3333
The Journal of Experimental Biology 202, 3333–3345 (1999)
Printed in Great Britain © The Company of Biologists Limited 1999
JEB2249
INVERTEBRATE PARAXIAL LOCOMOTORY APPENDAGES: DESIGN,
DEFORMATION AND CONTROL
ROBIN J. WOOTTON*
School of Biological Sciences, Exeter University, Exeter EX4 4PS, UK
*e-mail: [email protected]
Accepted 16 August; published on WWW 16 November 1999
Summary
Some principles governing the design of invertebrate
bending and torsional moments, and can exploit these to
paired propulsive appendages are discussed, with
assist in the deformations that are necessary to gain force
particular reference to the extent to which information
asymmetry between half-strokes. Swimming appendages
encoded in their skeletal structure determines their
normally employ both muscles and drag, but the wings of
insects lack internal muscles, and their changes in shape
instantaneous shape in locomotion. The hydrostatic paired
are largely complex aeroelastic responses to the constantly
fins of some cephalopods and marine gastropods,
polychaete parapodia and onychophoran lobopodia rely
changing aerodynamic and inertial loads, moderated by
entirely on musculature for shape control. The
muscles inserted at the base. For illustration, wings
modelled as thin shells with flexible hinge-lines are used to
deformations of walking limbs, though still under muscular
investigate how transverse distal flexion, essential for
control, are strongly influenced by the nature and sequence
controlling the angle of attack in the upstroke, is remotely
of movement of the joints. Limbs adapted for walking in
controlled by the indirect flight muscles.
air are effectively point-loaded, and their rigid components
need to resist axial forces as well as bending and torsional
Key words: annelid, arthropod, cephalopod, pteropod, appendage,
moments. Aquatic walking limbs have little axial loading,
limb, wing, walking, swimming, flight, mechanics, locomotion.
while swimming appendages and wings experience only
Introduction
If an animal is to move relative to its surroundings, it must
exert a net force on them and exploit the reaction. It may use
its entire body, or part of the body close to its longitudinal axis
(axial propulsion), or oscillate projecting appendages (paraxial
propulsion) or combine the two. Axial, paraxial and combined
propulsion all occur throughout the size range of animals. All
three are effective methods for locomotion on or in a
substratum and for swimming in water, but flight in air requires
paraxial action. Only wings are capable of accelerating enough
air to support the weight of an animal as well as to propel it
along.
The locomotion of invertebrates has been extensively
reviewed by Full (1997). The present paper will deal only with
paraxial locomotion, and particularly with some of the
mechanical principles that underlie the design of paired
appendages. Such appendages are either muscular hydrostats,
with or without rigid inclusions, or jointed exoskeletal
structures with clearly defined more-or-less rigid components
separated by, but often articulating across, areas of flexible
cuticle. The former comprise the parapodia of polychaete
annelids (Gray, 1939; Mettam, 1967), the fins of cephalopods
(Hoar et al., 1994; Packard, 1972) and of some marine
gastropods (Farmer, 1970; Satterlie et al., 1985) and the
lobopodia of Onychophora (Manton, 1950) and many insect
larvae. The latter include the typical legs and swimming
paddles of most arthropods (Cannon, 1933; Manton, 1977) and
the wings of insects (Wootton, 1981, 1992; Brodsky, 1994).
An animal can elicit propulsive force from its surroundings
in two ways: from the elastic reaction of a solid substratum or
by accelerating a mass of fluid, opposing its viscosity and
inertia. Intermediate conditions exist: walking on a particulate
substratum which yields underfoot; or burrowing in
waterlogged surroundings, whose effective density and
viscosity depend on particle concentration, size and geometry.
They will not be discussed here.
Substratum- and fluid-based locomotion create quite
different loading patterns on the appendages. Walking limbs
are subject to axial forces, usually compressive but sometimes
tensile, and to bending and torsional moments. In terms of
external forces, the legs of terrestrial walking animals will be
effectively point-loaded, and the ground reaction force will
have a strong vertical component, supporting the weight.
Fluid-dynamic forces at normal walking speeds will be low
and, if perceptible, generally adverse. In water, however, a
walking animal may be close to neutral buoyancy. Substratum
reaction forces will act mainly horizontally, and axial forces
3334 R. J. WOOTTON
on the limbs will be relatively low. Drag, however, will be 800
times greater (Martinez et al., 1998) so that the legs will be
receiving distributed loads, major bending and perhaps
torsional moments. So will burrowing limbs, in both air-filled
and water-filled surroundings. Paddles and wings experience
only bending and torsion, from fluid-dynamic forces and from
inertia, including the often significant inertia of the added mass
of fluid moved with the appendages.
Beside these external loads, the internally generated
muscular and hydrostatic forces will lead to a complex pattern
of local tensile, compressive and shear stresses in the skeleton
that are impossible to analyse with any precision.
These factors all influence the design of invertebrate
propulsive appendages. The latter need not only to withstand
the forces that they experience but also to deform as necessary.
Theoretically, this is not essential. Daniel (1984) and Daniel et
al. (1992) have shown that the net force gained by accelerating
the added mass in a symmetrical rowing stroke could be
enough to give a propulsive force, and the filtering limbs of
some copepods are known to operate in a transitional Reynolds
number range where a small change in stroke velocity can
determine whether they act as sieves or as paddles (Cheer and
Koehl, 1987; Koehl, 1995). Generally, however, the necessary
force asymmetry is achieved by cyclic alteration of the attitude
and/or shape of the appendages, involving bending, torsion and
changes in exposed surface area.
This account will be concerned principally with propulsive
deformation. In particular, it will explore how, and to what
extent, information encoded in the skeletal architecture can
mediate between the musculature and the inertial and external
forces to limit and control this deformation. We shall see how
the orientation and form of the joints of arthropod walking
limbs both facilitate and restrict their locomotion, how the
distributed loads associated with swimming and flying can
be enlisted to aid semi-automatic deformation and how
automation culminates in the complex, muscle-free wings of
pterygote insects.
Substratum locomotion
Terrestrial walking appendages: lobopodia and jointed legs
Walking legs are required to deliver appropriate and
appropriately timed forces to the ground, through non-slip tips
or elongate tarsi, and to withstand the resulting axial loads
and bending moments without rupturing or buckling. The
lobopodia of Onychophora, Tardigrada and some insect larvae
achieve this effectively as muscular hydrostats, with a thin,
flexible cuticle and terminal claws (Manton, 1950). Their short,
stout form prevents buckling. Some Cambrian presumed
relatives, such as Hallucigenia from the Burgess Shales, seem
to have had far more slender lobopodia, but were certainly
marine, so that axial forces would have been minimal.
Whereas controlled deformation in lobopodia occurs
throughout their length, it is restricted in other terrestrial
arthropods to the flexible joints. These are of three main kinds
(Fig. 1A–C). Pivot joints have a single degree of rotational
A
B
D
C
E
Fig. 1. Types of arthropod joint (diagrammatic). (A) Pivot joint.
(B) Hinge joint. (C) Monocondylar joint. (D,E) The role of arthrodial
membrane dimensions in determining joint excursion. The arrows
indicate the planes and extent of movement.
freedom. The axis joining the two condyles (points of
articulation) crosses the lumen of the tubular appendage, so
that antagonistic muscles can pass on either side of it, and the
podomeres (the ‘segments’ of the limb) beyond can be both
flexed and extended actively. Hinge joints also have one degree
of freedom, but lie at the edge of the section, so that they can
be flexed, but not actively extended. Monocondylar joints may
allow a little anteroposterior rotation as well as flexion, but
again no active extension. Within these categories, the field of
available movement of any particular joint can be precisely
defined by the details of its structure: its orientation in the three
planes of space, determining the plane of relative movement
of the adjacent podomeres; the amount of play between the
condyles, determining how strictly the theoretical degrees of
freedom are enforced; and the area and shape of the compliant
cuticle, determining the excursion angles permitted either side
of the joint (Fig. 1D,E).
The number and sequence of joints down the limb
exoskeleton impose the theoretical ultimate limit on its
freedom of movement. In life, however, the neuromuscular
system will restrict the limb kinematics to a range of
meaningful gaits and other movements. Manton (1977)
described the type and oriention of joints in sequence along the
walking limbs of a wide range of terrestrial arthropods, and
Fig. 2 is adapted from a selection of her illustrations. There is
considerable variation, but several common features are
apparent. Leg promotion and remotion are always facilitated
by monocondylar joints or dicondylar pivots, with a nearly
Invertebrate paraxial locomotory appendages 3335
Body
Toe
A
Coxa Femur
Diplopoda
Tibia
Trochanter
Tarsus
Chilopoda
Notopodium
B
Setae
Insecta
Pterygota
Acicula
Limulus
Neuropodium
Scorpion
Spider
Fig. 2. Diagrammatic representation of the sequence of joint types
along the walking legs of selected arthropod groups. Modified after
Manton (1977). The outer, thicker outlines represent the more
proximal podomere, the inner outlines the more distal podomere at
each joint. The shaded semicircles represent fixed coxae.
vertical axis, near the limb base, permitting the maximum
angle of overall swing (although note the scorpion and spider).
Horizontal pivots, allowing elevation and depression, are
always to be found in the proximal region of the limb. Manton
(1977) stressed the need for arthropod legs to flex and extend
during the propulsive stroke if the body is to progress in a
straight line, and flexion and extension always take place at
more distal joints, of all three types. The principal flexion joint
should logically be situated approximately half-way down the
limb, forming its highest point in the sprawling posture that
characterises many land arthropods; in general, this seems to
be so.
Fig. 3A is a diagram to illustrate the names of the main
podomeres of a leg of a generalised land arthropod. Of those
studied by Manton (1977), only insects have pivot joints
thoughout the pretarsal limb. Diplopoda, Chilopoda,
Pauropoda and Symphyla all have only hinge joints beyond the
femur, and in Chilopoda the trochanterofemoral joint too is a
hinge. Among chelicerates, Limulus, spiders and Opilionida
have no pivot joints beyond the femur, and scorpions and
Galeodes (Solpugida) have only one.
It follows that, while these arthropods can flex the distal, and
usually far longer, regions of their legs, they have no intrinsic
muscles that actively extend them. Further, Manton (1977)
Fig. 3. Diagrams of appendages, illustrating the names of the
components. (A) Walking limb of a land arthropod. Note that more
podomeres are often present and that the tarsus is often subdivided
(see Fig. 2). (B) Parapodium of an errant polychaete annelid.
maintained that, while hydrostatic pressure is capable of
extending the legs during the recovery stroke, with the
exception of the jumping legs of salticid spiders (Parry and
Brown, 1959) it is generally inadequate to do so while they are
on the ground. ‘Propulsive extension of these hinge joints is
done by the proximal depressor muscles, both intrinsic, near
the base of the leg, and extrinsic between the leg and the body,
which press the limb-tip firmly on the ground, and with the
force from the remotor swing, effect propulsive extension’
(Manton, 1977). In contrast, the pterygote insects have pivots
at the femorotibial and tibiotarsal joints. Extensor as well as
flexor muscles are present, and the tibia and tarsus can be
actively extended. This greatly increases the range of possible
movements and the uses to which the legs are put: digging,
swimming, jumping, defensive kicking. It may even have
assisted in the development of flight, since jumping is a widely
employed method of gaining initial flight speed.
In terrestrial locomotion, the legs need to support the weight
of the animal as well as to propel it, and the ground reaction
has a significant vertical component, giving appreciable axial
forces as well as bending moments. The podomeres need to be
adapted for rigidity in bending and torsion; they are normally
tubular, usually with a circular or slightly elliptical cross
section, close to the theoretical optimum for resistance to
multidirectional loads. When long, slender and therefore
potentially weak, they are almost invariably straight. This not
only reduces the probability of buckling in compression
(Currey, 1967) but also minimises the likelihood of dangerous
torsional moments, which would tend to dislocate and destroy
the joints as well as damaging the podomeres themselves.
The diversity of arthropod walking limbs is immense and
beyond the scope of this paper. Manton’s (1977) investigations
reveal a wide range of morphological adaptations to particular
3336 R. J. WOOTTON
gaits and locomotory patterns, expecially in Onychophora and
the myriapod classes. The mechanics of land crab locomotion
and of insect walking, running, jumping and pushing have been
extensively studied (Delcomyn, 1985; Full et al., 1991; Full
and Ahn, 1995; Full and Weinstein, 1992; Evans, 1977;
Forsythe, 1991; Bennet-Clark, 1977; Bennet-Clark and Lucey,
1967; Gabriel, 1986; Furth and Suzuki, 1992). Particularly
important is the discovery in Blaberus discoidalis
(Dictyoptera) that each pair of legs generates its own pattern
of ground reaction forces: the first pair tends to decelerate the
centre of mass, the third pair to accelerate it, and the second to
alternate between the two (Full et al., 1991). This contrasts
with vertebrate quadrupeds, in which all legs both accelerate
and decelerate the centre of mass, and is likely to be true of
many other insects and other arthropod groups with few leg
pairs, and even of scutigeromorph centipedes, whose long legs
are widely splayed and have very different fields of movement
(Manton, 1965, 1977). Also important in the present context,
and probably widely applicable, is the realisation that the large
ground reaction forces associated with typical arthropod
sprawling gaits may help to minimise muscle forces and energy
costs by counteracting the large moments of the vertical ground
reaction forces about the leg joints (Full et al., 1991). This, in
turn, would tend to increase the compression loads in the long
tibiae and enhance the need to optimise their section geometry
and overall design. These moments and loads would be
greatest in the rapid extensions associated with jumping.
Alexander (1995) has considered theoretically the optimal
design for jumping legs, including those of insects.
The metathoracic legs of locusts beautifully illustrate a range
of adaptations associated with jumping: compact coxae; pearshaped femora containing the pennate jumping muscle
appropriate for maximal energy storage in the apodeme and
semilunar process; femorotibial pivot joints with an
exceptionally large excursion (Heitler, 1977); slender, straight
tibiae with an elliptical cross section whose long axis is aligned
to minimise bending during the jump; and mobile tibiotarsal
joints.
Summarising in the context of this paper, we may note the
extent to which the available range of substratum movement
of terrestrial arthropods is encoded in the sequence, orientation
and detailed design of the joints of the limbs, including the
degrees of freedom, the form of the articulation and the angles
of excursion in the three dimensions of space. These, in turn,
are reflected in the arrangement of the muscles, the space
required to house them and the consequent form of the
podomeres. The design of both podomeres and joints is further
constrained by the need to avoid failure under the axial forces
and bending and torsional moments of walking, running and
jumping in air.
Walking under water
Aquatic substratum locomotion is found among polychaete
annelids and in many arthropods, particularly malacostracan
Crustacea, Pycnogonida, insect larvae and water beetles. It has
received less attention than has walking in air, and fewer
kinematic studies have been published (Mettam, 1967; Pond,
1975; Hui, 1992; Cavanagh and Long, 1994; Jamon and
Clarac, 1995, 1997; Domenici et al., 1998; Martinez et al.,
1998). The crucial difference lies in the nature of the forces
involved. In water, the vertical component of the ground
reaction force is proportionally far smaller than in air. If it were
wholly absent, purchase would be minimal, and it is no
coincidence that habitually walking Crustacea tend to have
thick, heavy cuticle reinforced with calcium carbonate rather
than adaptations for least weight, as seem general in terrestrial
arthropods. Fluid-dynamic forces, however, are many times
greater, and the added mass (=virtual mass) of the water moved
with the appendages may also be significant. The external
loads are therefore distributed along and across the limbs,
whose inevitable drag needs to be controlled and appropriately
centred.
Annelid parapodia (Fig. 3B) are essentially muscular
hydrostats, but they are stiffened by rigid acicula and bear
setae. They can act in substratum crawling, or swimming or
both, usually assisted in both cases by axial waves (Mettam,
1967; Cavanagh and Long, 1994). In crawling Nereis
diversicolor and Nephtys hombergi, there seems little sign of
externally driven flexion or torsion. Instead, they achieve force
asymmetry by altering the frontal area. The parapodia are
extended for the effector stroke by the acicular protrusor
muscles, the setae are extended by the muscles of the setal sac,
and the entire structure is retracted for the recovery stroke
(Mettam, 1967). The neuropodial (ventral) acicula and setae of
Sphaerosyllis (Manton, 1977) and of most other errant
polychaetes grip the substratum when crawling. Polychaete
setae vary appreciably in form (Gardiner, 1992) and many
appear to be variously adapted for locomotion. Jointed setae
occur in several families, the joint being external to the body,
with no muscular or nervous control. Merz and Edwards
(1998) found in the hesionid Ophiodromus pugettensis that
trimming the setae proximally to the joints affected both
crawling and swimming performance more than did more
distal trimming, suggesting that passive flexion of the setae
plays a role in both forms of locomotion.
While Limulus and the larvae of many insects also walk under
water, most aquatic walking arthropods are Crustacea. The
walking limbs are the thoracic pereiopods. Like those of
chelicerates, myriapods and insects, they are uniramous
(unbranched). Most joints are of the pivot type, with flexor and
extensor muscles, but with widely varying excursion angles.
Two examples illustrate how these operate. Fig. 4 shows semidiagrammatically the joint orientation in a typical leg of Astacus,
a freshwater crayfish. The first four podomeres are all situated
under the body, and this influences the orientation of their joints.
The first post-coxal pivot joint is oblique to the horizontal,
allowing elevation/remotion and depression/promotion. The
next three are orientated horizontally, but oblique to the limb’s
transverse axis: the first and second are somewhat inclined
anterodistally and the third posterodistally. Together, these allow
elevation and depression of the limb, and their oblique
Invertebrate paraxial locomotory appendages 3337
Cx
Mr
Is
Cp
Bs
Pr
Dt
Fig. 4. Joint orientations of the second left pereiopod of the crayfish
Astacus. Diagrammatic, anterodorsal view. Cx, coxopodite; Bs,
basipodite; Is, ischiopodite; Mr, meropodite; Cp, carpopodite; Pr,
propodite; Dt, dactylopodite.
orientation permits some axial rotation. The fourth joint,
between the meropodite and carpopodite, is a horizontal pivot,
and the principal site of leg retraction. The fifth, between the
carpopodite and propodite, is again in the vertical plane of the
extended leg. Its flexion is limited and asymmetrical, flexing
further anteromesally than posterodistally.The most distal joint,
to the short claw-like dactylopodite, is another horizontal pivot,
with little lateral play in the chelate first two legs, and rather
more in the non-chelate third and fourth pairs.
Locomotion has been studied in the related
Austropotamobius pallipes (Pond, 1975) and extensively in
Procambarus clarkii (Jamon and Clarac, 1995, 1997;
Domenici et al., 1998), and I have myself observed
Pacifastacus leniusculus. As in Blaberus, the various leg
pairs operate very differently. In Pacifastacus walking
forward on a level substratum, the two most anterior legs,
posterior to the chelipeds, are directed anteriorly and operate
by retraction, so pulling the animal forward. As the direction
of leg retraction is aligned with the axis of the
carpopodite/propodite pivot, these two podomeres operate as
one, with no mutual bending in the power stroke. The third
legs project laterally and operate like the mesothoracic legs
of insects, first pulling, then pushing the animal. The forward
component of the ground reaction force is aligned with the
horizontal meropodite/carpopodite pivot, which allows
retraction but resists anteroposterior bending. The vertical
carpopodite/propodite joint appropriately resists posterior
bending in the power stroke, but can flex forward a little
during recovery, allowing the leg to brush past obstacles on
a rough substratum. The last leg pair are smaller and thrust
backwards, but weakly. Their movement consists mainly of
extension about the meropodite/carpopodite pivot.
Their limb cross sections are interesting. Instead of the
round or slightly elliptical sections typical of insects,
myriapods and spiders, those of the first three leg pairs are
narrow ellipses, whose long axes are orientated in the plane of
limb retraction. The highest second moment of area of the
podomere sections is therefore in the direction of the greatest
bending moments, the sections are streamlined relative to the
movement of the limb, and the flexor and extensor muscles
gain space and mechanical advantage. Logical so far: but the
third leg pair is similarly shaped, and the long axis of its section
is normal to the direction of thrust, suggesting that the last two
functions may be the most significant. The weak last pair have
more-or-less cylindrical podomeres.
Carcinus maenas, the shore crab, can move forwards or
backwards by the usual combination of promotion/remotion
and flexion/extension, but its preferred gait is sideways, with
the flexion and extension of the limbs providing the thrust
(Manton, 1977). The orientation of the limb joints is similar to
that of crayfish, but with one fewer basal podomere and no
terminal dactyl. The sections of the podomeres are again thin
ellipses whose long axis is aligned with the plane of flexion
and, in this case, of movement. The most posterior legs are
flattened distally and are held horizontally and usually clear of
the substratum. They appear scarcely to contribute to the
walking movement. The crabs hardly swim, but the legs may
serve to stabilise the animals in, for example, falling from a
rock, perhaps generating some lift in the manner of the
portunid crabs, whose hind limbs are similarly but more fully
developed (Plotnick, 1985; Azuma, 1992).
In these Decapoda, available locomotory patterns are again
closely associated with the alignment and directional flexibility
of the joints, but the appendages are under full muscular
control. The sequentially differential orientation of the joints
gives considerable gait flexibility: just as Carcinus can walk
forwards if need be, prawns, e.g. Leander, can switch from the
preferred forward walk to lateral crabwise movement at will,
using the limb retractors for thrust.
Both crayfish and crabs are capable of walking in water and
in air, and both provide good opportunities for a comparison
of gaits in the two media (Hui, 1992; Martinez et al., 1998).
Drag-based swimming
Errant polychaetes, most Crustacea, adult water-beetles and
adult and juvenile aquatic Hemiptera swim using paddles. The
range of appendages is huge, but most are flattened or bear
numerous stiff bristles, often both. The appendages of some
(the legs of hydrophilid beetles and Pycnogonida and the
pereiopods of munnopsid isopods) move independently on the
two sides of the body, those of hydrophilids and munnopsids
in modified walking patterns, those of pycnogonids in
sequence from rear to front. The appendages of others operate
as a single, simultaneously stroking pair: the metathoracic legs
of most water beetles and bugs and the antennae of Cladocera,
Ostracoda and Copepoda. The appendages of yet others, such
as the parapodia of polychaete epitokes (Clark, 1961), the
phyllopods of notostracan, anostracan and leptostracan
Crustacea and the pleopods of swimming decapods and most
swimming isopods, operate in serial sequence, beating
metachronally. The kinematic patterns of many are wellknown (Cannon, 1933; Nachtigall, 1980, 1985; Alexander,
1988; Hessler, 1993; Daniel, 1995; Koehl, 1995).
3338 R. J. WOOTTON
En
Ex
stroke by an individual slender muscle, but folds automatically
for the recovery stroke, presumably under the influence of
drag. In the swimming legs of dytiscid and gyrinid beetles,
however, both the erection and folding of the bristles appear
to occur automatically under hydrodynamic pressure
(Nachtigall, 1980).
A few arthropods are able to swim with long filiform legs.
The total leg length of Nymphon (Pycnogonida) can can be as
much as 600 mm on a 12 mm body. It typically treads water
with its legs operating in postero-anterior series (Morgan,
1971). In the remarkable deep-sea munnopsid Isopoda,
Marshall and Diebel (1995) have identified four distinct gaits.
Three involve the pleopods, but the fourth is carried out by the
elongate pereiopods, with which the animals ‘walk’ through
the water. Their tips carry long, folding hairs. Not only do the
latter erect and fold automatically, but the terminal leg
segments apparently also lack muscles: a uniquely high degree
of automation in an arthropod leg.
Fig. 5. A right pleopod of Leander, anterior view. Insets show the
articulation of a seta, with its tensile apodeme and erector muscle,
and details of the joints. En, endopodite; Ex, exopodite; Bas,
basipodite.
Flying in water and air: mollusc fins and insect wings
In drag-based swimming, active and/or automatic flexion on
the recovery stroke is general and torsion not unusual. In liftbased propulsion, torsion is virtually essential if force
asymmetry between half-strokes is to be achieved, and
bending, if present, needs to be tightly controlled. In water, liftbased locomotion occurs in portunid crabs, using the last pair
of legs (Plotnick, 1985; Azuma, 1992), and in some
cephalopod and gastropod molluscs. The insects are the only
invertebrate aerial fliers.
Typically, paddles are adapted to maximise drag in the
effector stroke and to reduce it in the recovery stroke by
bending, torsion, change of section and/or effective area. Much
of this deformation is certainly drag-assisted and made possible
by asymmetric flexural and/or torsional compliance in the
appendages. In contrast with walking, in which torsion is
potentially highly damaging (Gordon, 1978), it can now be
advantageous. Most crustacean phyllopods are asymmetric in
planform, and the two rami (branches) of malacostracan
pleopods are usually unequal, so that some passive torsion is
probable. Bending is certainly crucial. Fig. 5 shows a pleopod
of Leander. The slender, leaf-like endopodite articulates with
the basipodite by a broad, nearly vertical hinge and can twist
to reduce drag on the recovery stroke. The larger exopodite has
a moncondylar joint with the basipodite and can swing
sideways to increase or reduce the effective frontal area.
During the effector stroke, the pleopod is straight, with the
endopodite and exopodite spread. During the recovery, they
flex and lie together. As in the swimming appendages of most
swimming Crustacea, aquatic Hemiptera and Coleoptera and
many insect larvae, the pleopods of Leander carry long
articulated setae, and these are themselves multibranched, with
serial setulae. Like the podomeres that bear them, the hairs are
asymmetrically hinged, articulated to the ramus by a single
condyle. Each bristle is actively erected for the propulsive
The flying fins of squids and pteropods
In the Mollusca, paired locomotory appendages are found
only among Cephalopoda (Packard, 1972; Hoar et al., 1994)
and Gastropoda (Farmer, 1970; Satterlie et al., 1985). Shapes
vary from the ultra low-aspect-ratio undulatory fins of Sepia
(Kier, 1989) to the short, flapping triangles of loliginid and
ommastrephid squids and the quadrilaterals of some pteropod
gastropods.
The fins of cephalopods show a range of complex propulsory
movements resembling those of skates and rays (Hoar et al.,
1994), and some ommostrephid squids show remarkably flightlike movements, with the fins clearly operating as lift
generators. The swimming kinematic patterns of Clione
limacina, a pteropod prosobranch mollusc, are strikingly
similar to those of hovering hawkmoths, apparently even
paralleling the ‘clap-and-fling’ method of unsteady lift
production of many flying insects (Satterlie et al., 1985). Yet
the means by which these effects are achieved represent
opposite ends of the automation spectrum. Clione fins are
hydrostats with no rigid components, and the deformations of
these and other mollusc fins are entirely under muscular and
neurosensory control. Significant torsion is visible, necessarily
distally to the fin base, since the latter is broad in every case.
In Clione, hydrodynamically generated torsional moments may
assist twisting at some stages of the stroke. Their magnitude,
Bas
Invertebrate paraxial locomotory appendages 3339
as in all hydrofoils and aerofoils, depends on the relative
positions of the centre of torsion and the centre of lift. The
anteroposterior symmetry of most squid fins suggests a torsion
centre close to the mid-chord, so that moments will probably
be small. Clione parapodia, however, are rather diamondshaped and show some anteroposterior asymmetry, so that
these moments will be relatively larger.
Insect wings: automation and fully remote control
Swimming appendages, whether operating by lift or by drag,
tend to be short, sturdy and muscular. Wings need to be large,
with minimal inertia, and those of insects have no internal
muscles at all. All the cyclic deformation necessary for force
asymmetry must therefore be remotely controlled from the
base and partly or wholly automatic, encoded in the structure
and in the distribution of material properties throughout the
wing (Wootton, 1981, 1992).
Torsion is important in determining and altering the wings’
angle of attack. The basal muscles are capable of actively
pronating and supinating the whole wing, but high-speed still
photographs and cine film show that most insect wings are to
some extent twisted like aircraft propellors along their length
during translatory movement, reflecting the base-to-tip
gradient in relative wind speed and in the direction of incident
flow. This spanwise torsion is largely automatic and principally
due to aerodynamic and inertial torques (Ennos, 1988a,b)
resulting from the general asymmetry of the planform and the
distribution of the supporting veins. Many wings are expanded
posteriorly and, even when they are relatively elliptical, the
principal supporting veins are closer to the leading than to the
trailing edge and the longitudinal veins tend to be curved,
favouring the chordwise transmission of torsional moments. In
combination with spanwise torsion, vein curvature has the
additional important effect of automatically depressing the
trailing edge and imposing a camber on the wing in direct
response to aerodynamic loading (Newman, 1982; Ennos,
1988a; Wootton, 1991, 1992).
Insect wings are enormously varied in shape and structure,
reflecting the great diversity of the group and their wide range
of flight techniques, performance and behaviour. Their
functional morphology and mechanics in flight and in folding
have been investigated in detail in many groups, particularly
Ephemeroptera (Brodsky, 1971), Odonata (Newman, 1982;
Newman and Wootton, 1986; Pfau, 1986), Plecoptera
(Brodsky, 1979, 1981, 1982), Hemiptera (Betts, 1986a,b; Betts
and Wootton, 1988; Wootton, 1996), Diptera (Ennos, 1988a,b,
1989; Wootton and Ennos, 1989), Mecoptera (Ennos and
Wootton, 1989), Orthoptera (Jensen, 1956; Zarnack, 1972,
1982; Pfau, 1977; Wootton, 1995), Coleoptera (Brackenbury,
1994; Haas and Wootton, 1996), a range of Lepidoptera
(Wasserthal, 1974; Grodnitsky and Kozlov, 1985, 1990;
Wootton, 1993), of Holometabola in general (Grodnitsky and
Morozov, 1995) and of Palaeozoic Paleoptera (Wootton and
Kukalová-Peck, 1999) (for general accounts, see Wootton,
1992; Brodsky, 1994). These have revealed a remarkable array
of adaptations, some of which are independent enough of the
insect’s musculature to be considered as ‘smart’ structures,
automatically adjusting the section and attitude of the wing in
direct response to the aerodynamic and inertial loading.
To illustrate how basal muscles, wing morphology and
external forces can interact to determine instantaneous wing
shape and deformation in flight, we will consider the general
question of the control of ventral transverse flexion. The wings
of many insects flex ventrally at the end of the downstroke
(Nachtigall, 1966; Weis-Fogh, 1973; Dalton, 1975; Wootton,
1981; Ivanov, 1985; Betts, 1986a,b; Ennos and Wootton, 1989;
Brackenbury, 1992, 1994; Zanker and Götz, 1990). This may
serve several functions, not all of which are yet clearly
understood, and it takes several forms (Wootton, 1981).
Sometimes, as in many Diptera and in the parasitic wasp
Encarsia formosa (Weis-Fogh, 1973), the whole wing flexes
near the base and straightens quickly during the upstroke
(Fig. 6A), almost certainly creating unsteady lift (Zanker and
Götz, 1990). Sometimes, as in many Plecoptera, Mecoptera,
Hemiptera, Megaloptera, Trichoptera and Lepidoptera, the
whole wing-tip bends ventrally and stays flexed for much of
the upstroke (Fig. 6B). Sometimes the leading edge stays
almost straight, but the rest of the wing flexes along an oblique
curved line (Fig. 6C). Both these latter situations serve to
create a ventrally convex camber in the distal part of the wing
and to modify its angle of attack, allowing favourably directed
lift during the upstroke. Ventral flexion permits many insects
to gain a greater degree of distal torsion than is allowed by the
structure of the wing base, and often, in combination with a
nearly horizontal stroke-plane, to gain weight support on the
A
C
B
D
Fig. 6. Transverse and oblique flexion in insect wings. (A)
Calliphora erythrocephala (Diptera, Calliphoridae). (B) Tibicina
haematodes (Hemiptera, Cicadidae). (C) Vespula vulgaris
(Hymenoptera,
Vespidae).
(D)
Camptogramma
bilineata
(Lepidoptera, Geometridae). All are traced from photographs of
insects in free flight. (A) After Wootton (1981); (B,D) after
Brackenbury (1992); (C) after Dalton (1975).
3340 R. J. WOOTTON
morphological upstroke as well as the downstroke, so allowing
slow flight and hovering. Flexion is presumably initiated by the
inertia of the wing and the added mass of air as the wings
decelerate at stroke reversal, but can be maintained and
augmented during the morphological upstroke by aerodynamic
pressure on the morphologically dorsal, though now
functionally ventral, side of the wing.
In some cases, flexion takes place over a large part of the
wing-span, with a large radius of bending (Fig. 6D), but in
many it is localised along a clear line that may be marked by
thinning or zones of soft cuticle in the veins or an abrupt
change in the overall rigidity of the wing structure (Wootton,
1981). In some Diptera and Hemiptera, flexion may take places
at two sites in the wing, and in Miridae at least this can
happen either separately or simultaneously (Betts, 1986a,b;
Brackenbury, 1992) (see Fig. 10B).
How is this flexion controlled? In a thin structure such as a
wing there is limited scope for hinge joints of the kind we have
seen in arthropod limbs, with an articulation between adjacent
hard elements on one side and a segment of flexible cuticle on
the other. Something similar, however, is found in the veins of
cicadoid Hemiptera, where the tranverse flexion line is
particularly clearly defined (Wootton, 1981). Frequently,
however, the location of the line appears primarily to be
determined by the form of the principal supporting veins, by
generally lower rigidity in the area between these veins and,
crucially, by the profile of the basal part of the wing.
The wings, or at least the fore wings, of most neopterous
(wing-folding) insects consist of a main area, the ‘remigium’,
and a posterior area, the ‘clavus’, hinged to the remigium along
a long flexion line.The area of the remigium proximal to any
transverse flexion line is frequently cambered, and in most
groups it is longitudinally divided by another flexion line, the
‘median flexion line’ (Wootton, 1979), which allows the
camber to be altered actively by pronating and supinating
muscles at the base.
Complete structural modelling of an insect wing, either
numerically or physically, is complex and time-consuming, but
much can be learned as a first approximation by treating it as
a thin plate or shell. A cantilevered flat plate, loaded in
bending, is equally flexible either way up (Fig. 7A). A
cambered plate, in contrast, is markedly asymmetric in flexural
rigidity. A force applied from the concave side at or around the
centre of the cross section is strongly resisted, and the shell
responds to increasing force by increasing the height of the
camber and, hence, the rigidity. A force from the convex side,
however, tends to flatten the section and lower the second
moment of area, and the shell eventually bends, with a small
radius of curvature, along a line where the section is totally
flat. If this line is straight, the camber of the base will decrease
linearly from the base to the line of bending and increase
linearly beyond it, remaining dorsally convex throughout
(Fig. 7B).
If flexion is encouraged to take place along a preformed
curved or angled flexion line, however, the structure is now
bistable. When unbent, the curvature is uniformly dorsally
A
B
C
E
D
Fig. 7. Bending and buckling in thin plates. Explanation in the text.
convex (Fig. 7C). When bent, the distal region snaps across to
a second stable position in which the section is dorsally
concave (Fig. 7D), and its height and angle relative to its
previous longitudinal axis are precisely determined by
geometry: the height of the basal camber and the shape of the
flexion line. If the anterior and posterior ends of the flexion
line are equidistant from the base of the shell, the alignment of
the induced concave camber is parallel to the sides. If the
flexion line is oblique, however, the apex of the induced
camber approximately bisects the curve, or angle, of the flexion
line (Fig. 7E).
If we apply this to a real wing, the implication is that the
orientation of the reverse camber induced by inertial and
aerodynamic forces at stroke reversal is significantly
determined by the shape and orientation of the line of
transverse flexion. This is beautifully demonstrated by the
scorpionfly Panorpa (Mecoptera) (Fig. 8). The fore and hind
wings of this insect (Fig. 8A) are rather similar and are not
coupled together in flight, so that they bend and twist
independently. The subcostal vein (Sc) of each wing, together
with the more anterior costa (C) and the more posterior radius
(R), form a high-relief supporting spar at the leading edge, and
the anterior and posterior cubitus veins (CuA and CuP) provide
a firm posterior support. A flexion line runs across the wing
from the end of CuA via a desclerotised area at the fork of the
median vein (M) approximately to the end of Sc. In the fore
wing, Sc is longer than CuA, and the flexion line is tilted
anterodistally. In the hind wing, Sc is shorter than CuA, and
the flexion line is if anything tilted anteroproximally. Highspeed film of the insects in free flight show the very different
positions assumed by the wing pairs during the upstroke
(Fig. 8B). The aerodynamic implications are discussed by
Ennos and Wootton (1989).
In real wings, bending and twisting will be further
influenced by the distribution of structural flexibility. Some of
this will be inbuilt, but it may also be actively modifiable by
Invertebrate paraxial locomotory appendages 3341
A
Sc
B
R
Rs
2A
1A cl.f.
M
CuP CuA
R
Sc
Rs
CuA
M+CuA
CuP
CuA
M
Fig. 8. Wings and wing flexion in Panorpa (Mecoptera). (A) Fore (top) and hind (bottom) wings of Panorpa communis; from Wootton and
Ennos (1989). Scale bar, 1 mm. (B) Tracings from high-speed cine film of P. germanica in free flight, showing difference in upstroke flexion in
the fore and hind wings; after Ennos and Wootton (1989). CuA, anterior cubitus vein; CuP, posterior cubitus vein; M, median vein; R, radius;
Sc, subcostal vein; Rs, radial sector; cl.f., claval furrow; 1A, 2A, 1st and 2nd anal veins.
altering the amount of camber in the basal part of the
remigium. If this is low, the second moment of area at the
flexion line will be low and the wing will bend more readily.
Fig. 9 shows a diagrammatic wing of thickness t arched along
a longitudinal flexion line. The second moment of area I about
the neutral plane is given by:
t
α
H
I = 4tH3/3cosα ,
where H is the distance from the neutral plane to the apex of
the section and α is half the angle included at that apex. For
small deflections, and ignoring buckling, the flexural rigidity
will therefore increase by rather less than the third power of
the height of the section, which is under fine control from the
muscles of the wing base.
The functioning of the flexion lines is particularly clear in
the heteropterous bugs, whose fore wings have a thickened
proximal section, the ‘corium’, and an unthickened distal
section, the ‘membrane’. The boundary between the two forms
a transverse flexion line. Within the corium, there is normally
a clearly defined median flexion line that approaches, but stops
short of, the corium/membrane boundary. However, since the
distal end of the corium is moderately compliant, flexing of the
proximal part along the median flexion line can alter the
camber along the boundary and control the wing’s resistance
to ventral bending.
In several families, of which the Miridae is the most
prominent, the corium boundary is oblique, and there is a
second, more proximal, flexion line, the ‘cuneal fracture’,
perpendicular to the leading edge (Fig. 10A). High-speed cine
film of two Stenodema species in free flight indicates that
flexion along the corium margin is habitual in the upstroke but
that flexion at the cuneal fracture is less common, although it
does occur (Fig. 10B). It seems probable that, by adjusting the
camber of the wing base, the bug is capable of determining
whether, under a given external load, the wing flexes along
both the cuneal fracture and the distal flexion line (Fig. 10B)
or at the latter alone (Betts, 1986a,b).
Fig. 9. Wing modelled as an arched plate. Explanation in the text. α,
half the angle included at the apex; H, distance from the neutral
plane to the apex of the section; t, thickness.
Discussion
What factors, then, influence the design of invertebrate
propulsive appendages?
Muscular hydrostats can function in aquatic substratum
locomotion and in drag-based and lift-based swimming, and
the Onychophora demonstrate that they can operate well on
land, with a surprising range of gaits (Manton, 1950).
However, exoskeletal appendages give scope for far greater
locomotory versatility in both water and air.
Walking legs in the various arthropod classes have some
fundamental similarities, but vary greatly in relative length, in
proportions and in the number of podomeres and the sequence
and orientation of joints. Not all these differences are easily
interpreted. Long legs can be adapted (a) for fast walking or
running, (b) for stepping over gaps in vegetation, (c) for raising
the body above a dangerously hot substratum, (d) for special
types of prey-capture, (e) for locomotion on the surface film of
water bodies, and also for various combinations of these.
Scutigeromorph centipedes, many lycosid spiders and the ant
Cataglyphis probably combine a and c; many Opilionida and
3342 R. J. WOOTTON
A
c.f.
m.f.l.
c.m.
B
c.m.
c.f.
c.m.
c.f.
Fig. 10. (A) Fore wing of Calocoris 2-punctatus (Heteroptera,
Miridae), showing the flexion lines. m.f.l., median flexion line; c.m.,
corium margin; c.f., cuneal fracture. (B) Tracing of Leptoterna sp.
(Miridae) in free flight; after Brackenbury (1992).
the spider Pisaura combine a and b; the spider Dolomedes
combines a and e. Most stick-insects (Phasmida) fit b;
hydrometrid and gerrid Hemiptera fit e; thomisid and pholcid
spiders fit d.
Podomere number is hard to interpret, except in general
terms. More joints can lead to faster locomotion because of
summation of angular velocities down the leg, but it need not.
Most arthropod legs have degrees of freedom to spare, but
extra joints can achieve similar movements with smaller
flexion angles at each, minimising soft cuticle and probably
gaining in strength, may increase the number of possible foot
positions within the total field of movement of the limb, and
may also help to minimise the bending moments about
individual joints. As we have seen, the distribution of pivot and
hinge joints is to some extent logical, but it remains obscure
why myriapods and arachnids have only hinge joints and
therefore only flexor muscles in the distal parts of their legs. It
may allow more slender legs, but the sturdy legs of millipedes
are constructed similarly, and the legs of many Pycnogonida
and Diptera are equally filamentous.
Of the various locomotory options, drag-based swimming
appears to make fewest demands on appendage design. Given
near-neutral buoyancy, all that is required is a muscular
paddle that is erect for the power stroke but folds, twists or
retracts for the recovery. A flat paddle would serve, but a
curved section, concave in the direction of the power stroke,
is stiffer and gives higher drag coefficients. Hydrostatic
paddles, as usual, need total muscular control, but an
arthropod exoskeletal one could function with one powerful
extrinsic muscle inserted near the base. This would be
necessary to drive the power stroke but, provided that any
joints were correctly orientated and constructed to deform
only on the recovery stroke, other deformations could in
theory be driven by drag alone.
These are minimum requirements. In practice, arthropod
swimming paddles are usually far more complex, with a suite
of adaptations, skeletal and muscular, for maximising and
directing thrust and minimising drag on recovery. These are
particularly evident when few appendages are involved, as
with the swimming legs of aquatic Coleoptera and
Heteroptera. Crustacean phyllopodia are broad and lobed.
The pleopods and uropods of Malacostraca are normally
biramous, and the rami are capable of being spread for the
power stroke and overlapped for the recovery. Hinged
fringing hairs, often branched, spread to enhance the drag and
fold automatically to minimise it. The situation is
complicated by the fact that many swimming appendages are
also concerned in creating feeding currents, or filtering, or
both. Nonetheless, drag is extensively recruited to assist
deformation, and the latter is controlled at least partly by the
skeletal architecture and properties.
If drag-based swimming is the mode of locomotion least
demanding on appendage design, flight must be the most.
Insect flight is costly, and flight muscle is surprisingly
inefficient. It is increasingly clear that most insects could not
support their weight in air without resorting to unsteady
aerodynamic mechanisms and without gaining useful force
on both the downstroke and upstroke: ‘feathering’ for a
recovery stroke is seldom adequate. These measures require
torsion, often with transverse bending, and any of a range of
other deformations including camber alteration, fanwise
bending along a series of flexible lines radiating from
the wing-base and alteration of effective area. They must
happen without sacrificing essential rigidity and without
allowing the wing to swing up into the wind like a flag. They
must take place at frequencies that may reach several hundred
hertz and be capable of rapid alteration as the insect
accelerates, manoeuvres and compensates for changes in
ambient flow.
All this must be achieved without internal musculature. The
wings are ultra light, with minimal mass, but even so inertial
forces are often well in excess of aerodynamic forces. Basal
attitude and camber are determined by the relative movement
of nearby thoracic sclerites and by muscles pulling directly on
the wing anteriorly and posteriorly to the pleural fulcrum over
which it is flapped, but their influence on wing shape is remote
and limited. Shape is otherwise determined by the overall
elastic response, encoded in the wing’s structure and materials,
to the instantaneous patterns of aerodynamic pressures and
inertial stress throughout the stroke. Insect wings hence
represent a high spot in skeletal engineering and the
culmination of automation in appendage functioning. Their
status as ‘smart’ aerofoils, structures responding autonomously
and advantageously to external forces, is perhaps unparallelled
in the animal kingdom.
Invertebrate paraxial locomotory appendages 3343
I am grateful to Paolo Domenici, Robert Full, Mimi Koehl
and Chris Smith for useful discussion, to Janice Shears for
technical assistance and to the Society for Experimental
Biology for financial support.
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