Lecture 14 BIO 325
Levers
Insect Flight
Elastic recoil: subalar arm
Elastic storage for power amplification: flea jump
Assigned reading:
Sutton G.P., Burrows M. 2011. Biomechanics of jumping in the flea. J. of exp. Biol
214: 836-847.
Patek S.N. et al. 2011. From bouncy legs to poisoned arrows: elastic movements in
invertebrates. J. exp. Biol. 214: 1973Rothschild, M. et al. 1973. The flying leap of the flea. Scientific American 222: 92-101.
Roberts T.J., Azizi E. 2011. Flexible mechanisms: the diverse roles of biological springs
in vertebrate movement. J. exp. Biol. 214: 353-
Levers
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A lever is a machine that moves (translocates) forces from one place to another, at the
same time changing the force magnitude and direction.
Lever arm of the force-in is the shortest distance from the axis of rotation to the load.
Lever arm of the force-out is the shortest distance from the axis of rotation to where
the load is considered to act (i.e., it’s centre of gravity).
Force advantage of a lever: the factor by which the force in is changed: FORCE
OUT/FORCE IN.
Distance advantage of a lever: the factor by which the distance moved is changed:
DISTANCE OUT/DISTANCE (speed) IN
[Since both effort (force in) and the load (force out) must move their distances in the
same time: distance advantage is the same as speed advantage.]
Force advantage and distance advantage have a reciprocal relationship: a lever with a
good force advantage will have a poor distance advantage; a lever with a poor force
advantage will have a good distance advantage. [The latter is the case with the insect
wing: muscles pulling (indirectly) close to the fulcrum: wing tips moving through a
maximal distance as one wants in flying.]
Muscles typically have to work with a poor force advantage.
3 classes of lever: classified on the basis of sequencing 3 items
force in, force out and fulcrum (axis)
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FIRST
SECOND
THIRD
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In order to place the load (force out) you need to decide the location of the
centroid of a structure, its centre of gravity: this is the point of balance.
Need to understand the idea of mechanical advantage: force advantage, distance
advantage, speed advantage. These are ratios (unitless).
Force advantage: force out divided by force in; Distance advantage: distance out
divided by distance in; Speed advantage: speed out divided by speed in.
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EFFORT
FULCRUM
FULCRUM
FULCRUM
LOAD
EFFORT
LOAD
EFFORT
LOAD
The wings of insects are first class levers
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The force in (EFFORT) is exerted by the longitudinal and tergosternal muscles
acting indirectly via changes in shape of the thorax. Consider the wing as a very
long lever. pivoted on the second axillary sclerite which sits atop a prominence on
the thorax side, the pleural wing process. The PWP and the 2nd axillary represent
the fulcrum. The force arm is a very short projection toward the body from the
fulcrum. It goes through a small distance up and down when the thoracic
movements push on it. The load lies far out on the wing and goes through a
relatively large distance up and down. The force in and the force out lie on
opposite sides of the fulcrum (hence FIRST CLASS LEVER) and though the muscles
work at a considerable force disadvantage they have a very large distance
advantage – this being the same thing as a speed advantage. Short movements of
the tiny force arm at a slow speed displace the load arm through long movements
at a much higher speed: just what you need for flying.
Scallop as a 2nd
class lever
The load is assumed to be
acting through the centre of
gravity of the bivalve; the force
out lifts this load.
Class 3 lever both up and
down
Tergum, sternum, pleuron
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Insects are segmented animals and the thorax is a locomotory tagma.
Contrast the segments of the abdomen with those of the thorax. The thorax is
‘fixed’ to create a firm base against which muscles can pull, for walking and for
flying. The pterothorax is the mesothorax + metathorax: two segments specialized
for bearing the wings and for flight.
Muscles involved in flight in insects (with exceptions) insert on the exoskeleton of
the thoracic box and move the wings by distorting box shape.
LONGITUDINALS DOWNSTROKE; TERGOSTERNALS UPSTROKE
Attitude of the wings (pronation, supination) is achieved by the elastic interplay of
the veins and membranes with the air flow. The wings don’t just go up and down
and maintain elevation they must scull through the fluid (air) like a fish fin.
Locust flight {Source: R.E. Snodgrass The thoracic mechanism of a
grasshopper, and its antecedents. Smithsonian Miscellaneous Collections 82,
pp. 111. } [This reference is given just for completeness; it is not something you
should try to obtain and read, but it is the source of much of the information
here and in the lab.]
Locusts are strong fliers. The flight-powering muscles of the locust are indirect:
meaning they don’t insert on the wings. They have their effect upon the wings by
distorting the pterothorax and by tergal tipping of the second axillary. (The pterothorax
is the flight tagma (just segments 2 & 3, not the prothorax.) There are two antagonistic
muscle sets: longitudinals (downstroke), and tergosternals (upstroke).
Sct2 is the scutum of the
second segment of the
thorax; scutum is the name
given to a part of the
tergum, as is Scl2 which is
scutellum.
Muscle 81, e.g., is a
longitudinal flight muscle
pulling between phragma 1
and 2, 112 is the same
pulling between phragma 2
and 3. These increase the
arching of the terga
creating forces at the wing
bases (PWP & 2nd axillary
sclerite).
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The longitudinals are situated high up in the pterothorax. Partially obscured behind
them, arrayed against the pleuron, are the many tergosternals (83,84,89 etc.), running
between the sterna (S2,S3) and the terga (Sct2,Sct3). The axes of the tergosternals all
lean headward (the insect’s anterior is to the left). Notice how the upper end of the
tergosternals insert on the terga where their contraction can reduce the convexity of
this region. Reducing tergal convexity is associated with elevation of the wings.
More diagramatic views: Snodgrass drew the phragmata (Aph anterior phragma, Pph posterior
phragma) of Fig. 129 purposely distorted, so as to show their interconnecting longitudinal
muscles both ahead and behind: notice the critical placing of the second axillary, 2Ax, atop the
pleural wing process, WP.
The wing is a double-layered outfolding of cuticle. At the wing base are 4 axillary sclerites and 2
median plates (m, m’) linking the basal/proximal ends of the veins (costa, subcosta, radius,
median) to the margins of the tergum. The tergum is to the left (not shown). The third axillary
serves in flexing the wing over the back when the insect is not flying. It is the anal field that
becomes involved in stridulation in crickets and katydids.
basilares2
2nd
axillary
subalare2
PWP2
Seen here in dissection, the heavily sclerotized pleural wing process with the second axillary
that contacts it above. See also the first basilare, 1Ba2, involved in wing pronation and
upstroke and primitively a leg muscle now co-opted for flight.
Seen from below the wing, some of the same veins (Sc) and axillary sclerites appear, the 2nd
axillary 2Ax, is crucial; it is concave and sits atop the wing process – providing the fulcrum of
wing up and down movement.
Power: rate of doing work and ‘springs’
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Forces can be exerted at different rates, quickly or slowly. When we say that a
muscle’s effect is more powerful, we mean it is working more quickly. Work is
Force X distance (force [mass X acceleration] is exerted over a distance to do
work). Power is the rate at which work is done: done slowly it is low power, done
quickly it is high power. A flea needs a powerful jump to get higher. Its muscles
alone cannot achieve the necessary power in ‘real time’ – so muscle is aided by
cuticular storage of energy.
Forces can be stored to be released at a later time. And when, at that later time
they are released, they can come back into action far more quickly than would
have been the case if this movement emanated from the muscle that originally
stored them.
Elasticity of cuticle can be used to aid locomotion by increasing power and
efficiency.
Explanation of
how the prealar arm
stores elastic
energy: basilare
muscle pulls on
basilare sclerite which
pulls on the ligament,
stretching the prealar
arm resilin. The two
resilin springs, prealar
arm of phragma 1 and
hinge at top of PWP
[red], store energy by
tension during the
upstroke, energy
derived from the
flight muscles.
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Shape change in the
tergum (reduced
convexity centrally,
with outward and
downward movement
at the tergal margins)
is brought about by
the tergosternals. So
over a very shortdistance a downward
force acts on the near
end of the 2nd axillary
(red arrow); this
rotates the proximal
end of the 2nd axillary
around the pleural
wing process (PWP)
and raises the wing
that is linked to the
axillary.
Elastic energy from
the upstroke is stored
in the wing hinge
resilin (as well as the
prealar arm [not
shown]).
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During the
downstroke energy
returns from the wing
hinge and prealar arm
contributing to the
rebound of the wing.
The longitiudinals,
antagonists of the
tergosternals are now
changing the shape of
the tergum back to
more convex and the
force acting on the
proximal 2nd axillary is
upward (red arrow).
The cat flea Ctenocephalides felis
Morphological features
form of the flea: no wings,
it’s flightless (its ancestors
had wings); body
extremely laterally
compressed; greatly
enlarged metathoracic
legs; unidirected body
spines. Apply the course
theme to this insect
thinking about where and
how the animal lives.
Course theme: the course is about the form of structures and their
behaviour; about what form a structure takes and why. Why have certain
features: shape, size, elasticity, colour, etc. evolved and not some others?
Look at animals functionally. Think about adaptive consequence.
A flea only 2 mm long can jump 200 mm,
100 times its own body length,
equivalent for a 6’ human of 600 feet!
Accelerates from rest to 1 metre/sec in a
distance of 0.4 mm; by extending its legs
in about 8/1000th of a second.
Jumping is by power amplification. Energy is loaded (relatively slowly by isometric
contraction of antagonistic muscles) into a pleural arch (the site of the wing-hinge in its
flying insect ancestors) and stored there in the rubbery protein resilin (insect rubber:
matrix between the chitin nanofibres is now of this particular protein). Once loaded the
energy is held there as potential energy by latching sclerites, so no ongoing effort
needed by the flea. Release is by body width change. The leg segments extend pushing
down on the substrate and because of the stored energy they do this very very fast. So
the ‘engine amplifier tool’ arrangement of Patek is: leg muscles as engine, resilin of
pleural arch as amplifier, flea hind leg as tool.
The muscle depressor of the
trochanter (green here) is a
relatively long way from the
trochanter; it originates on the
notum, it inserts on the trochanter.
The insertion is via a massive
apodeme which tapers down to
attach anterior to the (dicondylic)
axis of the trochanteral rotation (see
blue dots). So the contraction of the
trochanteral depressor pulls the
trochanter, rotating it forward on
the coxa and extending it (=
depressing it).
An antagonist of the trochanteral
depressor is the levator of the
trochanter. It originates on the
inner wall of the coxa and inserts on
the trochanter posterior to the axis.
And another muscle antagonistic to
the trochanteral depressor is the
epipleural muscle: this inserts on
the base of the coxa; on its
contraction, as with the levator, it
pulls behind the axis of rotation of
the trochanter on the coxa. Both
the epipleural muscle and the
levator of the trochanter have the
effect of flexing (levating) the limb,
i.e., raising it from the substratum.
Under normal walking movement
either the levator or the depressor
contracts: they are not shortening at
the same time. But in preparing
itself in the jumping position, the
flea eventually contracts all three
muscles simultaneously:
isometrically: no movement at the
joints: hence distortion.
Flea begins its jump by flexing
the limb (the levator and
epipleural muscles playing an
appropriate part in this). Then
all three muscles [levator of
trochanter, epipleural muscle
and depressor of the trochanter]
contract simultaneously. Since
the depressor opposes the
action of the other two, nothing
happens now to change the
relation of the segments of the
flexed hind limb [isometric].
Rather the force expended by
the muscles is "loaded into the
pleural arch", i.e., it goes to
compress the resilin pad located
above the pleural plate,
squeezing the resilin between
the plate and the notum.
Sutton G.P., Burrows M. 2011. Biomechanics of jumping in the flea. J. of exp.
Biol
214: 836-847.
In this paper the authors present arguments between two hypotheses of how the
flea jump works: 1) Rothschild Hypothesis 2) Bennet-Clark Hypothesis. Their
arguments are all in favour of the latter: the trochanters do not drive into the
ground, rather that “expansion of the spring applied a torque about the
coxotrochanteral joint that (is) carried through the femur and tibia and finally
resulted in a force applied to the ground by the hind tibia and tarsus.
Driving down the trochanters into the ground has some obvious arguments
against: animal would be propelled vertically and could have trouble jumping and
making horizontal distance (of course to reach a passing dog vertical might be
rather good).