.
For two animals of different sizes adopting the same type of gait, the length of the
stepping phase iss proportional t o the length of the legs, 1. For a bipedal running
animal (e.g. man and many birds) the length of a single stepping phaqe is 21 sin
or
approximately lor, where 01 is the angle in radians through which the leg rotates.
I n a galloping horse, each leg takes a step in turn, so thitt the total length of the
steppinq phase w
i approximrttelg 4/01.
619
SOME LOCOMOTORY ADAPTATIONS IN MAMMALS
In fig. 14 the path of t,he centre of gravity of a running animal is shown. Taking
thc height as zero a t the moment of take-off (B) and landing (A, C!), the centre of
gravity rises to a height h during the floating phase, and falls t o --d during the
stepping phase.
If v is the forward speed, and b the length of the floating phrase, then h=b2g/8v2,
where g is the acceleration of a body falling under the influence of gravity. This
follows from the fact that thc path of the centre of gravity of a n animal while its
feet are off tho ground is ail arc of a parabola.
1
\
A
‘C
d
tI
I,
b
n
b
floating phase
i phase
FXU.14.--Ptbth of coltre of gravity of a ruiiiiiiig mammal, showing points of take-off (B) arid
landing (-4,
C).
If a is the length of the stepping phase, then d=nh/b approx. (This assumes that
that the upward acceleration during the stepping phase is uniform, which is not
strictly true.)
If the total work done in a single stride be
W,+ W f , where W, is the work
done in accelerating the legs, and Wf the work done in raiving the centre of gravity,
and if w be the weight of the animal, then
(a+b) b y
Wf = ( h f d ) w =
8v2
’
arid W,=Oonst. x I w 2 , where I = t h e moment of inertia of a limb about the
acetabulum or glenoid,
and w=the maximum angular velocity of the limb.
and if E= the length of a limb, w=v/l during the backward stroke. Hence the work
done in the backward acceleration of the legs during a stride is proportioiial to Iv2)12.
The work done in the forward acceleration of the leg is complicated by two factors.
First, the angular velocity will be less, particularly if there is a long floating phase.
Second, the nioment of inertia I may be reduced by flexing the leg. Neither of
these factors is easy to allow for, but as both tend to make the work done in the
forward stroke less than that in the backward one, no great inaccuracy is involved
in assuming that
w=
VZ
W8=Const. x I - ,
12
and hence
If there are two floating phases instead of one in a single sequence, as in the
leaping gallop of a dog (fig. 8), IVf will be reduced, while W , remains unchanged.
For example, if there are two equal floating phases, each of length f b, and two
stepping phaws of length a,
1 (a+!)) b PI’ g
t,lieu
=
2
8VZ
*
If p is the total work doiie in unit time, then
rvf
620
SMITH AND SAVAGE
- v
P = W X -=a+b
bwg
8v
z us
+ Const. x (a+/))
12
*
Considering a set of geometrically similar anitnals, of different sizes and travelling
a t different speeds, but adopting the same type of gait (e.g. a gallop) :a cc 1, w a lag and I cc l6
and writing h/a= j,a measure of the relative length of the floating to the stepping
phase, equation (2) becomes
-
g2 14
pzA--..j+S12
V
v8
.1 +.?'
(3)
where A and B are collSltaiit8, The value of j for which the work done will be
minimum is given by
or l+j=Const. x
212
-
(4)
gl'
It follows that the work done will be minimized if j increaves with forward speed,
and decreases with size.
This is in accord with the walking, trotting and galloping gaits adopted by the
smie animal at different speeds, and also with the gaits adopted by animals of'
different sizes a t top speed, namely leaping gallop, horse gallop and amble.
However, although equation (4) gives a picture of the relationship between gait,
speed and size which is qualitatively correct, the relative length of the floating phase,
j,does not in fact increase as rapidly with speed, v, as is suggested by the equation.
Although very long leaps may be an advantage a t high speed in minimizing the work
done, they may, because of other factors, be impossible.
The distance an animal can leap when travelling at a given speed iu dependent on
the height ' h to which it can mine its centre of gravity. If T be thc vertical fbrce
exerted by tho legs on thc ground, and d the distancc in a vertical direction through
which the centre of gravity moves while the feet are on the ground, then the work
done by the legs is T x d , and if w is the weight of the animal, then
w (k
d) = T d
(5)
or, if'h is much greater than d, then
+
T
h= 21!
- x d approx.,
and for a net of geometrically similar animals, where 1 is u representative dimension,
d cc 1 and 11' rx: P. Also, because of the limits set by the rnechanical ntrength of bone
and tendon, T cc P. It follows that ( h + d ) will not vary with size. For small
animals, where h is much greater than d, the height to which an animal can leap
will be independent of size. The length of a leap when travelling fast may decreane
in small mammals, since deceleration due to air retlistance is inversely proportional
to linear dimensions. In large mammals the height and length of a leap will decrease
with size. This limitation in the length of a single leap may mean that i t is
impossible for cursorial mammals to adopt the optimum gait suggested by
equation (4).
Hill (195O), by considering the physiological properties of muscles, and the rate
at which oxygen can be supplied to them, concluded that the work which can be
done by an aiiiinal in unit time is not proportional to its niass (13) but more nearly
t_o its surface area (P). If there is no floating phase in the gait, equation (3) becomes
PCCl2 w3. Hill used essentially this argument to show that the power required to
travel a t r7 given npeed is also proportional to mrface area, and h e l m explained the
fact that animals of very different sizes can travel a t approximately the same speed
SOME LOCOMOTORY ADAPTATIONS I N MAMMALS
621
on a level surface. He also concluded, using arguments similar to those given above,
that the height to which an animal can leap is independent of size. I n the present
treatment however consideration is given to the way in which energy is divided
between stepping and leaping. This is important in explaining t,he reasons for the
different gaits in mammals, and the different ways in which the skeleton may be
modified.
The following conclusions concerning the gait of mammals and adaptations of
their skeletons may be drawn.
When travelling on a level surface, work must be'done in raining the centre of'
gravity a t each leap and in accelerating the legs a t each step. The work done will
be a minimum if the relative length of the floating phase of the gait decreases with
the size of the animal, and increases with the speed a t which it is travelling.
The distance which an animal can leap when travelling a t a given speed is roughly
independent of size, but will decrease in very small mammals due to air resistance,
and will also decrease in large mammals. This fact will prevent large cursorial
mammals adopting the gait which would minimize the work done a t high speeds.
It follows that in large mammals adopting the horse gallop most of the work
will be done in accelerating the legs. The most important adaptation will therefore
be the reduction of the moment of inertia of the limbs about the acetabulum and
the glenoid. The same conclusion holds for bipedal running animals. Apart from
man, who is little specialized in this direction, there are no bipedal running mammals.
However many birds (e.g. h'truthio) adopt this gait, and show the expected lightening
of the distal part of the limb.
In bipedal jumping mammals most of the work will be done in raising the centre
of gravity. There is therefore much less need to reduce the moment of inertia
of the legs. The height t o which an animal can leap is proportional to the distance
in a vertical direction through which it can move its feet relative to the centre of
gravity (equation 6). In, for example, a jerboa, which has very long tibia and
metatarsus, the legs can he SO folded that when a t rest the centre of gravity in kept
near the ground. When however the long limbs are straightened, the centre of
gravity is elevated to a relatively great height.
These principles for bipedal jumping mammals hold to a lesser degree for small
mammals adopting the leaping gallop. I n the latter the movement of the feet
relative to the centre of gravity is increased by the alternate flexing and straightening
of the backbone.
ACKNOWLEDGEMENTS.
Our thanks are due to the many colleagues with whom we have d i m m e d this
paper. I n particular we are grateful to Professor J. B. S. Haldane, F.R.S., who
has pointed out a number of implications of our work which might otherwise have
escaped us.
SUMMARY.
The pectoral girdle and fore limb of Equus and Dasypus are compared. It i s
shown that the shoulder muscles of the horse have a small mechanical advantage
(1/13 for the m. teres major) and are therefore adapted to produce rapid movements
of the limb ; these muscles in the armadillo have a larger mechanical advantage
(1/4 for the m. teres) to produce slower movements, while exerting a greater force.
The broad scapulae and short legs of fossorial mammals are adaptations producing
powerful movements of the foot, unually with strong abductor action. Aquatic
mammals show similar modifications, though without the emphasis on abductor
movements.
The high, narrow senpulac and long legs of crvsorial inanimals are esplained as
adaptations to speed, though the detailed arrangements by which this is achieved
differ in cursorial ungulates and carnivores. The sharp angles at the ends of the
622
LOCOMOTORY ADAPTATIONS IX MAMMALS
vertebral border of the scapula in cursorial ungulates provide p i n t s of iiixertioii
for two parts of the m. serratus, which act &B antagonists in the fore-and-aft movement
of the shoulder. Similarly in the dog, and probably all curnorial carnivores and
lagomorphs, the sharp vertebro-axillary angle affords a point of insertion for the
posterior digitations of the m. serratus.
The mechanical adaptations of the olecranon process and the ni. triceps are
described.
The structure of the vertebral column and axial musculature i8 shown to tlcpeiid
upon gait. Two types of gallop, the h o w gallop and leaping gallop (c.g. do~g)
are analysed and the awociation between gait and structure described. The
meuhanics of gaits are d i s c u d in an appendix.
The extensor muscles from the pelvis to the femur fall into two groups, uii iliac
group adapted to rapid extension of the thigh, and an ischio-pubic group adapted
to dower but more powerful thigh extension. The relative proportions of the two
regions of the pelvis vary according to the gaits adopted. In cursorial ungulates
the ilium is long and the ischio-pubic region short, whereas in aquatic nianiiiials
the latter region predominates.
The lengths and cross-sectional areas of the bones of the hind limb are shown
to be correlated with gait in aquatic, cursorial (leaping gallop and horse gallop),
saltatorial and graviportal mammalr.
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