Download Lecture 2

Sept. 10. Materials for force transfer
Skeletal constitutents: composites: matrix & fibres: mesoglea (pliant), mollusc shells,
clockwise, counterclockwise, shell as locomotory organ?, insect cuticle, calcite
(trilobite eyes), wood (carpenters and framing), bone, tendon, chitin, apodemes,
collagen and crossed-fibre helical connective tissue arrays. Viscoelastic materials:
mucus and cilia and slugs sliding on snot. Sclerotization and stridulation; resilin,
abductin as antagonists; allometry and geometric morphometrics, size and scaling.
Bad plan to try to stick to this original syllabus – need to be able to change content.
Picture shows-lectures and lab preambles define course content – not the syllabus. I
will try to update the syllabus as to what actually happened in the lectures as we
proceed.
Announcement:
As I finish the projected part of lectures, the ‘picture shows’, I will post them,
after editing, on the website as ‘Picture Shows’. The old ‘picture shows’ from a
previous incarnation will remain there for a bit. But the new ones will be added
as they occur within a few days of each lecture. These picture shows will not
include all that was said in lecture.
I also plan to add material as ‘essays’ from time to time. There is one there on
the tentorium at the moment that you should read and another coming shortly on
Materials.
First assigned readings
Denny Mark 1980. The role of gastropod pedal mucus in locomotion. Nature 285:
160-161.
“The yield-heal characteristics of this mucus are ideally suited to the locomotion of A.
columbianus. During locomotion 12 to 17 muscular waves are present on the slug’s
foot...”
Ritchie Robert O. 2011. The conflicts between strength and toughness. Nature
Materials 10: 817-822. See Website essay under ‘Essays source paper’.
Vincent Julian F.V. & Wegst Ulrike G.K. 2004. Design and mechanical properties of
insect cuticle. Arthropod Structure and Development 33: 187-199.
You are not ‘responsible’ for understanding everything in these
papers: read to clarify and add to the points made in lecture.
Skeletons both exoskeletons and endoskeletons, move forces about.
They translocate them, they leverage them. What are the functions of
levers? To amplify forces, to set forces against one another: antagonize.
Three classes of lever are named on the basis of
sequencing effort, load, fulcrum.
• FIRST
• SECOND
• THIRD
EFFORT
FULCRUM
FULCRUM
FULCRUM
LOAD
EFFORT
LOAD
EFFORT
LOAD
• For more background on levers see Vogel 2nd ed. Chapter 24, p. 473.
Scallop adductor is
a 2nd class lever
Abductin at the hinge is a
material not a muscle, a
rubbery antagonist of the
adductor muscle; it acts
elastically, storing energy in
distortion when the adductor
contracts, to return it at a later
time.
Abductin as inner and outer
ligament: one acts as a 2nd
class other as 1st .
The load of the shell is
taken as acting through
the centroid of the
bivalve, this being
closer to the hinge than
the muscle; the effort
of the adductor muscle
‘lifts’ this load.
Leverage involves a
force causing body-part
rotation: the force from
shortening adductor
muscles pulls on the
adductor apodeme
inserted on the
mandible base; this
rotates the whole
structure through a
short arc toward the
midline (fat blue arrow)..
[Force can be represented as a vector,
showing magnitude and direction.]
To decide where the load should
be considered to act, you need
the point of balance, i.e., the
centroid or centre of gravity.
“Levers are practical applications of ...moments” Vogel
Force moment
When “a force has a line
of action lying to one side
of an axis of rotation...
we call the shortest, or
perpendicular, distance
between the force’s line
of action and the axis,
the ‘moment arm’ or the
‘lever arm’ of the force”
(Vogel 2nd). A moment of
force is the product of
the force magnitude and
this lever-arm distance to
the line of action.
Force-advantage levers vs distance- (or) speed-advantage levers
•
•
•
•
•
Vogel advocates using the term force advantage instead of mechanical advantage,
because mechanical advantage can be misleading: a muscle often actually works at
a leverage ‘disadvantage’.
Force advantage is the ratio by which the applied force is multiplied (amplified) by
the lever.
Where force is more important than speed in the life of an animal evolution will
want a force-advantage lever, one where the effort arm is longer than the load
arm, so maximizing the moment of the effort – the force-in or effort moment.
Distance advantage is force advantage’s reciprocal: the ratio of the distance the
load moves to the distance moved by the effort. [“Distance advantage must
correspond to ‘speed advantage’ – if an action takes a given time, then going
farther means going faster”.]
When speed and distance are more important than force you will want a longer
load arm than effort arm giving a relatively greater moment to the load.
Redrawn Fig. 24.1 of Vogel
Force advantage: ratio by which
the effort is multiplied by the
lever; moment arm of effort
divided by moment arm of the
load.
Distance advantage: ratio of the
distance moved by the load relative to
that moved by the effort.
Speed advantage: ratio of the
speed at which the load moves
relative to that of the effort.
Force and distance/speed
advantage are inversely related:
good force advantage goes with a
relatively poor distance/speed
advantage; good distance/speed
advantage with a relatively poor
force advantage.
Both up and down insect-wing movements are a (first class) distance-increasing lever – a lever
with good speed advantage, and a relatively poor force advantage; there is a very short force
arm, the moment arm of the effort is divided by the much larger moment arm of the load – the
centre of gravity of the wing being much farther from the fulcrum.
“A muscle... is relatively
good at producing force
and relatively bad at getting
shorter. ...any engine that gets
only 20 % shorter will have to
operate with a substantial
distance advantage to move a
long limb [wing] through an
angle that may approach 180
degrees. For that good
distance advantage it will
necessarily suffer a poor force
advantage because the
product of the two must be
unity...” (Vogel 2nd , p. 475)
Class 3 lever for both up
and downstrokes of the
wings
As with the insect wing, the bird wing
is a distance (& speed)-increasing lever.
Distance advantage will be >1: put in a
small distance get out a large.
Distance advantage: ratio of the
distance moved by the load (weight of
the wing) relative to that moved by the
effort (contracting muscle) is much
greater than 1.
The effort arm in a flying bird is not
longer than the load arm, so not
maximizing the moment of the effort.
Paired antagonistic
muscles, blade apodemes
and a dicondylic joint in
the flexion (depression)
and extension (levation)
of the jumping,
(metathoracic) leg of the
locust
Pinnate muscle via apodeme: more powerful than orthogonal
(direct) fibres
To avoid having to draw, and only use words for organ description: see
this wonderful old book of terminology for entomologists.
•
Torre-Bueno, J.R. A Glossary of Entomology. Brooklyn Entomological Society
•
•
•
•
•
•
•
acclivous – rising gently
acetabulum – cavity into which an appendage is articulated
acicular – needle-shaped (e.g. spine of Chestnut is acicular)
aculeate – armed with short sharp points (e.g., burr of burrdock is not aculeate)
acuminate – tapering to a long point
adnate – adjoining (e.g., radius and subcosta are adnate)
alate – winged etc. Takes a while to get to ‘unguis’: one of the claws at the end of
the tarsus, plural ungues
unguiform – shaped like a claw; unguiflexor – muscle flexing the ungues of an
insect; unguifer – the median dorsal process or sclerite on the end of the tarsus to
which the pretarsal claws are articulated etc. Unguiflexor lets me illustrate a rope
apodeme, one specialized to convey tensile stress as well as the fact that not all
antagonists are other muscles.
•
Locust rope apodeme and unguiflexor muscles
Apodemes can also be designed for tension
unguiform – shaped like a claw; unguiflexor –
muscle flexing the ungues of an insect;
unguifer – the median dorsal process or
sclerite on the end of the tarsus to which the
pretarsal claws are articulated etc. Unguiflexor
lets me illustrate a rope apodeme, one
specialized to convey tensile stress as well as
the fact that not all antagonists are other
muscles.
ungue
Like the scallop the antagonist of the
unguiflexor is elastic material
Arthropod cuticle: a hierarchical composite material
source: Vincent J.F.V. & Wegst U.G.K. 2004. Design and mechanical properties of insect cuticle. Arthropod
Structure and Development 33: 187-199. (see Assigned reading)
•
•
•
•
•
Many animal materials are composites: a material made by combining two other
materials: soft composites are made of a “rubbery matrix reinforced by fibres… a
material that is composed of two quite different materials… can have better
properties than either material on its own” (Ennos 2012).
My canoe is made of a composite material, isolated glass fibres embedded in a
continuous resin matrix. Cuticle, the integument of all animals in the phylum
Arthropoda, functions as exoskeleton and is a composite material.
Arthropod cuticle consists “…of arrangements of highly crystalline nanofibres
embedded in a matrix of protein, polyphenols and water, with small amounts of
lipid.”
It is “praeternaturally (surpassing the ordinary) multifunctional” (Vincent 2004).
“The cuticle… not only supports the insect, it gives it its shape, means of
locomotion, waterproofing and a range of localised mechanical specialisations
such as high compliance, adhesion, wear resistance and diffusion control. It can
also serve as a major barrier to parasitism and disease.”
Ennos Roland 2012. Solid Biomechanics. Princeton Univ. Press, Princeton, Oxford.
Matrix: imagine a
spider web of
interconnecting
silk in 3
dimensions.
Chitin is a polysaccharide akin to cellulose. One chitin nanofibre (see the 19 chains in Vincent’s Fig. 1) is 3 nm
in diameter, 0.3 micrometeres long. “The fibrous composite cuticle derives its properties from its components,
which can be varied in orientation... and volume fraction to produce the wide range of mechanical properties:
chitin nanofibres, type of protein, water content and degree of cross-linking of the protein [sclerotization], lipid,
metal ions, calcium carbonate.” Fig 1. Section of chitin nanofibre looking along the chitin.
Praeternaturally functional
•
•
•
.”..the insect cuticle also has to form sensors, joints, wear-resistant mandibles,
devices for elastic energy storage, effective attachment systems...” (Vincent &
Wegst 2004)
Cuticle composition varies topographically in an animal’s skeleton – varies in
thickness, toughness, elasticity – so it can bend effectively at a joint, or as a
blade apodeme give broad surface to muscle fibre origins, act as a brace in a
tentorium, or function like a pulling rope, resisting tension created by
unguitractor muscle; it can be very thin in gills to allow the gas exchange of
aquatic insects, or become thick and tanned and resist compression in a
crushing mandible. [Sclerotization and tanning are chemical processes that
toughen cuticle by creating stable cross-linkages within the composite.]
The important point is that adaptive form (the theme of 325) extends down through
hierarchially organized material structure showing adaptation throughout. Not only is
cuticle shaped for crushing food at the organ level (e.g., a grasshopper mandible) but
the cuticle’s microstructure – the structure of “crystalline chitin nanofibres embedded
in a matrix of protein, polyphenols and water” (Vincent & Wegt 2004) has evolved to
e.g., offset fracture: exoskeleton substance is adapted to make toughness where it is
needed.
•
•
•
•
•
“The tensile and shear stiffnesses and strengths… are much larger when fibres are
alligned parallel to the applied load.”
The cuticle is secreted by a single layer of epidermal cells that covers the entire
surface of the insect, extending into the tracheal system, fore- and hind gut, and
part of the genital system. …It can be as thin as 1 micrometre in the hindgut and
over gills [where transport matters] and as thick as 200 micrometres “(wingcovers, of large beetles) [where mechanical protection strength and toughness are
needed].
The cuticle “…frequently is multilayered with a plywood-like structure “
Plywood analogy: “If high stiffness in more than one direction is required , as is
the case in most parts of the cuticle, ‘laminating unidirectional layers in a variety
of directions produces the desired properties.”
(Vincent & Wegst 2004)
The shell is an important extracellular feature (organ) of animals in the
phylum Mollusca.
This mollusc, a
gastropod
(snail), carries
about its shell
as a refugium, a
protective
retreat. The
microstructure
of the shell has
evolved be able
to resist the
mechanical
forces directed
at it by
predators.
Assigned reading: see R.O. Ritchie The conflicts between strength and
toughness. 325 website Essay source paper
•
“Mollusc shells are also another fine example of nature’s design of damagetolerant materials. ...these materials have a ‘brick-and-mortar structure; the
‘bricks’ are ~0.5 µm thick, 5-10 µm wide, platelets of the mineral aragonite (a
polymorph of calcium carbonate) that comprise some 95% of the structure,
separated by an organic biopolymer mortar in-between (Fig. 5a).”
See further comments on the
importance of this paper in the section
of the website headed Essays source
papers
the platelets (I think) are missing their
matrix in this scanning electron micrograph
Wikkipedia on ‘nacre’
•
Nacre is composed of hexagonal platelets of aragonite (a form of calcium
carbonate) 10–20 µm wide and 0.5 µm thick arranged in a continuous parallel
lamina. These layers are separated by sheets of organic matrix composed of elastic
biopolymers (such as chitin, lustrin and silk-like proteins). This mixture of brittle
platelets and the thin layers of elastic biopolymers makes the material strong and
resilient, with a Young's modulus of 70 GPa (when dry). Strength and resilience are
also likely to be due to adhesion by the "brickwork" arrangement of the platelets,
which inhibits transverse crack propagation. This design at multiple length sizes
greatly increases its toughness, making it almost as strong as silicon.
Young’s modulus (values from Gordon 1978) is the ratio of stress to strain
(stress/strain) and measures stiffness. Cuticle of a ‘pregnant’* locust 0.2; rubber
7; human tendon 600; wood along the grain 14000; iron 210000.
*Locusts in a reproductive state are not said to be ‘pregnant’ by any entomologist.