ree ee
Pen ey as
~~, Aye

Nt
val

oo Sieh
etralel

Fo Pl

Peat
AA ate
et greey eae mm

Sharer
- aera

ere

oor

etn
ore.

PE ane
oy Senet

ee ied
ate eee

pe
Rater

a ars

meme

HARVARD UNIVERSITY

HG S00)
Si

LIBRARY

OF THE

Museum of Comparative Zoology

vi'US. COMP. ZOOL

aed ™m =) AD Y

a “3 16 4965
UNIVERSITY

PEABODY MUSEUM OF NATURAL HISTORY

YALE UNIVERSITY
NEW HAVEN, CONNECTICUT, U.S.A.

—

Number 88 December 24, 1964.

A FUNCTIONAL ANALYSIS OF JAW MECHANICS
IN THE DINOSAUR TRICERATOPS

By
JOHN H. OstTROoM

PEABODY MUSEUM OF NATURAL HISTORY AND
DEPARTMENT OF GEOLOGY, YALE UNIVERSITY

INTRODUCTION

The many species of ceratopsian or horned dinosaurs were
characterized by several peculiar and conspicuous features: 1)
very large heads, 2) great bony “neck shields,” 3) strong, later-
ally compressed, turtle-like beaks, 4) unique shearing dentitions
of great power, and 5) prominent brow or nasal horns—the lat-
ter absent in very primitive ceratopsians. These structures, as
shown by Lull (1933) and Colbert (1948), dominated ceratopsi-
an evolutionary trends. All but the last of these characters were
either part of, or were directly involved with, the feeding appara-
tus. Thus, ceratopsian evolution appears to have been dominated
by progressive structural modification of the feeding mechanism.

The present paper is part of a more extensive investigation of
the significance of mandibular mechanics in ceratopsian evolution,
The purpose of this paper is to present a functional analysis of
ceratopsian mandibular mechanics and mastication as they are

2 Postilla Yale Peabody Museum No. 88

reflected in Triceratops, the last and most common ceratopsian
genus. The several components of the masticating apparatus,
including the dentition, musculature and those skeletal structures
directly involved, are reconstructed and described, and a mechani-
cal analysis of the mandibular lever is presented for five species of
Triceratops.

MATERIALS AND METHODS

The skulls and jaws of seven specimens of Triceratops were
selected without regard to species assignment on the basis of qual-
ity and completeness of preservation of the pertinent structures.
Although any other advanced ceratopsian would have served as
well, Triceratops was selected simply because of the greater avail-
ability of good material, Triceratops specimens being far more
abundant in existing paleontologic collections than are specimens
of any other advanced ceratopsian. Linear measurements were
made with a steel tape, or with calipers where practicable, to the
nearest quarter centimeter. Angular measurements were made
directly from the specimens with a large protractor nine inches
in radius. All measurements were taken at least twice and where
possible these were checked against dimensions of the opposite
side. In most instances, only slight differences were noted in dimen-
sions of opposite sides, major discrepancies occurring only where
crushing or incomplete preservation obscured original dimensions.

The materials used in this study are housed in the paleonto-
logic collections of the following institutions, the names of which
are abbreviated as follows:

AMNH—The American Museum of Natural History.

USNM—United States National Museum.

YPM—Peabody Museum of Natural History, Yale University.

Specimens included in this analysis are:
Triceratops brevicornus, YPM No. 1834
Triceratops elatus, AMNH No. 5116
Triceratops elatus, USNM No. 2100
Triceratops flabellatus, YPM No. 1821
Triceratops prorsus, YPM No. 1822
Triceratops serratus, AMNH No. 907
Triceratops serratus, YPM No. 1823

Dec. 24, 1964 Jaw mechanics in Triceratops “US ~3
i’ i>, CS OMP. ZOOL

MASTICATING APPARATUS FERARY

Dentition.—The dentition of Triceratops, like that of alPother | 965
advanced ceratopsians, is highly specialized and not at all oune
parable to that of any other vertebrate, although there a bY ARD
ficial resemblances to the grinding dentitions of the ere aE meSSITY
ous hadrosaurs. Teeth are arranged in long, solid and tightly com-
pacted magazines or batteries deeply implanted in the dentary and
maxilla. These batteries, approximating 50 per cent of the total
mandibular length, consist of from fifteen to thirty-five closely
packed, vertical columns of functional and replacement teeth, each
column or series being capped by a single functional tooth (see
Figs. 1 and 2).

Individual teeth of Triceratops have a slightly curved, wedge-
shaped crown, which is enameled on one side only (lingual side in
lower teeth and labial side in upper teeth), and a broad, double-
fanged root that straddles the succeeding replacement tooth (see
Fig. 2). The enameled face is marked by a prominent keel or ridge
that extends vertically over the full height of the crown. This
keeled, triangular crown face curves transversely across the long
tooth axis so that the thin enamel layer of any functional tooth is
transected by the steep occlusal surface (see Figs. 2 and 3).

The number of replacement teeth in a particular vertical series
is dependent on the position of that series within the battery, those
series near battery mid-length consisting of the greatest number

Fig. 1. A segment of the right mandibular battery of Triceratops
brevicornus (YPM No. 1834), in medial view, showing the arrangement of
functional teeth and the underlying non-functional replacement teeth. The
lingual wall of the dentary has been removed to expose the dental battery.

4 Postilla Yale Peabody Museum No. 88

(four or five) while series near either end of the battery may
contain as few as two teeth. In lingual aspect (Fig. 1) these tooth
columns are straight and nearly vertical, but in transverse section
(Figs. 2 and 3) the mandibular series curve up and outward, while
the maxillary series curve down and inward.

As reported by Edmund (1960), tooth replacement in cera-
topsians is typically reptilian, with the eruption of functional teeth
occurring sequentially in alternate vertical series and progressing
in wave-like fashion from back to front. Thus adjacent vertical
series are nearly one half cycle out of phase and a given functional
tooth is erupted slightly more than one half crown height higher
than the functional tooth immediately in front. Consequently, the
lingual aspect of an exposed mandibular battery of Triceratops
(Fig. 1) presents a rhombic mosaic of closely packed teeth, not
unlike the rhombic pattern of hadrosaurian dental batteries. Unlike
the latter, however, there is never more than one functional tooth
in each vertical series of the ceratopsian battery. This is because
the plane of occlusion is nearly parallel to the axial plane of the
dental magazine in higher ceratopsians, whereas there is a signifi-

internal

Fig. 2. Transverse section at mid-battery through the left mandible of
Triceratops brevicornus (YPM No. 1834). Notice the vertical orientation
of the occlusal surface (O.S.) and the succession of replacement teeth.

Dec. 24, 1964 Jaw mechanics in Triceratops

nm

cant angle of intersection (usually at least 30°) between the oc-
clusal plane and the axial plane of the hadrosaurian battery.

Dental Occlusion.—The most critical feature of ceratopsian
dentitions is the manner of occlusion. With the exception of Proto-
ceratops and the apparently aberrant Leptoceratops, occlusion in
all members of the Ceratopsia was exclusively one of shear. Crush-
ing or grinding was not possible in any of the known higher
ceratopsians. Figure 2, a transverse section through the lower jaw
and dentition of Triceratops brevicornus (YPM no. 1834), shows
the relationship of the occlusal plane to the mandibular battery.
It is apparent in this illustration that the surface of wear is nearly
vertical, parallel to the plane of mandibular adduction, and that
no grinding or crushing component existed. Examination of the
occlusal surfaces in any of the other higher ceratopsians reveals
them to be exactly the same; nearly straight antero-posteriorly
and vertical in orientation, extending continuously over the full
length of both mandibular and maxillary batteries. The occlusai
surface of the lower dentition extends along the labial side of the
battery (the side lacking enamel), and that of the upper battery
along the lingual side (see Fig. 3). Notice that the unilateral dis-
tribution of enamel on opposite sides of upper and lower teeth,
together with the respective curvature of crown faces, and the
vertical occlusal surfaces, places the resistant enamel at the most
critical site—the cutting edges of each of the opposing batteries.
Notice also that the keels of the enameled crowns produce strongly
“serrated” cutting edges over the full length of these batteries.
The worn dental surfaces conclusively establish the manner of
occlusion and mastication in Triceratops.

The dentition of these creatures functioned exclusively as cut-
ting structures with the mandibular batteries shearing up inside of
the maxillary batteries precisely in the manner of two pairs of
adjacent shears.

The occlusal surfaces of two specimens examined (Triceratops
serratus, AMNH No. 907 and YPM No. 1823) are so straight
longitudinally and so nearly vertical that the scissors analogy made
above is no exaggeration. Most specimens, however, show varying
degrees of warp in the occlusal surfaces, so that the total worn
surface of a particular battery may not be absolutely planar or

6 Postilla Yale Peabody Museum No. 88

_ SS
50 mm

Fig 3. Diagrammatic transverse section of the upper and lower jaws
and dental batteries of Triceratops brevicornus (based on YPM No. 1834),
showing the occlusal surfaces (O.S.), manner of occlusion, and the pattern
of tooth succession. The heavy dark lines indicate the position of the
enamel. Notice the strategic location and the oblique transection of these
enamel plates.

perfectly vertical at every point. These irregularities are natural
in part, but in many instances they are the result of post-mortem
distortion and crushing. Even where natural, however, such irreg-
ularities are minor and do not lessen the significance of the peculiar
and specialized nature of ceratopsian occlusion.

While a shearing occlusion is not unusual, it is commonly asso-
ciated with a carnivorous mode of life. Ceratopsians, however,
have repeatedly been judged as herbivores. Limited dental shear
is characteristic of numerous herbivores, both mammalian and
saurian (artiodactyls, perissodactyls, rodents, multituberculates,
tritylodonts, diadectids, turtles, etc.) but in each of these, shearing
capacities are associated with, and usually overshadowed by, grind-
ing or crushing capabilities. Apparently, shear is of only minor or
secondary importance in most herbivorous species. Thus it is par-

Dec. 24, 1964 Jaw mechanics in Triceratops 7

ticularly significant that virtually all known ceratopsian dentitions
were specialized shearing dentitions totally devoid of any crushing
or grinding properties.

It must be emphasized at this point that the shearing action
described here is not a new interpretation. It was first noted by
Hatcher (p. 46) and Lull (p. 193) in their monograph on the
ceratopsian dinosaurs (Hatcher, Marsh and Lull, 1907) and was
referred to subsequently by Lull (1908), Tait and Brown (1928)
and Russell (1935). These authors gave brief consideration to
this dental specialization and to possible diets and modes of life.
But, in my opinion, the full significance of this peculiar dental
adaptation has not been fully explored. If the dominant and unique
anatomical structure in ceratopsian evolutionary trends (the parie-
tosquamosal frill or “neck shield”) was indeed an extended plat-
form for the attachment of enlarged mandibular muscles, as sug-
gested by Lull (1908) and later by Russell (1935) and Haas
(1955), is it not possible—in fact, is it not probable—that this
unique structure was correlated with the unusual manner of dental
occlusion and mastication in ceratopsians?

Mandibles.—The mandible of Triceratops is heavy and
robust, forming a solid foundation for the large mandibular battery
(see Figs. 4 and 5). It is composed of five bones (dentary, splenial,
angular, surangular and articular) and articulates rostrally with a
sixth, unpaired, median element (predentary). The dentary is by
far the largest bone, constituting more than 70 per cent of the
lower jaw length. Rostrally it is laterally compressed but deep and
meets the opposite dentary in a long, shallow and rather weak
symphyseal suture. This junction, however, is strengthened by the
overlapping and “enclosing” articulation of the deeply excavated,
beak-like predentary.

Posteriorly, the width of the dentary increases very rapidly so
its posterior width is about four times its anterior width. This
transverse thickening at the rear of the lower jaw (see Fig. 5)
results from a pronounced lateral expansion of the dentary that
forms the broad base of a high and very stout coronoid process.
Aside from the dentition, this prominent coronoid process is the
most critical and revealing structure of the lower jaw. Unlike the
usual vertebrate coronoid process that rises from the dorsal surface

8 Postilla Yale Peabody Museum No. 88

of the dentary behind the dentition, that of Triceratops (and all
other higher ceratopsians ) extends out and upward from the lateral
surface of the dentary, well below the dental battery and far lateral
to the plane of occlusion. This process rises well above the man-
dibular dentition as a massive, laterally convex shaft. Its summit
is usually rugose and strongly expanded antero-posteriorly. The
location, height, massive construction, and expanded, rugose sum-
mit all point to a very prominent role for this structure in mandib-
ular mechanics.

150 mm [>see

Fig. 4. Right mandible of Triceratops brevicornus (YPM No. 1834)
in medial view, showing the relative positions of the dental battery with its
continuous serrated shearing edge, the coronoid process, and the glenoid
facet. Abbreviations: A, mid-point of the glenoid articulation (fulcrum);
F, zone of muscular attachment (force application); R’ location of resist-
ance (food at the dentition); R”, extreme rostral position of resistance
(food between the beaks).

Directly beneath the base of the coronoid process, immediately
anterior to the glenoid facet, is the deep Meckelian fossa opening
dorso-caudally toward the quadrate. This cavity is bordered by the
dentary laterally, dorsally and medially, by the splenial ventro-
medially and by the angular, surangular and articular posteriorly.

The posterior end of the mandible is composed of three
bones—the angular ventrally, the surangular laterally, and the
articular dorsally. The surangular, largest of the three, forms a
strong posterior buttress at the base of the coronoid process,
extending dorsally in some specimens almost to the crest of that
process. The surangular also contributes to the anterior part of

Dec. 24, 1964 Jaw mechanics in Triceratops 9

Fig. 5. Mandibles of Triceratops brevicornus (YPM No. 1834) in
dorsal aspect showing the massive construction of the rear half of the
jaws, the large glenoid facet (A), the scoop-like beak (B), the stout
coronoid process (C), and the dental batteries (D). Note the anterior con-
vergence of left and right dental batteries.

the glenoid, but the major part of that surface is formed by the
articular. The angular underlies and articulates with both the
surangular and articular, forming the ventral surface of the caudal
extremity of the lower jaw. Although none of these bones are large
or massive, they are firmly united by strong sutural contacts to
form a solid unit for articulation with the suspensorium of the skull.

The articular facet or glenoid is a prominent, but shallow,
broad, obliquely transverse groove situated immediately behind
the Meckelian fossa and the posterior extremity of the mandibular
battery (see Fig. 5). Although slightly irregular and gently con-
cave, this articular facet has a distinct inclination, facing dorso-

10 Postilla Yale Peabody Museum No. 88

caudally (parallel to the axis of the quadrate and toward the
parietosquamosal frill) instead of directly upward. It is this
inclined attitude of the glenoid surface that reflects the direction
of greatest stress at the jaw joint — viz., rostro-ventral. This
substantiates a point to be made later, that the resultant or com-
posite line of action of the mandibular adductors was dorso-
caudally oriented. Although not of primary importance, the
inclination of the glenoid also clearly precludes any significant
retraction of the mandibles, just as the rostral convergence of the
dentition prevents any mandibular protraction. Notice that the jaw
articulation is placed well below the mandibular dentition (see
Fig. 4).

The lower dentition, situated entirely within the dentary in the
posterior portion of the jaw, extends from just in front of the
glenoid to a point anterior to the midpoint of the mandible. Its
length is approximately half the total mandibular length, the ante-
rior portion of the lower jaw, including the beak, being edentulous
As noted elsewhere, a critical character of the lower jaw and its
dentition is the fact that the dental magazine extends well behind
the coronoid process to a point very close to the jaw articulation.
Thus, a significant fraction of the dentition lies posterior (and
medial) to the coronoid process.

Cranial Structures.—The skull of Triceratops is well known,
those of several species having been described and illustrated in
earlier publications (see Hatcher, Marsh and Lull, 1907 and Lull
1933). For this reason, a detailed description will not be presented
here. However, it is necessary to point out several cranial features
that are directly related to mastication and jaw mechanics.

The maxilla, as the foundation for the large upper battery, is
of obvious importance. Like the dentary, it is a massive bone
containing a deep, ventrally facing groove for the dental battery
extending over most of its length. In lateral aspect, it is sub-trian-
gular in shape with irregular and rugose superior surfaces for firm
sutural unions with the adjacent bones of the skull. Although there
is little evidence to indicate that these sutures fuse, evidence of
strong sutural unions does exist in the fact that the maxillae are
rarely separated from adjacent skull elements. Extensive sutural
contacts, particularly with the pterygoid, palatine and ectoptery-

Dec. 24, 1964 Jaw mechanics in Triceratops 11

goid postero-medially, the jugal and lachrymal postero-laterally
and dorsally, and the premaxilla anteriorly resulted in a solid and
firm dental platform entirely comparable to that of the mandibles.
An unpaired, beak-like rostral bone, articulating with both pre-
maxillae, further strengthened the maxillary foundation. The
rostral, the dorsal counterpart of the predentary, is very similar
to the latter except that it is much deeper and slightly broader,
thereby permitting the predentary to fit up inside of the rostral
upon full adduction of the lower jaw.

The suspensorium of Triceratops consisted of a very stout
quadrate which was heavily reinforced laterally by iarge jugals and
quadratojugals and posteriorly by expanded squamosals. The shaft
of the quadrate is very stout, both transversely and longitudinally.
It is joined to the pterygoid medially by means of extensive suture,
dorsally to the squamosal, and overlapped laterally by the bones of
the lower temporal arch. Of particular importance is the orienta-
tion of the quadrate, which instead of being perpendicular to the
axis of dental occlusion, or leaning forward, as in most reptiles, is
inclined caudally at an angle of 30° to 40° to the axis of occlusion,
nearly parallel to the principal axis of the frill and normal to the
gienoid facet. The distal end of the quadrate has the form of a
slightly distorted, transversely oriented cylinder with inflated ends
and a moderately restricted center. It is evident from the expanded
distal end, the stout quadrate shaft and its inclined attitude, and
the buttressing of the quadrate by adjacent bones of the skull that
the suspensorium of Triceratops was constructed to resist unusually
high stresses.

The great “neck shield” is the most conspicuous feature of the
skull of Triceratops, as it is in virtually all ceratopsians. As early
as 1908, this frill was correlated with mastication and interpreted
by Lull as an area of origin for powerful jaw muscles. Subsequent
studies by Lull (1933), Russell (1935) and Haas (1955) have
reinforced this interpretation, although a possible secondary func-
tion (protection) has been noted. In all ceratopsians, the frill
consists of a great dorso-caudal expansion of the squamosals and
parietals, reaching far behind the condyle and completely over-
lapping the cervical region. Colbert (1948) has plotted the relative
lengths of various ceratopsian frills, showing that this structure
ranges from about 45 per cent of the total skull length in Proto-

12 Postilla Yale Peabody Museum No. 88

ceratops to 66 per cent in Pentaceratops. In Triceratops, although
there is some variation, the frill constitutes about half of the total
adult skull length.

Of critical importance to the hypothes:s which correlates the
ceratopsian “neck shield” with jaw musculature is the proposed
muscle passage—the path from the mandible to the dorsal surface
of the shield through the supratemporal fenestra. Ceratopsians,
being diapsids, are characterized by both lateral and supratemporal
fenestrae. In Triceratops (and all higher ceratopsians) the lateral
fenestra is extremely small, presumably as a consequence of the
buttressing of the quadrate by adjacent bones of the lower arch
and temporal region. The supratemporal fenestra on the other
hand exists as a shallow, but broad, slit-like opening in the ante-
rior region of the frill just behind the brow horns. In all Tricera-
tops specimens examined, this passage extends dorso-caudally
as an absolutely straight tract from the summit of the adducted
coronoid process through the upper temporal opening to the dorsal
surface of the frill. A similar, broad, slit-like passage is charac-
teristic of all higher ceratopsians, but in some (Monoclonius,
Anchiceratops, Pentaceratops, and Torosaurus) the passage is
slightly deflected within the supratemporal channel and thus is
not perfectly straight.

The topographic evidence preserved on the upper surface of
Triceratops frills is highly suggestive, but not conclusive, as regards
the scars of muscle attachment. For most ceratopsians, surface
topography and patterns suggest that the frill was almost entirely
covered by large muscle sheets (see Russell, 1935 and Haas,
1955). Triceratops, however, shows no such evidence, but instead
possesses a relatively large frill which seems to lack distinct scars
of muscle attachment, except in the immediate vicinity of the
supratemporal fenestra. As a result, Russell (1935) reconstructed
the mandibular muscles as attaching in a restricted area around the
fenestra and immediately behind it, in marked contrast to the very
large posterior muscular extension postulated for Chasmosaurus
and others. However, a few specimens of Triceratops (T. flabel-
latus, YPM No. 1821; T. hatcheri, USNM No. 2412; and T. ser-
ratus, YPM No. 1823) suggest that muscle attachments on the
frill may have been more extensive than Russell suggested. It is
quite possible that a deeper pars profundus of the M. adductor

Dec. 24, 1964 Jaw mechanics in Triceratops 13

externus was attached by a strong fleshy origin about the borders
of the supratemporal fenestra, leaving a distinct scar of origin.
This would account for the features preserved in nearly all Tri-
ceratops frills. A longer pars medialis of the M. adductor externus
may have attached by a thin sheet of fascia to the frill margins
and left little or no indication of its attachment.

MANDIBULAR MUSCULATURE

Before considering the jaw mechanics of Triceratops, it is
appropriate for us to examine the probable arrangement of man-
dibular muscles as they have been reconstructed by various stu-
dents. Several works over the last half century have reviewed
ceratopsian jaw musculature, beginning with that of Lull (1908)
and followed by that of Russell (1935) and Haas (1955}.
Although there are several points on which these authors differ,
including terminology, all agree that the ceratopsian frill was
primarily concerned with mandibular musculature. Both Lull and
Russell maintained that the frill may secondarily have provided
protection for the neck region in Triceratops, chiefly because of
the afore-mentioned indications that the frill in this genus may not
have been entirely covered by muscular tissues.

Lull (1908), in what must be regarded as one of the first
significant attempts at reconstructing the musculature of an extinct
animal, presented a careful analysis of the muscles of mastication
in Triceratops, relating their possible points of attachment and
operation, and drawing an analogy with the modern frilled chame-
leon. The fact that Lull’s reconstruction is chiefly mammalian in
character should not detract from the worth of this paper, for
with the exception of Dollo’s (1884) effort, reconstructions of this
type had not been attempted before.

Briefly, Lull pictured 1) a powerful temporal muscle extending
from the anterior region of the frill (adjacent to the supratemporal
fossa) downward and forward to the posterior margin of the
coronoid process, 2) external and internal pterygoid muscles run-
ning nearly vertically from the pterygoid to the postero-medial and
ventral surfaces of the mandible, and 3) a depressor mandibulae
extending from the retroarticular process to the posterior and inner
surface of the quadrate and quadratojugal. The latter origin is

14 Postilla Yale Peabody Museum No. 88

improbable, of course, for such a location would have restricted or
entirely obstructed the stapedial canal and tympanum. Lull also
suggested that a masseter and buccinator may have been present—
the former he placed between the coronoid process and the ventro-
anterior margin of the jugal, the latter between the lateral ridges
of the maxilla and dentary forming a short but broad cheek muscle
along the full length of the dentition.

Russell (1935), in an analysis of Chasmosaurus featuring
reconstructions of the neck, trunk and limb musculature as well as
the cranial muscles, presented a reconstruction similar to that of
Lull’s with only minor differences in detail and terminology. He
visualized a more prominent M. temporalis extending from the
inner side of the coronoid process up through the supratemporal
fossa and passing back to the caudal margin of the frill in Chas-
mosaurus. Russell considered this the principal adductor and,
although his efforts were concerned chiefly with Chasmosaurus,
he presented a similar interpretation for the temporal muscle in
Protoceratops, Styracosaurus, Centrosaurus (Monoclonius) and
Anchiceratops. Like Lull he restricted this muscle in Triceratops
to that portion of the frill just posterior to the supratemporal fossa,
believing that a defensive function had become dominant in the
frill of this genus at the expense of the temporal muscles. Russell
also represented the M. pterygoidei as attaching to the ventro-
posterior surfaces of the mandible and the M. massetericus as
extending from the medial surface of the jugal to the external
surface of the coronoid process. He similarly followed Lull’s inter-
pretations regarding the buccinator and the M. depressor man-
dibulae, although he referred to the latter as the Parieto-mandib-
ularis and suggested that its origin may have been situated further
back on the underside of the frill near the extremity of the paroc-
cipital process.

The most recent reconstruction of ceratopsian cranial muscula-
ture is that of Haas (1955) based on a number of skulls of
Protoceratops. It is largely on Haas’ interpretations that the fol-
lowing muscular reconstructions of Triceratops are based. Of these
three studies, only Haas adhered to the typical sauropsid muscular
pattern and terminology in considering the trigeminal musculature.
Figure 6 illustrates the basic plan of the jaw musculature of Proto-
ceratops as reconstructed by him.

Dec. 24, 1964 Jaw mechanics in Triceratops 15)

As the present paper is concerned chiefly with the mechanics
of mastication, only those muscles directly concerned with this
activity are included in the following discussion. These include the
various elements of the adductor mandibulae group of Luther
(1914) and Lakjer (1926) (the M. adductor mandibulae exter-
nus, M. adductor mandibulae internus and M. adductor mandib-
ulae posterior) and the M. depressor mandibulae, but exclude the
other cranial muscles such as the constrictor dorsalis and con-
strictor ventralis groups. Since the ceratopsian skull was akinetic,
the constrictor dorsalis, even if present, could not have contributed
to mandibular adduction or mastication.

In accordance with Luther’s work, the reptilian adductor man-
dibulae group is separable into three principal adductors—the
external, internal and posterior, according to their positions with
respect to the three branches of the trigeminal nerve. Haas has
postulated a tripartite M. adductor mandibulae externus for Pro-
toceratops originating on the upper surface of the parietosquamosal
frill and the medial surface of the upper temporal arch, the fibers
passing forward and downward through the supratemporal fossa
to the mandible. The insertion he believed to have been in the
mandibular fossa for the deeper fibers and along the crest and
posterior border and lateral surface of the coronoid process for the
more superficial fibers. This interpretation is supported by osteo-
logic features of the Protoceratops skulls examined by Haas and
by muscle patterns of certain modern sauropsids. But from a
purely mechanical point of view, it would seem more probable that
the bulk of the adductor externus fibers were applied against the
dorsal extremity (rather than the base) of the prominent coronoid
process. This most certainly was the point of attachment of the
principal adductor in the higher ceratopsians with their much
larger and higher coronoid processes and larger frills. A point of
major significance is that Haas, like his predecessors, considered
the frill as the enlarged platform of attachment for the principal
jaw adductors—the M. adductor mandibulae externus (M. tem-
poralis of Lull and Russell). The force of contraction of this
large, complex muscle acting in the region of the coronoid was
chiefly up and backward, a force vector oriented at approximately
60° to 70° back from the axis of the mandible.

Of the two portions of the adductor internus (M. pseudotem-

16 Postilla Yale Peabody Museum No. 88

150 mm

JL /
eee ee a Ui;
—_ SX Wy toy
iM i; Kf
A yy,

Fig. 6. Protoceratops andrewsi with the mandibular muscles recon-
structed. Abbreviations: A, M. pseudotemporalis; B, M. pterygoideus; C, M.
adductor mandibulae externus superficialis;s D, M. adductor mandiulae
externus medialis and profundus; E, M. depressor mandibulae; F. M.
_ adductor mandibular posterior.

poralis and M. pterygoideus), Haas reconstructed the former as
occupying a peculiar anterior position with the origin located in
the orbital area and the fibers descending almost vertically to an
insertion on the anterior slope of the coronoid process. Although
the insertion is still open to question and may actually have been
more intimately associated with the summit of the coronoid proc-
ess, I am not able to support such a possibility with any concrete
evidence for either Protoceratops or Triceratops. The strange
orbital origin postulated by Haas is amply supported by good
osteologic evidence, namely, the location of the trigeminal fora-
men, which is situated behind the pseudotemporalis in all living
sauropsids. Contraction of the postulated pseudotemporalis would
have produced strong vertical adductive forces. The second portion
of the adductor internus, the M. pterygoideus, is reconstructed by
Haas as a more complex muscle connecting the postero-lateral,
ventral, and medial surfaces of the rear of the mandible with the

Dec. 24, 1964 Jaw mechanics in Triceratops t7

ectopterygoid—pterygoid process of the basi-cranium. This is con-
sistent with the condition of modern sauropsids. With the rostral
ascent of the pterygoideus fibers in Protoceratops, contraction
would have produced a dorso-anteriorly directed adductive force.
It is important to note that both adductor internus muscles (as
reconstructed here for Protoceratops) are oriented at distinct
angles to the other mandibular muscles and therefore would have
generated adductive forces in directions quite different from those
of the other jaw muscles.

The remaining trigeminal muscles, the M. adductor mandibulae
posterior, is placed medial to the external adductors by Haas,
extending from the anterior face of the quadrate to the splenial
on the ventro-medial surface of the mandible and to the region
immediately adjacent to and surrounding the entrance to the man-
dibular fossa. In my opinion this muscle probably accounted for
the bulk of the muscular fibers that must have inserted in and
around the Meckelian fossa, as in crocodilians and certain lacerti-
lians, with the major part of the external adductors inserting more
superficially on the upper extremities of the coronoid process.
Contraction of the adductor posterior in this position would have
produced a strong dorso-caudally oriented adductive force almost
parallel to that generated by the more superficial adductor
externus.

Although not a trigeminal muscle, the M. depressor mandib-
ulae is intimately involved in jaw mechanics, as it is the sole man-
dibular diductor or depressor. Haas postulated this muscle as
passing ventrally from the latero-ventral margin of the squamosal
behind the quadrate to the medially expanded but caudally re-
stricted retroarticular process. This position provides ample space
for a superficial tympanum behind the quadrate, even though Haas
suggests that the postquadratic region is perhaps too far distant
from the fenestra ovalis to have permitted retention of a functional
stapes and tympanum. In view of the extremely short postarticular
length of the retroarticular process in Protoceratops (and in all
higher ceratopsians, for that matter), and of the orientation of the
proposed depressor fibers (a particularly critical point for higher
ceratopsians), there is considerable doubt as to the functional
value of this muscle. Whatever its position and orientation, it had

18 Postilla Yale Peabody Museum No. 88

negligible leverage and consequently could not have been a signifi-
cant factor in jaw depression.

The trigeminal musculature summarized below and illustrated
diagrammatically in Figure 7 is reconstructed on the basis of 1)
Haas’ reconstructions for Protoceratops, 2) preservation of dis-
tinct muscle scars in one or more of the Triceratops skulls
examined, 3) the spatial and mechanical requirements of the
particular muscles, and 4) Luther’s classification of sauropsid
trigeminal musculature together with reference to the position of
the trigeminal foramen.

Adductor internus group:

M. pseudotemporalis (A): Origin in the posterior region
of the orbit on the lateral surface of the laterosphenoid
anterior to the trigeminal foramen. Insertion on the
anterior expansion of the summit of the coronoid
process.

M. pterygoideus (B): Origin along the posterior surface
of the ventral wing of the pterygoid and along the
ventral margin of that process. Insertion on the ventro-
lateral, ventral and ventro-medial surfaces of the rear
of the mandible adjacent to the articulation.

Adductor externus group:

M. adductor externus superficialis (C): Origin on the
medial surface of the upper temporal arch. Insertion
on or adjacent to the summit of the coronoid process.

M. adductor externus medialis and profundus (D): Ori-
gin on the dorsal surface of the parietosquamosal frill
adjacent to the supratemporal fenestra and possibly
extending back to the frill margin. Insertion on the
summit of the coronoid process.

Adductor posterior group:

M. adductor posterior (F): Origin on the anterior face
of the quadrate. Insertion along the margins and
within Meckel’s cavity.

Dec. 24, 1964 Jaw mechanics in Triceratops 19

Whether or not the precise locations and orientations here
proposed for these muscles are accepted, several points must be
emphasized. As illustrated in Figures 4 and 5, the available man-
dibular areas in Triceratops that could have served as sites of
attachment for these muscles are much restricted. The two most
obvious and likely sites are the coronoid process and the Meckelian
fossa. Any muscle fibers that inserted in or near the latter almost
certainly extended up and back, if not to the anterior surface of
the quadrate (which shows distinct muscle scars), then higher

Fig. 7. Triceratops brevicornus with the location and action of the
mandibular muscles indicated by arrows A — F. Abbreviations as in Fig. 6.

toward the supratemporal fenestra. There was no other place for
these fibers. Those fibers that inserted along the summit of the
coronoid process (attested to by very clear osteologic evidence)
similarly could only have passed up and back. There was limited
space behind the orbit, but the greatest portion of these fibers must
have passed dorsocaudally to the supratemporal fenestra and
beyond to the upper surface of the frill. There simply was no
other space available to house these muscles within the temporal
region of the Triceratops skull. Most significant of all, however,
is the fact that the direction of action of these proposed “coronoid
muscles” (the long arrow of Figure 7) is mechanically the most

20 Postilla Yale Peabody Museum No. 88

effective line of action possible in a mechanical system such as
that of Triceratops, in spite of the fact that this vector was not
oriented perpendicular to the mandibular or lever axis. As the
following discussion attempts to demonstrate, any other orienta-
tion of these “coronoid muscles” would have resulted in reduced
leverage and thus lower adductive force.

MANDIBULAR MECHANICS

The vertebrate lower jaw during adduction operates as a third
class lever (see Fig. 8) with the force (muscular contraction)
applied at a point (or points) between the fulcrum (jaw articula-
tion) and the resistance (dentition). As Davis (1955) noted,
“this is a remarkably poor arrangement for masticatory purposes,”
for there is no mechanical advantage in a simple third class lever.
The effective masticating force available at the dentition is less
than the force of muscular contraction because the resistance lever
arm (distance from the dentition to the articulation) is greater
than the force lever arm (distance from the point of muscle attach-
ment to the articulation). Force is sacrificed for a gain in speed of
jaw adduction or displacement.'

The collective effect of contraction of the mandibular adductor
muscles is rotation of the mandible through a limited vertical arc
about a horizontal transverse axis. Disregarding friction, the effi-
ciency with which this rotation is accomplished is determined by
the moment arm or leverage through which the adducting forces
act. The moment arm, by definition, is the perpendicular distance
between the line or direction of force action and the fulcrum. The
force which can be exerted at any point along the dentition, then,
is a function not only of the magnitude of the applied force, but
of the lever or moment arm as well. The product of force and its
moment arm length is termed the moment of that force.

In the simple third class lever of Figure 8A, the moment arm
of the applied force is distance b and that of the resistant force is

‘Displacement has generally been overlooked by most functional anatomists

in their analyses of jaw mechanics, but obviously it is of considerable
importance. Speed of adduction may be critical in predaceous vertebrates,
but it cannot be considered important in herbivores. Gape of the mouth,
however, ts significant in both. Construction of the lower jaw as a third
class lever permits maximum depression of the jaw with a minimum
length of adductor muscle fibers.

Dec. 24, 1964 Jaw mechanics in Triceratops zt

distance a + b. Both moment arms are perpendicular to the line
of action of the respective forces, which themselves (in this
instance) are perpendicular to the lever axis. If the applied force,
instead of acting perpendicularly to the lever, acts at some other
angle, say 45° back toward the fulcrum (as in Figure 8B), the
available force at any point along the lever will be less because
the moment arm (or leverage) of the applied force is shorter.
Distance b is no longer perpendicular to the line of force action
and therefore is no longer the moment arm. The new moment arm,
perpendicular to the new inclined force vector is b’ and its length
(and therefore the leverage of the applied force) is a function of
the angle of inclination of the applied force (in this instance, 45°).
The length of this moment arm then is the product of b and the
sin of 45° (.707Ib).

Applying these mechanics to the vertebrate jaw, it would
appear that the most effective mechanical arrangement is one in
which the muscle fibers are oriented vertically, perpendicular to
the jaw ramus and attached as far forward of the articulation as

A Force

Resistance Fulcrum

Resistance Fulcrum

Fig. 8. Simple third class levers. A, Third class lever with parallel
opposing forces. Moment arm of applied force equals b. Moment arm of
resistant force equals a + b. B, Third class lever with nonparallel opposing

forces. Moment arm of resistant force equals a + b. Moment arm of
applied force equals b’.

22 Postilla Yale Peabody Museum No. 88

possible. There are some obvious disadvantages in this arrange-
ment, however, as has already been inferred. First, with the adduc-
tor muscles shifted forward away from the fulcrum, a correspond-
ing reduction in possible jaw gape results. Second, the forward
position of the adductor fibers would presumably restrict the size
(and thus the power) of the jaw musculature, because the areas
of origin would of necessity be concentrated in the facial region,
beneath or in front of the orbits and along the snout.

The critical factor in a mechanical system of this type is the
length of the moment arm (and ultimately the magnitude of the
moment of the applied force). The effective force acting perpen-
dicular to the structural member (jaw ramus) can only be mag-
nified by 1) increasing the magnitude of the applied force or 2)
lengthening the moment arm by shifting the point of force applica-
tion away from the fulcrum. The first solution requires muscle
enlargement and increased effort, whereas the second does not.

Where the applied force acts at some angle other than 90° to
the structural member of the lever (as with the inclined force
vector of Figure 8B), it is possible to increase the moment arm
(and thus the effectiveness of the applied force) without shifting
the point of force application along the jaw ramus away from the
fulcrum (and thereby reducing the amount of gape possible).
This can be accomplished simply by elevating the point of force
application (muscle attachment) above the axis of the lever (as
is achieved by the development of a coronoid process) or by
depressing the fulcrum below the lever axis or both.

From these simple mechanics we may conclude that the devel-
opment of a prominent coronoid process (as in Triceratops) or
the depression of the jaw articulation (also as in Triceratops)
results in an increase in the length of the moment arm of the
principal mandibular adductors and therefore an increase in
adductive force.

The ceratopsian mandibular lever is not a simple third class
lever, but is one that has been modified in several ways. The prin-
cipal differences are that the forces involved (resistant force
between opposing dentitions and principal adductive force of
muscular contractions) did not act in opposite directions, as in
Figure 8A, but instead acted at a distinct angle to each other.
Also, the three critical points of the ceratopsian lever (fulcrum,

Dec. 24, 1964 Jaw mechanics in Triceratops 23

point of action of the applied force, and point[s] of resistant
action) did not lie on a simple straight axis. The fulcrum (articula-
tion) lies well below the dentition or plane of resistant action and
the principal point of force application (the coronoid process) is
situated far above and lateral to the dental plane. The dentition, of
course, marks the primary axis of the lever and those points at
which the resistance acted.

The mandibular lever of Triceratops is illustrated in Figure 9
translated into diagrammatic terms. In this diagram, the combined
lengths of the solid horizontal lines (b + e’ + a) represent the
total length of the mandible anterior to the center point of the
jaw articulation (fulcrum). This distance is 76 cm in Triceratops
brevicornus (YPM No. 1834). It represents the maximum moment
arm of the resistant force. The double horizontal line (e’ + e”)
corresponds in length and position to the mandibular battery (37
cm long in T. brevicornus). The solid vertical line (h) represents
the vertical distance from the top of the coronoid process to the
level of the jaw articulation (17.5 cm in T. brevicornus) and its
location corresponds to the position of the coronoid process along
the mandibular ramus. The resistance (food), acting either at
the beak or at any point along the dentition, is assumed to have
acted perpendicularly to the jaw ramus. The applied force, however,
(that generated by the dominant or principal adductor muscle—

ae
ye?
a“

oo

resistance ___ articulation

Fig. 9. Diagrammatic representation of the mandibular lever of Tvi-
ceratops. Battery length equals e’+ e”. Mandibular length equals a +
e’ + b. Moment arm of principal adductor as labeled (see b’ of Fig. 8B).
Moment arm of resistant force equals a + e’ (with the resistance placed
as shown here). Height of coronoid process equals h.

24 Postilla Yale Peabody Museum No. 88

M. adductor mandibulae externus) is interpreted as having acted
along a line (long broken arrow of Figures 7 and 9) trending
approximately 30° to 40° to the lever axis. This last interpretation,
including the selection of the principal adductor, is based on the
following assessment of the relative mechanical significance of
the several mandibular adductors summarized on page 18 and in
Figure 7.

M. pseudotemporalis (A)—a minor adductor, probably
of small size but with a long moment arm.

M. pterygoideus (B)—a very minor adductor of moderate
to possibly large size, but with a negligible or ex-
tremely short moment arm.

M. adductor externus (C, D)—a very important adduc-
tor of large to very large size with a very long moment
arm.

M. adductor posterior (F)—probably a minor adductor
of small to moderate size with a rather short moment
arm.

As shown in Figure 7, the only mandibular muscles with
moment arms of significant length, and therefore potentially domi-
nant adductor muscles, were the pseudotemporalis (A) and the
external adductor (C, D). Morphologic evidence indicates the
latter to have been a very large muscle. No such evidence indicates
a large size for the pseudotemporalis. The adductor externus,
therefore, has been selected as the dominant Triceratops jaw mus-
cle and the angle between its line of action and the dental row is
angle 6, or approximately 30° in Triceratops brevicornus (see
Fig. 10).

The length of the principal adductor moment arm of Tricera-
tops cannot be measured directly with any accuracy when the
lower jaw is in articulation and fully adducted (the critical posi-
tion), but it can be calculated from other measurements taken
from the skull and jaws (see Fig. 10). In Triceratops, the moment
arm of the applied force is a function of the height (h) of the
coronoid process above the level of the articulation, the lever
distance (a) between the center of the articulation and the mid-
point of the base of the coronoid shaft, and the attitude (angle 4)

Dec. 24, 1964 Jaw mechanics in Triceratops 25

of the line of action of the applied force (F) relative to the
fulcrum. Angle # can only be determined when the lower jaw is
in the fully adducted position because 1) the line of action of the
applied force relative to the mandibular lever is not constant but
changes during elevation and depression of the jaw, and 2) we are
concerned here only with the mechanical efficiency of the ceratop-
sian jaw in the act of shearing or masticating, and therefore in the
occluded state. With the jaws fully adducted, a line passing from
the summit of the coronoid process up and back through the
supratemporal fenestra to the dorsal surface of the frill represents
the line of action of the principal adductor—the adductor externus.

It is immediately apparent from the diagrams of Figures 7 and
9, that in spite of the close proximity of the jaw articulation and
the coronoid process, the moment arm of the applied force (prin-
cipal adductor) is very long. Consequently, we may conclude that
the adductive efficiency of this part of the mandibular muscula-
ture of Triceratops was very high and presumably, that the masti-
catory powers were correspondingly great.

With these parameters, we can calculate the relative force
that could be generated by the principal adductor at any point
along the mandible of Triceratops as follows:

According to the laws of lever mechanics, rotation of the lever
about the fulcrum can only occur when the lever is not in
equilibrium. That is, when the moment of adduction or elevation
exceeds the moment of depression, an elevating rotation of the
jaw about the fulcrum will take place. When there is no resistance
(food) between opposing dental batteries, the required adduction
moment is small, just sufficient to overcome friction and the weight
of the mandibles. When the dentition encounters resistance in the
form of plant fibers to be cut or crushed, further rotation is accom-
plished only when the applied force exceeds the resistance of the
food substance, or, in other words, when the moment of the
applied force exceeds that of the resistance.

In Figure 10, the resistant moment is
S (e’ + a)

where S equals the resistant force and e’ + a the moment arm
of the resistance. The moment of the applied force is
F (m)

26 Postilla Yale Peabody Museum No. 88

where F equals the applied force and m the moment arm of that
force. Because m cannot be measured directly with any accuracy,
it must be calculated: m= sin (¢ + 8) d

where d represents the diagonal distance between the fulcrum and
the point of muscle attachment at the summit of the coronoid
process. (The diagonal d can either be measured directly or
calculated by the Pythagorean theorem from h and a.) Angle 3 is
that between the diagonal and the lever axis.

From these we can calculate the usable force that could be
generated at any point along the mandibular lever from:

S (e’ + a) =F sin (6+ 8) d

where e’ equals any desired distance anterior to the coronoid
process dependent upon the selected location of the food, and F

is assumed to be unity or 100 per cent.
Substituting the appropriate values from Triceratops brevi-
cornus (YPM No. 1834):

S (28 + 15) = 100 sin (30° + 50°) 23
43S = 100 (.9848 x 23)
ASS — 2750)

The selected distance for e’ (28 cm) in the above calculation
places the resistant force (food) at the anterior end of the man-

|
|
|
Vv
S

Fig. 10. Mechanical model of the mandibular lever of Triceratops,
the basis of the accompanying calculations.

Dec. 24, 1964 Jaw mechanics in Triceratops Pa

dibular battery. The calculations demonstrate that with the
mechanical system described above for Triceratops brevicornus,
one gram of occlusal force was available at the rostral extremity
of the dentition for every two grams of contractile force exerted
by the principal adductor.

TABLE I
2

Measurements of the 5 2 Ss § % we.
Sx Se VSS eet et eS) Ses
* =omn ~— —~ AN nan — rN
Mandibular Lever of See es ce EO tS, a ice Sk Son
SS. me Zo Sie ar 2 Oo Se
T 2 a = ~ z ~ Z. ~ Z => Bs i= 6 i] Z. =) S

riceratop: nm a a a x = 2
P QZ Qs Q 27 QZ Qo &Z

(see Figures 9 and 10) S 27 8 = & £ 27
S= § SS. See LS se
DO vu = UN Vu v Ay o = U Ay
Set AS SS) See Sea

Linear measurements in cm ‘= = SS ‘= = SS =

|

(a)

Distance from the center of glenoid 15.0 23.0 21.0 14.0 14.0 12.5 13.5
to center of coronoid process.
(h) :
Vertical height of coronoid process 17.5 22.0 24.0 19.0 17.5 22.0 17.0
above glenoid.
(d)
Diagonal distance from center of ZShO) SSIES ees 20 6239" 3225. 7 27S DES
glenoid to crest of coronoid process.
(al SR @% ae Jo)
Mandibular distance from center of 76.0 102.0 88.0 82.0 75.0 90.0 72.0
glenoid to extremity of the beak.
Cat =e")
Mandibular distance from center of 43.0 68.0 58.0 46.0 45.0 55.0 42.0
glenoid to rostral end of dentition.
(a —e”)
Mandioular distance from center of US MSO Leo) 9.0 9.0 9.0 7.0
glenoid to posterior end of dentition.
(ce? -- e”)
Length of mandibular battery. 37205 55:0 46:0) 38:0) 37:0) 50:0 3720
(@)
Attitude of principal adductor action 30° 35 38 BIS) ) SIS) SU isi
relative to jaw axis.
(8)
Angle between jaw axis and 50° 44° 49° 54° 51 60° 52

diagonal (d).

28 Postilla Yale Peabody Museum No. 88

By the same procedure, the usable force at the beaks can be
determined. Here the resistant moment arm is a + e’ + b (of
Fig. 10) or 76 cm. The available force (S) at the beaks equals 29
per cent of the applied force or approximately one gram for every
four grams of contractile force. This seems to be a rather low
value, but when the total length of the mandible is considered, it is
a remarkably high value, and it is consistent with the existence of
the ceratopsian beak. It is highly unlikely that a specialized struc-
ture such as the ceratopsian beak would have been adaptive unless
significant forces could have been generated between the beaks,
but it is also clear that the beaks probably did not serve as an
important shearing mechanism because of the great length of the
mandibles and the correspondingly long resistant moment arm.

The full significance of the Triceratops mandibular lever is yet
to be established. It is hardly necessary to point out that maximum
occlusal forces are available at the rear of the vertebrate jaw,
between opposing teeth closest to the fulcrum. But, in nearly all
vertebrates, the available force at the rear of the tooth row is.
somewhat less than the total applied force. In Triceratops, how-
ever, this is not the case. As mentioned earlier, the mandibular
battery extends far back in the jaw, almost to the articulation and
well behind the coronoid process. The last tooth of the mandibular
battery in Triceratops brevicornus (YPM No. 1834) is only 7.5
cm anterior to the center point of the jaw articulation. Thus, the
resistant moment arm for the rear of the battery is

S 7.5 cm
and the lever equation now becomes

ido —= 100. sin (S070 50 jaes
ISS = 2250
S = 300%

At the caudal extremity of the batteries, an occlusal force of 3
grams is available for every one gram of contractile force applied
to the mandibular lever by the principal adductor!

Similar analyses of the other six specimens of Triceratops
produced essentially similar results. For all seven specimens, the
adductive pressure that could have been generated at the beaks
was approximately 30 per cent of the applied force (28% to

Dec. 24, 1964 Jaw mechanics in Triceratops

TABLE II
: = o &§ < a
Mechanical Parameters of Sy s = E = ee aa SS S 7
- Y CO 8 - = co veo x ~ 00
the Mandibular Lever of ee a is ge = Ke) vo
a6 4@& 2% 26 256 2H ac
Triceratops are Sas ss ae 2 on CZ
5S sZ 8 SS] es 2 ss
Sen bus ee eee Se
See 8S Sy Sa Ot 1S
Linear dimensions in cm = = = ES = = =
(m)
Calculated length of moment arm. 22S Sil Byiloz Daye DN i fg aie
Moment arm as percentage of length
of mandibular lever. 30% 30% 36% 29% 30% 31% 30%
Calculated force available at the
beak as a percentage of force ap-
plied by the principal adductor mus- 29% 30% 36% 28% 30% 31% 30%
cle.
Calculated force available at the
rostral end of the dentition as a
percentage of force applied by the 52% 45% SS% 51% 50% 50% 51%
principal adductor muscle.
Calculated force available at the
caudal end of the dentition as a ‘
percentage of force applied by the 300% 206% 288% 260% 250% 308% 305%

principal adductor muscle.

36% ). The available force at the rostral extremity of the dentition
approximated 50 per cent (45% to 55%) and at the caudal
extremity of the dentition, the available shearing force ranged
from 250 per cent to 300 per cent. The comparative mechanical
efficiency of the mandibular lever of all seven specimens is sum-
marized in Table IH. Although differences do appear, there is
remarkable consistency among the seven specimens for the several
mechanical parameters calculated.

DISCUSSION

The most critical element in this analysis is the basis for the
principal vector or assumed line of action of the applied force
This aspect of the problem may be approached in two ways: first,
by calculating the average direction of adductor action (the com-
bined action of all adductor muscles), or second, by determina-

30 Postilla Yale Peabody Museum No. 88

tion of the probable line of action of the dominant or principal
adductor muscle. The second approach was used in this analysis
for several reasons. First, the combined effect of all the adductor
muscles cannot be determined without some measure of the rela-
tive power of the respective muscles, even though their individual
lines of action may be known. Any “average vector” calculated
without these data would be highly subjective and speculative.
Second, morphologic and mechanical evidence in both the skull
and jaw clearly indicates that those muscles which occupied the
“temporal” region in Triceratops were the dominant adductor
muscles with the greatest bulk and the longest moment arm and
therefore had the greatest impact on mandibular mechanics. Cal-
culations based on such a dominant factor, although specifically
applicable only to that solitary force, can be expected to approxi-
mate closely the combined effect of the total adductor complex.?

The summit of the coronoid process almost certainly served as
the principal (if not exclusive) site of attachment of the adductor
externus, but regardless of what specific muscle inserted here, that
muscle must have been the most important of the jaw muscles. It
had the longest possible moment arm and very probably the great-
est bulk of any of the trigeminal muscles. The primary function of
this muscle was adduction. The Meckelian fossa, by analogy with
modern reptiles, probably represents the insertion area of the
adductor posterior, which in Triceratops must have been a short,
compact muscle originating on the anterior face of the quadrate
and situated immediately adjacent to the jaw articulation. Although
the adductor posterior may have been a powerful muscle, the very
short moment arm indicates that it could not have been the domi-
nant adductor muscle. The adductor posterior may well have
served to prevent disarticulation of the mandibles as well as elevat-
ing the lower jaws. The fact that its orientation was almost parallel
to that of the larger adductor externus suggests that its action
would not significantly have altered the assumed actions of the
above analysis. The moment arm, however, which was only one

*It is perhaps significant that when the vectors (the magnitudes of which
are proportional to the respective moment arms rather than the unknown
absolute power of the muscles) of each of the trigeminal muscles of
Triceratops are added vectorally, the resultant vector orientation closely
approaches (deviates by less than 10° in T. brevicornus) the direction of
action reconstructed for the principal adductor.

Dec. 24, 1964 Jaw mechanics in Triceratops 31

third that of the adductor externus, means that this muscle had
one third the adductive power of the adductor externus— if the
two muscles were of equal size (an assumption deemed very doubt-
ful in view of cranial evidence indicating the adductor posterior
to have been much smaller than the adductor externus).

The position of the pseudotemporalis is not as certain as are
those of the other adductors, but it is clear from cranial evidence
that unless it occupied a most unlikely position, such as that postu-
Jated for the adductor externus (in which instance the above
analysis would still apply), the pseudotemporalis could not have
been a large muscle. In fact, it must have been a rather small
muscle for there simply is insufficient space available within the
anterior part of the temporal region of a Triceratops skull to house
a large muscle. Regarding the pterygoideus muscle, the most prob-
able position and orientation of these fibers (as shown in Figure 7 )
dictates that this muscle be disregarded as far as mechanics of
adduction and mastication are concerned. Inserting on the ventral
and medial (and probably also on the ventro-lateral) surfaces of
the mandible immediately beneath and adjacent to the jaw articula-
tion, its line of action passed virtually through the fulcrum and
therefore its moment arm was of almost negligible length. Thus
the adducting moment of the pterygoideus was very small regard-
less of how large a muscle it may have been. From its position and
orientation, we may conclude that it served primarily to prevent
disarticulation of the mandibles and with its sling-like form, passing
beneath the rear of the mandible, counteracted the high stresses
that must have occurred at the articulation during mastication.

The various linear dimensions included in the analyses fre-
sented here are perhaps the most reliable factors involved, in spite
of the fact that the application of the applied force has been
arbitrarily reduced to a point, just as the broad articular facet has
been represented as a simple pivotal point. The greatest potential
source of error lies not in the linear measurements but in the
angular determinations. The attitude of the applied force relative
to the lever axis is particularly critical and sensitive, for even very
slight dorso-ventral crushing of the ceratopsian skull would result
in a significant reduction of angle 6. Every effort was made to
eliminate this source of error by ruling out any and all specimens
distorted by post-mortem crushing. An indication of the degree

32 Postilla Yale Peabody Museum No. 88

of success achieved in avoiding this source of error is reflected in
the values obtained for 6. Among the seven specimens included
in this report, the range of variation of 6 was only 8 degrees (see
Table I). We can assume, therefore, that the principal vector
plotted for these calculations is dependable.

In spite of what may seem to be a gross over-simplification of
a complex mechanical system (complex in the sense that several
different vectors of unknown magnitude and uncertain orientation
were responsible for the mechanical actions under consideration),
it is believed that the analysis presented here contributes to our
understanding of the functional significance of a highly specialized
adaptation—the ceratopsian masticating apparatus. The values
obtained for the relative adductive pressures at various points
along the mandibular lever may not be precise, but they certainly
represent reasonable approximations. More significant, however,
they permit a quantitative assessment of the functional significance
of particular component structures constituting this mechanical
system, specifically, the precise role of the coronoid process, the |
significance of glenoid depression (or elevation), the importance
of dental placement, and the attitude and construction of the
suspensorium.

Two very important points stand out, as regards Triceratops.
First, the shearing dentition, consisting of highly specialized dental
magazines of great length located in the rear half of the jaws, func-
tioned exclusively as shearing blades. Second, the great mechanical
power of the mandibular lever, reflected in the massive jaw con-
struction, the design of the articulation, the robust coronoid proc-
ess, and the mechanical design of the mandibles, provided a very
long moment arm relative to jaw length. To the latter must be
added the enlarged mandibular musculature, indicated by the great
dorso-caudal expansion of the parietosquamosal frill.

ECOLOGIC IMPLICATIONS

It is hazardous to speculate about such matters as ceratopsian
food preferences, but the feeding apparatus of these animals, and
that of Triceratops in particular, is so unusual that failure to at
least consider these matters would be a serious lapse. The observa-
tions and interpretations presented here demand some response to

Dec. 24, 1964 Jaw mechanics in Triceratops 33
the obvious question—what did ceratopsians feed on that required
such unusual dentures and powerful jaws?

It is quite evident that Triceratops species were highly spe-
cialized for feeding on specific and probably rather unusual plant
foods. But what types of plants these might have been is not nearly
so evident. The fact that shearing power has been so highly per-
fected at the complete expense of all crushing and grinding powers
points to the exclusion from ceratopsian diets of any ordinary
leafy plant tissues, fruits or seeds. The uniqueness of the dentition
further suggests that ceratopsians probably were the only animals
equipped to feed on these particular plants. The indications of
great power in all ceratopsian mandibular systems lead to the con-
clusion that ceratopsian food was very tough and resistant.

C.ushing or grinding are effective means of reducing most
edible plant tissues to small, easily digested particles, but highly
fibrous tissues are best cut or sliced. It therefore seems reasonable
to suppose that ceratopsian food differed from more normal herb-
age by a highly fibrous texture. Of the plant varieties available dur-
ing Late Cretaceous times, two seem to be reasonable candidates
for ceratopsian feed — at least in terms of the resilient and highly
fibrous character suggested. These are the cycads and palms. Both
of these are characterized by numerous long, palm-like fronds that
radiate out from the top of a simple, unbranched trunk. The fronds
of living palms and cycads often are tough and highly fibrous and
those known from Late Cretaceous sediments appear to have been
of similar character. In most living and fossil cycads, and in some
palms, the trunk is quite short, thus the fronds are close to the
ground and well within the reach of “ceratopsian-sized” animals.

Whether or not either cycad or palm fronds could have pro-
vided sufficient nourishment for these Late Cretaceous dinosaurs
is not known, but I know of no other plants from ceratopsian-
bearing strata that possessed the physical characteristics suggested
by ceratopsian dentitions.

SUMMARY

1. The dental batteries of Triceratops were elongated, highly
specialized, continuous shearing blades completely devoid of all
crushing or grinding capacities.

34 Postilla Yale Peabody Museum No. 88

2. The mandibular lever was constructed for maximum
mechanical efficiency and the highest adductive stresses through
a) the lateral positioning, b) the prominent height, c) the robust
construction of the coronoid process, d) the caudal expansion of
the dentition, and e) the depression, inclination and buttressing
of the glenoid facet, all of which contributed to either lengthening
the effective moment arm of the applied force, or reducing that
of the resistant force, or resisting the resulting high stresses at the
articulation.

3. Adductive forces apparently were increased also by enlarge-
ment of certain mandibular muscles, this being reflected in the
greatly expanded parietosquamosal frill and the prominent rein-
forcement and caudal inclination of the suspensorium.

4. Occlusal forces available at the beaks, and the rostral and
caudal extremities of the dental batteries approximated 30%,
50% and 250% to 300% respectively of the force exerted by the
principal adductor muscle. These are the result of the unusual
mechanical construction of the mandible and of the dorso-caudal
extension of the Triceratops skull.

ACKNOWLEDGMENTS

I am indebted to several colleagues who contributed through
discussion and criticism to the development of some of the inter-
pretations presented here. I gratefully acknowledge these contribu-
tions by John S. McIntosh, James A. Hopson, and Dale A. Russell.
Thanks are also due C. Lewis Gazin of the United States National!
Museum and Edwin H. Colbert of the American Museum of Nat-
ural History for making available certain specimens under their
care. To the following, who read and criticised all or part of the
manuscript, my sincere thanks: H. Barghusen, E. H. Colbert,
J. A. Hopson, A. L. McAlester, J. S. McIntosh, D. A. Russell,
B. Schaeffer. The illustrations, with the exception of Figure 5,
were prepared by Mrs. Martha Erikson.

Dec. 24, 1964 Jaw mechanics in Triceratops 35

LITERATURE CITED

Colbert, E. C., 1948. Evolution of the horned dinosaurs. Evol., v. 2, p.
145-163.

Davis, D. D., 1955. Masticatory apparatus in the spectacled bear. Fieldiana.
Zoology, v. 37, p. 25-46.

Dollo, L., 1884. Cinqui¢me note sur les Dinosauriens de Bernissart. Bull.
Musée Royale d’hist. nat. de Belgique, 3, p. 136-146.

Edmund, A. G., 1960. Tooth replacement phenomena in the lower verte-
brates. Roy. Ont. Mus. Contrib. no. 52, p. 1-190.

Haas, G., 1955. The jaw musculature in Protoceratops and in other cera-
topsians. Amer. Mus. Nat. Hist. Novitates no. 1729, p. 1-24.

Hatcher, J. B., O. C. Marsh and R. S. Lull, 1907. The Ceratopsia. U.S.
Geol. Surv. Monograph no. 49, p. 1-198.

Lakjer, T., 1926. Studien iiber die Trigeminus-Versorgte Kaumuskulatur
der Sauropsiden. Copenhagen, C. A. Reitzel. 153 p.

Lull, R. S., 1908. The cranial musculature and the origin of the frill in
the ceratopsian dinosaurs. Amer. Jour. Sci., v. 25, p. 387-399.

1933. A revision of the Ceratopsia or horned dinosaurs.

Peabody Museum Memoir no. 3, p. 1-135.

Luther, A., 1914. Uber die vom N. trigeminus versorgte muskulatur der
Amphibien. Act Soc. Sci. Fennicae, v. 44, p. 1-151.

Russell, L. S., 1935. Musculature and Functions in the Ceratopsia. Nat.
Mus. Canada, Bull. 77, p. 39-48.

Tait, J. and B. Brown, 1928. How the Ceratopsia carried and used their
head. Roy. Soc. Canada, Trans. no. 5, p. 13-23

nu

wi

|

ee es

ae
ee ee
rr

25

nt

ne

ante
ee awe
Sree

Ee eres
cparegn oes

rn a pages
ae

ae
a

~ vee we
eT ati
pea Ae