Transcript Lecture 9

POWER AND SPRINGS
Patek, S.N. et al. From bouncy legs to poisoned arrows: elastic movements in
invertebrates. J. exp. Biol. 214: 1973-1980.
Rothschild M. et al. 1973. The flying leap of the flea. Scientific American: 92Sutton G.P., Burrows M. 2011. Biomechanics of jumping in the flea. J. of exp.
Biol. 214: 836-847.
Montealegre-Z F. Et al. Generation of extreme ultrasonics in rainforest
katydids. J. Exp. Biol. 209: 4923-
Springs (materials storing energy by distortion) can be critical in animal
locomotion and a much better way to catch prey.
“… springs can provide outstanding efficiency and stability for continuous,
long-term movements. These rhythmic movements include mechanisms
ranging from flying fruit flies to singing katydids …(Montealegre-Z et al.
2006).
Power ultrasonics
achieved by a cuticlular amplifier
scraper
file
mirror
See Montealegre-Z 2006
Sphagniana sphagnorum
Katydid wings are used
to stridulate. A raised
edge of the right wing
(scraper) engages from
below with a row of
teeth lining the
transversely running
file vein of the left
wing. The wings are
moved against each
other and the scraper
moves tooth to tooth,
shocking the glassy
wing cells (mirror) into
motion making sound.
This species powers its way along a few teeth at a
time using scraper elasticity. The scraper lodges
behind a tooth the cuticle behind it bends storing
energy; as the scraper slips free it strikes a number
of teeth much more quickly than the overall wing
movement.
Power: rate of doing work
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When we say a muscle’s effect is more powerful, we mean it is doing work
faster. Work is force times distance [W=FS] . Force is mass times
acceleration [F= mA] . Power is the rate at which work is done.
A stridulating katydid accelerates its scraper mass through the distance
between a number of file teeth, doing a certain amount of work: the faster it
jumps between teeth the higher the power. There is a limit to the speed at
which wing muscles can move the scraper. But higher tooth contact rates –
more power -- can be achieved by using the springiness of the scraper cuticle.
Forces arising in muscles can be stored in materials to be released at a later
time. And at that later time they may give back their action faster, i.e., are
more powerful.
Arthropod cuticle is a composite material: chitin nanofibres (sugar chains)
embedded in a protein matrix. Sometimes the protein is almost completely
dominant giving resilin or ‘insect rubber’.
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Resilin is a protein; it is protein chains joined by covalent bonds crosslinking between tyrosine amino acids (residues).
“this amino acid lacks a side chain and is nonpolar, characteristics that
prevent the formation of the sort of electrostatic bonds that would otherwise
constrain the shape of the molecule. Freedom from constraint allows
formation of random-coil chains.” This is the topographical basis of great
elasticity; one gets a material that is a cord-like tangle of highly variable
topography which can be easily distorted.
Resilin is 50% water in its natural state.
Young’s modulus
• Young’s modulus is an index of the stiffness/elasticity of a material.
Stiffness and elasticity are opposite ends of a ‘spectrum’.
• E = change in stress/change in strain
• Stiff materials have a high Young’s modulus and rubbery deformable
materials have a low Young’s modulus.
• Coral skeleton YM= 60000 very stiff
• Mollusc nacre YM= 30000 very stiff
• Abductin YM= 4
• Resilin YM=1.8 remarkably elastic.
• See Vogel for a table of values: p. 298, 2nd edition Comparative
Biomechanics
Power amplification (Patek 2011 et al.)
• Archer uses muscles slowly to bend a bow, storing elastic energy in
the material of the bow and the bow string. When ready to shoot the
tension in the bow and string is suddenly released.* “The arrow is
shot far more rapidly than would have been possible if the archer
had simply thrown the arrow.”
• “The basic building blocks of archery and any fast biological system
are an engine (the archer’s muscles) an amplifier (the springy bow
and latch-like fingers) and tool (arrow). The unifying principle is
called power amplification: the amplifier reduces the time to perform
the engine’s work.”
• Resilin is an amplifier. But it is not the exclusive basis of elasticity in
cuticle. Cuticle can be relatively stiff and carry out amplification.
The basic building blocks of …any fast biological system are an
engine (horse’s muscles), an amplifier (the pole) and a ‘tool’, in this
case the horse is the (inadvertent) tool or perhaps ‘payload’.
Dark Side of the Horse by Samson
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A bow should never be ‘shot’ without an arrow
(Gordon 1976, p.92): this is because there is no
way of getting rid of stored strain (elastic) energy.
It is possible to shatter a bow in this way. The
strain energy stored in the bent bow can no longer
be dissipated in the kinetic energy of the arrow and
is used to make cracks in the substance of the
bow.
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A makes a nice example of tension and
compression surfaces in a ‘beam’ (Vogel 1988, p.
202). Bending an object of thickness has the
effect of creating a gradient of tension on the
outside of the curve and one of compression on
the inside. In the middle there will be a neutral
plane where there is no stress in either tension or
compression (but not in shear). From this middle
plane toward both surfaces, stresses increase.
This means that central regions of structures
contribute less strength; it is also the reason why
bones can be (nearly) just as strong when hollow.
Rothschild or Sutton & Burrows Sources
Morphological features
form of the flea: no
wings, it’s flightless (its
ancestors had wings);
body extremely
laterally compressed;
greatly enlarged
metathoracic legs;
unidirectional body
spines. Apply the
course theme to this
insect: thinki about
where and how the
animal lives.
The cat flea Ctenocephalides felis
A flea only 2 mm long can jump 200
mm, 100 times its own body length,
the equivalent by a 6-foot human
would be 600 feet!
Accelerates from rest to 1
metre/sec in a distance of 0.4 mm;
by fully extending its legs in about 8
milliseconds.
Jumping is by power amplification. Energy is loaded (relatively slowly by isometric
contraction of antagonistic muscles) into a pleural arch [amplifier] (the site of the winghinge in its flying insect ancestors?) and stored there in the rubbery protein. Once
loaded the energy is held there as potential energy by latching sclerites, so no ongoing
effort is 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 as tool (payload).
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
long apodeme which attaches
anterior to the (dicondylic) axis of
the trochanteral rotation. 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: without
movement at the joints: hence
cuticular 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, deforming it.
Some of the wonderful
Illustrations by Rothschild
explaining the same
jumping process
isometric
contraction
and resilin
the basis of
high-power
leaping in
fleas
isometric means
antagonistic
muscles generate
force without
changing length
figure is from
Rothschild’s
Scientific American
article
Sutton G.P., Burrows M. 2011. Biomechanics of jumping in the flea. J. of
exp. Biol. 214: 836-847.
In this paper the authors evaluate two hypotheses as to how
the flea jump works: 1) Rothschild’s Hypothesis: ‘trochanters driven
into ground’ 2) Bennet-Clark’s Hypothesis: ‘overall extension of leg
speeded up’. They decide in favour of the latter: the trochanters do not
touch the ground, rather the “expansion of the spring applied a torque
about the coxo-trochanteral joint”; this torque is “carried through the
femur and tibia” and finally resulted in a force applied to the ground by
the hind tibia and tarsus. In other words the whole chain of leg
segments extends with speed enhanced by the resilin at the leg base.
Driving down the trochanters into the ground has some
arguments against: the flea would be propelled more vertically and
could have trouble making horizontal distance (though of course to
reach from beside a standing dog vertical might be rather good).
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Saltatorial: animal modified for
leaping and jumping.
Forelimbs small, hindlimbs
enlarged, powerful muscles
Sources
• Heitler, W.J. 1974. The locust jump, specialisations of the
metathoracic femoral-tibial joint. Journal of comparative
Physiology 89: 93-104.
• Burrows M., Sutton G.P. 2012. Locusts use a composite of
resilin and hard cuticle as an energy store for jumping and
kicking. J. exp. Biol. 215: 3501-3512.
• Bayley T.G., Sutton G.P., Burrows M. 2012. A buckling region in
locust hindlegs contains resilin and absorbs energy when
jumping or kicking goes wrong. J. exp. Biol. 215: 1151-1161.
•
See : JEB highlight by Kathryn Knight same issue: Buckling
zone protects locust legs
Orthoptera Species File
The migratory locust
from Wikkipedia
Video of jumping locust
Anatomy and leverage of locust
metathoracic leg femorotibial joint
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Flexion/extension: joint angle
goes from 0 to 150⁰
Dicondylic joint: condyles [=
pivot pegs] are part of femur, the
sockets part of tibia.
Lump [apodeme] (dome-shaped
inflection) can lock via forked
‘pocket’, part of flexor apodeme.
Extensor of tibia, flexor of tibia are
antagonists, yet their muscles pull
in nearly the same direction. The
extensor works as a 1st class
lever; the flexor is 3rd class.
Lever arm has a crooked shape
which also affects force direction. muscles
The angles of ‘force in’ change as not shown, just
apodemes
the tibia moves from completely
flexed to maximally extended (see
below).
Geometry/anatomy of the
joint see Heitler’s Fig. 1:
find the parts on his figure.
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a) Fully flexed locked joint:
bifurcate pocket of apodeme of
flexor sits astride the lump. Note
apodeme of extensor and two
accessory muscles.
b) Lock is disengaged and joint
extended midway; flexor
apodeme is now riding pulleylike on top of the lump.
c) The two condyles of the
dicondylic joint (sockets in tibia)
seen dorsally along with the
lump.
Diagram based upon Heitler’s Fig. 2 c.
“The thick blue and purple lines “represent a
mechanical analogue of the joint structure”.
Simplified diagram
of joint. Tibia
represented as a
light blue member,
bent. The femur as
a purple member.
Paradox
[Logical statement that
apparently contradicts itself.]
For cuticular amplification of
the jump of a grasshopper there
must be isometric muscle
contraction: a smaller flexor
muscle must hold the tibia
flexed against the force of a
much larger extensor muscle.”
Levers are the basis for solving
this paradox
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A moment of force
about an axis is the
product of force
magnitude and the
perpendicular
distance to the axis
(Newton metres).
To keep the two leg
muscles in isometric
contraction at 5⁰, the
moment of force of
the weaker muscle
must be made equal
to the moment of
force of the stronger.
Paradox resolved: The force advantage of the flexor muscle is different at different
angles of flexion of the femorotibial joint. When the angle of flexion is less than 5⁰ (top)
the moment of the flexor muscle is better than that of the extensor.
It is better for two reasons
Better distance from axis
Better pulling angle
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With joint angle at 5⁰ (top), the apodeme of the flexor makes an angle with the effort arm
of the lever of almost 90⁰; because it rides up over the 'lump'. The lump functions as a
pulley and changes the ‘force-in’ direction, making it nearly 90⁰ to the tibia; by contrast, at
5⁰, the stronger extensor has a force-in direction at a very poor angle of 6⁰. Perpendicular
distances (lever arms) and angle of force application are in favour of the smaller muscle, so
the moments of force for the two antagonists can be equal when leg is flexed.
•
So isometric contraction becomes possible as a way for both muscles together to
store energy in cuticle, i.e., elastic distortion gets involved. Resilin regions of
exoskeleton in the neighbourhood of the joint store elastic energy: they are called
semilunar processes. Just like the flea this stored energy can be stored relatively
slowly then made available much more quickly so achieving power amplification.
Think of the bow shot without an arrow that fractures: shock
aborbers in the cuticle of the grasshopper’s tibia are material
adaptations to dissipate energy of fracture.
• Energy of a bow shot without an arrow or a kick that misses its
target is dissipated by a specialized proximal region of the tibia.
There is resilin in this region, revealed as a band that fluoresces
blue under UV illumination (with appropriate filters to confirm resilin’s
identity). There are also special campaniform sensilla in the cuticle
(proprioceptors, mechanoreceptors) that monitor the buckling. “The
features of the buckling region show that it can act as a shock
absorber as proposed previously [by Heitler] when jumping and
kicking movements go wrong.”
Photographs of the distal femur of the right hind leg taken under white and UV epi-illumination,
and then combined.
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
©2012 by The Company of Biologists Ltd
Locking to minimize energy cost while waiting to jump
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Quoting Heitler: “Once the tibia is fully flexed a lock is engaged which can
hold the tibia in this position against the developing extensor tension. Just
proximal to its insertion onto the tibia the strap-like flexor tendon
effectively bifurcates into strands which insert on either side of the tibia,
leaving a strengthened pocket of connective tissue in the middle. At any
angle of extension greater than about 5 degrees the flexor tendon rides on
top of the femoral lump, which thus acts as … [a] pulley…. As the tibia
approaches the fully flexed position …, the two arms of the tendon slide
down on either side of the lump, fitting into grooves at its base, while the
lump fits snugly into the connective tissue pocket in the middle (Fig. 1a). In
this position the tibia is now locked against the femur, and considerable
extensor tension can be developed without the tibia moving.”
• With the lock in place the muscles can bend the exoskeleton and resilin can
begin to contribute its power amplification ability.
Special shock aborbers for kicks gone astray
• Gordon’s comments about bows needing arrows apply readily
to locust kicks that go wrong .
• From the abstract of Bayley et al. 2012. “If a hindleg of a
locust slips during jumping, or misses its target during kicking,
energy generated by the two extensor tibiae muscles is no
longer expended in raising the body [jumping] or striking a
target.”
• Bayley found a special region of the proximal hind tibia that is
adapted to buckle under these conditions through the agency
of resilin.
• Both muscles work with a poor mechanical advantage due to constraints of
body shape* but a good speed-distance advantage – its good to have speed and
distance working for you when trying to jump.
• “Myograms show that there is co-activation of the extensor and flexor muscles
during the pre-jump crouch...”
• “Complete extension of the tibia takes some 20 ms... to develop peak power
...in the jump the extensor muscle must first build up tension isometrically.”
The two antagonists simultaneously contract, but there is no movement at the
joint.
• “The extensor muscle is much larger and occupies the greater part of the
femoral volume.” Its pinnate [angled like a feather] fibres are many more and
short; an arrangement which enables the muscle to develop a very large force
at its tendon [apodeme], though moving through a shorter distance. The flexor
muscle, by contrast, is composed of long thin parallel fibres, and is of
comparatively small cross-sectional area. “This weak muscle must hold the
tibia flexed against the full force of the powerful extensor muscle.” This is an
apparently contradictory statement.
• How is a stalemate achieved during isometric contraction? The answer: special
adaptations of leverage at the joint and the flexor apodeme lock.
Burrows M. & Sutton G.P. 2012. Locusts use a composite of resilin and hard cuticle as
an energy store for jumping and kicking. J. exp. Biol. 215: 3501-3512.
• Burrows & Sutton
have explained
where the energy
of isometric
contraction is
stored. It goes into
paired semilunar
processes of the
femur, located at
the sides of its
distal extremity,
lateral to where
the condyles
protrude into the
sockets of the
tibia.
semilunar process
Photographs of the femoro-tibial joint of a right hind leg of an adult locust
“Externally visible resilin was compressed
and wrinkled as a semi-lunar process was
bent. It then spr[a]ng back to restore the
semi-lunar process to its original shape.
“It is suggested that composite storage
devices that combine the elastic properties
of resilin with the stiffness of hard cuticle
allow energy to be stored by bending hard
cuticle over only a small distance and
without fracturing. In this way all the stored
energy is returned and the natural shape of
the femur is restored rapidly so that a jump
or kick can be repeated.”
©2012 by The Company of Biologists Ltd
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
Burrows & Sutton 2012
Photographs of the femoro-tibial joint of a right hind leg of an adult locust.
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“The inside surface of a
semi-lunar process consists
of a layer of resilin,
particularly thick along an
inwardly pointing ridge and
tightly bonded to the
external, black cuticle.”
There is (shown by imaging
[movie]) distortion/bending
in all three dimensions
during the isometric
contraction.
Wikki: A recombinant
form of the resilin protein
of… Drosophila
melanogaster, pro-resilin,
was synthesized in 2005
by expressing a part of
the fly gene in the
bacterium Escherichia
coli. It is expected to have
many applications in the
athletic footwear,
medical, microelectronics
and other industries.
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
©2012 by The Company of Biologists Ltd
The buckling region of the right hind-tibia viewed under white and UV illumination.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd