Bio 325 Lecture 15
‘Sudden appendages’: lunging and jumping
The jump of the flea involves a kind of spring enabling power amplification,
widespread in animal locomotion, both invertebrates and vertebrates.
Roberts T.J. & Azizi E. 2011. Flexible mechanisms: the diverse roles of biological
springs in vertebrate movement. J. exp. Biol. 214: 353-361.
“Springs deform when a force is applied and recoil to their resting shape when
the force is released. Materials [resilin, abductin are just extremes of rubbery
flexible skeletal materials -- chitin and collagen also store energy even when
relatively stiff] can act like springs when loaded in tension, like a rubber band, or
in compression, like a rubber ball. Both kinds of loading are important in nature.
When springy materials deform, they store energy in the form of elastic strain
energy, and when they recoil this energy is released. The amount of energy
stored depends on the material stiffness and the deformation.”
“Elastic mechanisms can act as power amplifiers, by storing muscle work slowly
and releasing it rapidly.” This is the flea using resilin as described last lecture.”
Sources re sudden appendages
*Assigned reading
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*Heitler, W.J. 1974. The locust jump, specialisations of the metathoracic femoral-tibial
joint. Journal of comparative Physiology 89: 93-104.
*Bayley, T.G. 2012. A buckling region in locust hindlegs contains resilin and absorbs
energy when jumping or kicking goes wrong. J. exp. Biol. 215: 1151-1161.
*Patek, S.N. et al. 2011. 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 222: 92-101
Gordon, J.E. 1978. Structures or Why Things Don’t Fall Down. Penguin.
Sutton, G.P. & Burrows, M. 2011. Biomechanics of jumping in the flea. J. exp. Biol. 214:
836-847.
Romaleinae
Eumastacinae
Theme of the course
applied to the
metathoracic
leg of Orthoptera.
This colourful insect (left)
is a eumasticid
grasshopper from
Colombia.
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Saltatorial: animal modified for
leaping and jumping.
tracks in snow
Forelimbs small, hindlimbs
enlarged
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 present two hypotheses of how the flea jump
works: 1) Rothschild Hypothesis ‘trochanters driven into ground’ 2) Bennet-Clark
Hypothesis ‘overall extension of leg speeded up’. They decide in favour of the
latter hypothesis: the trochanters do not touch the ground, rather the “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. In other words the whole chain of leg segments
extends with enhanced speed derived from the resilin.
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).
Orthoptera Species File
Locusta migratoria in a prejump crouch.
Heitler W.J. 1974. The locust
jump. J. comp. Physiol.
89: 93-104
from Wikkipedia
Heitler W.J. 1974. The locust
jump. Journal of comparative
Physiology 89: 93-104.
Well-written and clear; read it in
detail to understand the paradox
(see below).
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Heitler starts with behaviour: what the structure does: the mechanics of the jump in
increasing detail. There is passing reference to the adaptive context.
“The locust jumps to escape from danger, to launch itself for flight, or simply to achieve
a more rapid form of locomotion than walking. Prior to a jump the locust assumes a
crouched position, with the metathoracic tibiae flexed, and it may maintain this for
some seconds until it either jumps or relaxes. The jump is achieved through a rapid
extension of both the metathoracic tibiae... [through a femorotibial joint “excursion of
about 150 degrees”].
Anatomy and leverage of locust
metathoracic leg femorotibial joint
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Flexion and extension: during a
jump or kick the joint angle goes
from 0 to 150 º
Dicondylic joint: condyles [= pivot
pegs] are part of femur, the
sockets part of tibia.
Extensor of tibia, flexor of tibia are
antagonists, yet their muscles pull
in nearly the same direction. The
femorotibial (dicondylic) joint is
the axis about which the tibia
pivots relative to the femur.
The extensor works as a 1st class
lever; the flexor is 3rd class.
Notice that the lever arm is bent
in a distinctive shape which affects
force direction (see below).
The angles of ‘force in’ change as
the tibia moves from completely
flexed to maximally extended (see
below).
Pocket and lump = flexor
apodeme lock.
Geometry/anatomy of the
joint see Heitler’s Fig. 1
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a Fully flexed joint, lock engaged:
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 readily visible and rides pulleylike on top of the lump.
c The two condyles of the dicondylic
joint seen dorsally along with the
lump.
Paradox
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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.
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“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.”
How is this achieved during isometric contraction? The answer: special adaptations of
leverage at the joint and a flexor apodeme lock.
*For the force/effort arm of the tibia to have greater length relative to its load arm giving
better advantage, we would have to change the shape of the femur’s distal end drastically.
We need to think about moments of force in analysing the movements at the joint.
Here is a diagram based
upon
Heitler’s Fig. 2 c.
“The thick blue and
purple lines “represent a
mechanical analogue of
the joint structure”.
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Go back to the paradox: how is it that during isometric contraction the smaller, weaker muscle is able to
match the effort of the larger?
The force advantage of the flexor muscle is different at different angles of flexion of the femorotibial joint.
Part of the answer to the above question is that when the angle of flexion is less than 5 degrees (top) the
mechanical advantage of the flexor muscle is superior to that of the extensor.
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With the joint angle at 5º (top), the apodeme of the flexor makes an angle with the effort
arm of the lever of almost 90º; this is because it rides up over the 'lump'. The lump functions
as a pulley: (a pulley changes force direction); it changes the ‘force-in’ direction of the flexor
apodeme making it nearly 90 º; by contrast the stronger extensor, exerting more force, has a
force-in direction at a very poor angle of 6 º. So the moments of force for the two
antagonists can be equal.
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Locust gets extra force into its leap by isometric contraction. This distorts the exoskeleton in
the neighbourhood of the joint and so stores elastic energy in the leg exoskeleton (semilunar
processes, see below) that will later be released during the jump. This stored energy,
available much more quickly than it was stored adds power. It contributes to the forces the
leg exerts against the ground. The pocket is pulled over the lump during the early stages of
the flexion and so the distortion can be retained even if the antagonists relax, i.e., the leg can
be ‘cocked’.
The effort arm (the distance between the point of insertion of the apodeme on the tibia and the
axis of rotation) is quite short for the extensor; much longer for the flexor. So the moments of force
can be balanced at 5º. To keep the two leg muscles in isometric contraction the moment of force of
the weaker muscle has been made equal to the moment of force of the stronger
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.
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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
Burrows & Sutton 2012
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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.
Photographs of the femoro-tibial joint of a right hind leg of an adult locust.
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
©2012 by The Company of Biologists Ltd
“Externally visible resilin was compressed and
wrinkled as a semi-lunar process was bent. It then
sprung 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 Photographs of the femoro-tibial joint of a right hind leg of an adult locust.
repeated.”
Burrows M , Sutton G P J Exp Biol 2012;215:3501-3512
©2012 by The Company of Biologists Ltd
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
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 also: JEB highlight by Kathryn Knight in same issue: Buckling zone protects locust legs
• Energy of a kick that misses its target (or a foot that slips on the
substrate) 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
identity). There are also special campaniform sensilla
(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.”
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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 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 bow 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 the reason why bones
can be nearly as strong when hollow.
Why are the long-bones of
the vertebrate limb hollow?
Special shock aborbers for kicks gone astray
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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 presence of a special rubbery cuticular
protein, resilin.
As we now analyse in some detail the jumping of several insects, resilin will be
seen to play an important role.
Selected images of a jump by a male locust.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd
Buckling of the right hind-tibia of a locust during a kick that missed its target.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©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
Scanning electron micrographs of the buckling region and adjacent sensory structures.
Bayley T G et al. J Exp Biol 2012;215:1151-1161
©2012 by The Company of Biologists Ltd