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MUS. COMP. ZOOLL
LIBRARY

DEC 1°7 1971

HARVARD

POSTILLA

PEABODY MUSEUM
YALE UNIVERSITY

NUMBER 152 29 JULY 1971

FUNCTIONAL SIGNIFICANCE OF
MANDIBULAR TRANSLATION IN
VERTEBRATE JAW MECHANICS

PHILIP D. GINGERICH

POSTILLA

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FUNCTIONAL SIGNIFICANCE OF MANDIBULAR TRANSLATION
IN VERTEBRATE JAW MECHANICS

PHILIP D. GINGERICH

Department of Geology and Geophysics and Peabody Museum of
Natural History, Yale University, New Haven, Connecticut 06520

(Received April 14, 1971)

ABSTRACT

Fore-aft translatory freedom of jaw articulation and alignment of
muscle fibers with the bite point make the chief adductor muscles
of most reptile and mammal jaws mechanically very efficient. The
force generated by the adductor muscles acts directly against the
food at the bite point with no reaction force wasted at the jaw joint.
The jaw is functionally a link and not a lever.

Translatory freedom of the jaw joint is provided either by a slid-
ing jaw joint (in most mammals, birds and some reptiles) or by a
two-jointed jaw suspension (in most lizards and snakes).

POSTILLA 152: 10p. 29 July 1971

POSTILLA

ABBREVIATIONS

moment arm of F,

human jaw articulation

quadrate-jaw articulation of lizard

quadrate-cranium articulation of lizard

moment arm of F,,

bite point considered in the analysis

force of contraction of the mandibular adductor muscles of
lizards

equal and opposite reaction force to F,, equal to the bite
force at B

bite force at B

component of F,, perpendicular to bite force F,,

force of contraction of human masseter muscle

reaction force at the jaw joint

component of F, perpendicular to bite force F,

force of contraction of human temporalis muscle

equal and opposite reaction force to F,, equal to the bite
force at B

lizard quadrate bone

VERTEBRATE JAW MECHANICS 3

INTRODUCTION

Many recent papers interpret the mechanics of vertebrate jaws by
treating the jaw as a functional lever rotating about the jaw articu-
lation (see Turnbull, 1970; Barghusen and Hopson, 1970; Kemp,
1969; Crompton and Hiiemae, 1969; Szalay, 1969; Crompton and
Hotton, 1967; Ostrom, 1964; Davis, 1964; Crompton, 1963a,b;
Olson, 1961; Schaeffer and Rosen, 1961; Smith and Savage, 1959).
This interpretation is illustrated in Fig. 1A. The relatively long
length of the bite lever arm and the great amount of force wasted
as reaction force at the jaw joint make this proposed mechanical
system generally very inefficient.

FIG. 1. Human skull illustrating previous interpretations of jaw mechanics:
A. Lever interpretation. F, produces a clockwise turning moment a X
F, opposing the counterclockwise turning moment b X F, produced at the
bite point B. In equilibrium the force F, acts on the jaw at the articulation
A. For clarity vector F, is shown with its head at the point of application.
The bite force at B is approximately 14 the muscle force applied to the jaw.
B. Previous nonlever interpretation (after Robinson, 1946). The lines of
action of F,, F,,, and F,, all pass through a common point. Components of
force f, and f,, act against each other. The bite force at B is approximately
24 the muscle force applied to the jaw by F, + F,,. This interpretation also
requires that F, be oriented unreasonably far back on the cranium.

Alternatively, the a priori assumption that there is no reaction
force at the jaw joint in some mammals and mammal-like reptiles
has led to the interpretation of relative muscle forces illustrated in
Figure 1B. (This interpretation has been proposed by Robinson,

4 POSTILLA

1946; Smith and Savage, 1959; and Crompton, 1963a, b.) This sys-
tem is inefficient because major components of the temporalis and
masseter muscle forces act against each other.

The commonly accepted hypothesis that the mammalian jaw is
functionally a lever implies that the jaw joint, the fulcrum of the
lever system, is fixed with respect to the cranium. In most reptiles,
birds, and mammals this is not true. The lower jaw is generally free
to translate fore-aft with respect to the cranium by either of two
mechanisms. Translatory freedom is provided either by a sliding
jaw joint (present in most mammals, birds, turtles, and Sphenodon)
or by a two-jointed jaw suspension (streptostylic quadrate present
in most lizards and snakes). The sliding jaw joint mechanism is il-
lustrated in this paper by a human skull; the two-jointed jaw sus-
pension is illustrated by the lizard Crenosaura.

THE SLIDING JAW JOINT

The jaw joint in man (Fig. 2) consists of the articular fossa of the
temporal bone above, an intermediate fibrocartilagenous articular
disk, and the mandibular condyle below. The mandibular condyle
and articular disk are separated by a synovial cavity permitting the

oss

& POSTERIOR

STYLOID
PROCESS

ARTICULAR
TUBERCLE
ANTERIOR
EXTERNAL

PTERYGOID —
MUSCLE

MANDIBULAR
CONDYLE

FIG. 2. Parasagittal section through the human jaw articulation. As the jaw
is protruded by contraction of the external pterygoid muscle, the mandibular
condyle slides forward on the articular tubercle. See text for further discus-
sion.

VERTEBRATE JAW MECHANICS 5

condyle to rotate with respect to the articular disk. Both mandibular
condyle and articular disk form the insertion for the external ptery-
goid muscle. The articular disk and temporal bone are also sep-
arated by a synovial cavity, permitting the articular disk-mandibular
condyle assembly to translate forward when the external pterygoid
muscle contracts. Mandibular depression-elevation is accompanied
by simultaneous fore-aft translation of the mandible (Rees, 1954).

The chief muscle adducting the human jaw is the temporalis; it
originates from the side of the cranium and inserts on the coronoid
process of the mandible. The areas of origin and insertion of the
temporalis muscle are shown in Figure 3B. As is shown in Figure

—— LING

FIG. 3. Mechanics of human temporalis muscle. A. Orientation of temporalis
muscle fibers. Collectively the envelope of temporalis fibers is aligned with
the entire tooth row. B. Origin and insertion of temporalis muscle shown
stippled. F, represents the maximum force of contraction of the entire tem-
poralis muscle. F, is aligned with a bite point between the upper and lower
first molars. C. Diagram of forces acting on the mandible. The bite force F,’
is equal to the muscle force F,. D. Diagrammatic representation of the
mandible as a link between forces; see Figure 3C.

6 POSTILLA

3A, the muscle fibers of the temporalis muscle are arrayed fan-like
on the side of the skull. The envelope of temporalis fibers pro-
jected through the insertion on the coronoid includes the entire
tooth row; thus some muscle fibers are aligned with any potential
bite point along the tooth row. The maximum force F, produced by
contraction of the whole temporalis muscle will lie along a line bi-
secting the muscle mass. In Figure 3B, this line passes through the
bite point between the upper and lower first molars.

Analyzing the mechanics on the side of chewing statically, the
force F, of contraction of the temporalis muscle acting on the man-
dible will be opposed by a reaction force F,’, the sum of whose
components will be equal to and opposite F,. The mandible is in
contact with the cranium at two points: one through the mandibular
condyle, the other through the food. Components of reaction force
can only occur at these two points. In the mandibular position
shown in Figure 3B, at the beginning of a bite, the mandibular con-
dyle is separated from the cranium by a well-lubricated, low-friction
plane of sliding. As the condyle is free to slide posteriorly with con-
traction of the temporalis muscle, an insignificant component of
reaction force will occur through the mandibular condyle at the jaw
joint. Virtually the entire reaction force F,’ must therefore occur at
the other contact between the mandible and the cranium, i.e.
through the food (Fig. 3C). The force resulting at the bite point is
thus virtually equal to that produced by the muscle itself. Align-
ment of the temporalis origin, temporalis insertion, and the bite
point, and the presence of a low-friction sliding jaw joint permit
generation of a very efficient bite force by the temporalis muscle. No
force is wasted as reaction force at the jaw joint. As illustrated in
Figure 3D the jaw is functionally a link between two forces, rather
than a lever. A simple model constructed with springs of known
stretching constants and a sliding jaw articulation based on Figure
3C confirms the fact that the muscle force F, is equal to the bite
force F,’ if the jaw is free to translate until these forces are aligned.

THE TWO-JOINTED JAW SUSPENSION

The lizard jaw articulation is mechanically different, though func-
tionally similar to the example just presented. In the lizard the jaws
and cranium are separated on each side by an intermediate bone,

VERTEBRATE JAW MECHANICS 7

the quadrate (see Figure 4). The dorsal end of each quadrate is at-
tached to bones of the cranium by an interosseus ligament permit-
ting limited fore-aft rotation of the quadrate about the quadrate-
cranium joint A, (Oelrich, 1956). The quadrate is thus streptostylic.
The quadrate articulates with the quadrate process of the pterygoid
bone by a diarthrosis, permitting the quadrate to rotate fore-aft in-
dependently of the kinetic maxillary segment of the skull. Each jaw
is attached to the ventral end of a quadrate by a hinge joint A,,. As
the quadrates rotate about the quadrate-cranium joints the jaws
translate fore-aft with respect to the cranium.

Mandibular depression in lizards is accompanied by forward ro-
tation of the quadrates (Frazetta, 1962). As the jaws are elevated
they are therefore also free to translate posteriorly. Figure 4 shows
a skull of the lizard Ctenosaura, illustrating the orientation of the
force vector F, representing the mandibular adductor muscles
and with food at a bite point B. As in the human example
above, components of reaction force can only occur through the
food and through the jaw joints. The quadrates are free to rotate
posteriorly, furnishing little reaction force through the joint. Vir-
tually the entire reaction force F,’ occurs through the food. The
force resulting at the bite point is approximately equal to that pro-
duced by the adductor musculature itself. Alignment of the origin
and insertion of the mandibular adductor muscles with the bite
point, and translatory freedom of the jaw articulation permit gen-
eration of a very efficient bite force by the adductor muscles.

y
Wee mq me

a *
: aa rysmmaee ane? efirrs

FIG. 4. Mechanics of the mandibular adductor muscles of Ctenosaura (skull
after Oelrich, 1956). The bite force F,’ is equal to the muscle force F,.

8 POSTILLA

DISCUSSION

Two factors of jaw construction affect muscular efficiency in pro-
ducing bite force. To be highly efficient, the line of action of the
contracting muscles must pass directly through the food, eliminating
force couples (which would have to be equilibrated either by addi-
tional muscle forces or force at the jaw joint), and the jaw joints
must be free to translate, eliminating reaction force at the joints. As
shown in Figures 3 and 4, and as discussed above, both these con-
ditions are satisfied in man and in the lizard Ctenosaura. The coro-
noid process functions in both to align the fibers of the adductor
muscles with the bite point. A sliding jaw joint, or rotating quadrate,
minimizes the component of reaction force at the joint. During
powerful biting the jaw is functionally a link, rather than a lever,
between the adductor muscle force and the bite point.

The efficiency of jaw adduction described above applies particu-
larly to orthal retraction of the jaws. Chewing in reptiles involves
only a tooth-food-tooth phase consisting of a series of orthal re-
tractions of the lower jaws. This corresponds to the tooth-food-
tooth phase of mastication described by Crompton and Hiiem4ae
(1970) in the opossum. Presumably the most powerful biting occurs
during this phase. The following tooth-tooth contact phase of masti-
cation, generally involving transverse movements rather than orthal
retraction of the mandible, occurs after the food has already been
partially reduced. During the tooth-tooth contact phase of mastica-
tion, a large occlusal area is more important than a powerful bite.

The temporalis and mandibular adductor muscles of mammals
and reptiles are not the only muscles involved in producing bite
force. Other adductor muscles (for example, the masseter and me-
dial pterygoid muscles in man) are not aligned with any bite point;
their force of contraction is divided between useful bite force and
wasted reaction force at the jaw joint.

Translatory freedom in jaw joints, together with alignment of bite
point and muscle fibers, results in a high mechanical efficiency of
the temporalis or mandibular adductor muscles in producing bite
force. Any study of the mechanics of vertebrate jaw adduction must
consider the morphology and action of the jaw articulations as well
as the placement and orientation of the muscles.

VERTEBRATE JAW MECHANICS 9

CONCLUSIONS

Fore-aft translatory freedom is present in the jaw articulations of
most vertebrates. This freedom is provided either by a sliding jaw
joint or by a two-jointed jaw suspension. The most powerful mus-
cles adducting the jaws are aligned with potential bite points along
the tooth row. Translatory freedom of the jaw joint allows precise
alignment of muscle force and bite point and reduces force wasted
as reaction force at the jaw joint. During powerful biting the jaw
is functionally a link between the muscle force and the bite force
rather than a lever.

ACKNOWLEDGMENTS

I thank K. S. Thomson, J. H. Ostrom, D. R. Pilbeam, E. L. Simons,
and P. Dodson for their comments, assistance and encouragement.

10 POSTILLA

LITERATURE CITED

Barghusen, H. R. and J. A. Hopson. 1970. Dentary-squamosal joint and the
origin of mammals. Science 168: 573-575.

Crompton, A. W. 1963a. On the lower jaw of Diarthrognathus and the origin
of the mammalian jaw. Proc. Zool. Soc. Lond. 140: 697-753.

1963b. The evolution of the mammalian jaw. Evolution 17: 431-439.

Crompton, A. W., and K. Hiiemée. 1969. How mammalian molar teeth work.
Discovery 5 (1): 23-34.

1970. Molar occlusion and mandibular movements during occlusion
in the American opossum, Didelphis marsupialis. Zool. J. Lin. Soc. 49:
21-47.

Crompton, A. W. and N. Hotton. 1967. Functional morphology of the mas-
ticatory apparatus of two Dicynodonts (Reptilia: Therapsida). Postilla
109: 1-51.

Davis, D. D. 1964. The giant panda, a morphological study of evolutionary
mechanisms. Fieldiana: Zoology, mem. ser. 3: 1-339.

Frazzetta, T. H. 1962. A functional consideration of cranial kinesis in lizards.
J. Morph. 111 (3): 287-320.

Kemp, T. S. 1969. On the functional morphology of the gorgonopsid skull.
Phil. Trans. Roy. Soc. Lond., B. 256: 1-83.

Oelrich, T. M. 1956. The anatomy of the head of Ctenosaura pectinata
(Iguanidae). Misc. Pub. Mus. Zool., Univ. of Michigan. 94: 1-22.
Olson, E. C. 1961. Jaw mechanisms: rhipidistians, amphibians, reptiles.

Amer. Zoologist. 1: 205-215.

Ostrom, J. H. 1964. A functional analysis of jaw mechanics in the dinosaur
Triceratops. Postilla 88: 1-35.

Rees, L. A. 1954. The structure and function of the mandibular joint.
Brit. Dent. J. 96(6): 125-133.

Robinson, M. 1946. The temporomandibular joint: theory of reflex controlled
nonlever action of the mandible. J. Amer. Dent. Assoc. 33: 1260-1271.

Schaeffer, B. and D. E. Rosen. 1961. Major adaptive levels in the evolution
of the actinopterygian feeding mechanism. Amer. Zoologist. 1: 187-204.

Smith, J. M. and R. J. G. Savage. 1959. The mechanics of mammalian jaws.
School Sci. Rev. 141: 289-301.

Szalay, F. S. 1969. Origin and evolution of function of the mesonychid con-
dylarth feeding mechanism. Evolution 23: 703-720.

Turnbull, W. D. 1970. Mammalian masticatory apparatus. Fieldiana: Geol-
ogy 18: 149-356.

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