"The form, then, of any portion of matter, whether it be living or dead, and the changes of form which are apparent in its movements and in its growth, may in all cases alike be described as due to the actions of force. In short, the form of an object is a 'diagram' of forces..."

-D'Arcy Thompson

Course Theme

The quote above by D'Arcy Thompson (1917) points up the central focus of Biomechanics*: it is a study of forces. The book by Ennos, Solid Biomechanics (2012), defines the subject as "...how the adaptations of animals and plants are constrained to their mechanical environment". In other words biomechanics is the evolution of form by selection contstrained by physics.

There is no assigned text for this course. We use original scientific papers as our sources and these papers will be assigned in lecture as we go. For each topic (animal or plant situation) we ask you to read a relevant scientific paper, which naturally contains 'more than you want to know'. You address just those parts of the paper needed to understand the basic 'working' of the structures involved: you make the basic model your own.

Books by Ennos, by Vogel, by Gordon and others (on reserve) should be treated as important references. If you need insight into what is meant by Newton 's Law of acceleration, composite material, Reynolds number or Hooke's Law, etc., consult these books . Of course one may also (cautiously) consult the web. (I do trust Wikipedia.) The approach is to try to understand specific animal and plant examples: the jump of a locust, the swimming of a fish, the dispersal of spores etc., and to incorporate just those parts of mechanics (physics) needed for understanding. Many topics in the course have to do with locomotion, the forces in play when an organism moves in relation to solids liquids or gases: crawls through sand or soil, jumps or flies through air, swims in lakes and oceans, hangs on in surf or in a gale, disperses seeds or spores on the wind, etc.

There is a modest acoustic bias to the content of BIO 325, arising out of the professor's research interest in animal sound signals. Bioacoustics can easily be considered a subset of Biomechanics: how animals listen and call, the evolution of ears and sound generators constrained by the physics of sound. Examples in lecture and lab sometimes involve structure adapted for the making of sound signals.

Don't be frightened away by 'mechanics'. "Solid mechanics ... studies the behavior of solid materials, especially their motion and deformation under the action of forces..." (Wiki). Fluid mechanics "studies the mechanics of fluids [air, water] and the forces on them" (Wiki). These solid and fluid force situations may be static or dynamic. This subject matter is surely challenging, but BIO325 is not aiming to train engineers. The intent is modest insight using intuitive simpler models, with a minimum of mathematics and a maximum of morphology.

Approach with curiosity. You should puzzle at body parts. Study an organ, dissect it, if possible watch it working/behaving. Even experiment with it. Observe and describe form: shape, symmetry, stiffness, colour, transparency, texture, etc. Then ask the linked evolutionary questions: why might natural (or sexual) selection have favoured this particular form, these particular features? Imagine it as it isn't : if the feature had some other form would it work as well? Most of the time most people are (mostly) devoid of curiosity: they don't puzzle, they accept. A central goal of BIO 325 is to turn you into a confirmed form puzzler. Most structural features of an animal have an evolutionary history and if you wonder about structures you may gain some insight into that history.

D'Arcy Thompson and the hollow bones

As an example of body-part form puzzling, which also introduces you to the founder of biomechanics, D'Arcy Thompson, consider: The I girder's solid of revolution (D'Arcy Thompson p. 223, 225, 226…). In his readable book 'On Growth and Form' he explains the adaptiveness of tubular bones.

Imagine examining a vertebrate skeleton wired together, on display in a museum, a dinosaur perhaps. The hind leg bones are really huge and they have (they 'had' before extinction) behaviour: e.g., the femur pivots against the tibia and fibula during extension and flexion. Muscles and tendons (usually missing from the display) hold these bones 'stacked' into a pillar that supports the animal's weight. There are many structural features associated with the hind limbs we could ask about, but let's just take one to 'puzzle': as dissection with a saw would show, the long bones are hollow. Why hollow? Imagine them as they aren't: wouldn't they be stronger solid? Surely they could be of smaller dimension if the same mass of bone material was present but solid. Is there anything adaptive about the long bones of vertebrates being a tube or cylinder of bone?

D'Arcy Thompson answering this question:"The case of a loaded beam is a familiar one…when the beam is loaded in the middle and supported at both ends, it tends to be bent into an arc, in which condition its lower fibres are being stretched, or are undergoing a tensile stress, while its upper fibres are undergoing compression. It follows that in some intermediate layer there is a 'neutral zone', where the fibres of the wood are subject to no stress of either kind.

"When the engineer constructs an iron or steel girder, to take the place of the primitive wooden beam… we know he saves weight and economizes material by leaving out as far as possible all the middle portion, all the parts in the neighbourhood of the 'neutral zone' and in doing so he reduces his girder to an upper and lower 'flange', connected together by a 'web', the whole resembling in cross-section, an I.

But it is obvious that, if the strains in the two flanges are to be equal as well as opposite*, and if the material be such as cast-iron or wrought iron, one or other flange must be made much thicker than the other in order that they may be equally strong; and if at times the two flanges have, as it were, to change places, or play each other's parts, then there must be introduced a margin of safety by making both flanges thick enough to meet that kind of stress in regard to which the material happens to be weakest. There is great economy, then, in any material which is, as nearly as possible, equally strong in both ways; and so we see that, from the engineer's or contractor's point of view, bone is a good and suitable material for purposes of construction."

[*this has something to do with effectiveness of iron in compression being different from its effectiveness in tension]

"The I or H girder or rail is designed to resist bending in one particular direction, but if, as in a tall pillar, it be necessary to resist bending in all directions alike, it is obvious that the tubular or cylindrical construction best meets the case; for it is plain that this hollow tubular pillar is but the I-girder turned round every way, in a 'solid of revolution', so that on any two opposite sides compression and tension are equally met and resisted, and there is now no need for any substance at all in the way of web or 'filling' within the hollow core of the tube. And it is not only in the supporting pillar that such a construction is useful; it is appropriate in every case where stiffness is required, where bending has to be resisted.

A sheet of paper becomes a stiff rod when you roll it up, and hollow tubes of thin bent wood withstand powerful thrusts in aeroplane construction. The long bone of a bird's wing has little or no weight to carry, but it has to withstand powerful bending-moments; and in the arm-bone of a long-winged bird, such as an albatross, we see the tubular construction manifested in its perfection, the bony substance being reduced to a thin, perfectly cylindrical, and almost empty shell. The quill of the bird's feather, the hollow shaft of a reed, the thin tube of the wheat-straw bearing its heavy burden in the ear, are all illustrations which Galileo used in his account of this mechanical principle…

"The same principle is beautifully shown in the hollow body and tubular limbs of an insect or a crustacean [Arthropoda]; and these complicated and elaborately jointed structures have doubtless many constructional lessons to teach us…"

This drawn-out example from D'Arcy Thompson incorporates the essence of how we try to approach the adaptive consequence of body parts in BIO325: observe and describe, investigate behaviour, ask why, imagine it as it isn't. And also: compare. Different species are like different 'experiments' run under different conditions leading to different structural adaptive ends. Some animals have legs designed to run, some have legs designed to bear weight. Comparing is one way of testing hypotheses.

Using the web but holding on to reality in lab

The digital 'age' has given us picture-diversity overload. The web offers expanses of visual 'virtual' exposure to organisms, both stills and videos. Use this of course, to clarify the structures mentioned in the course. But I would argue real experience is preferable to a picture (nobody normal prefers a virtual friend over a real one). 'Real' is why it still matters to study animals and plants in labs. To hear a frog on an understorey Heliconia leaf, puffing out his round throat sac as he calls in the rainforest night, to scuba below a whale shark or among clouds of schooling fish on a coral reef and be pursued fearlessly by a 4- inch bicolour damselfish defending his territory, etc. Reality is very important – the experience of reality is different. BIO325 labs aim at modest reality: in the lab we study and examine a real body part. It would be better reality of course if it actually were a walk in a rainforest or a live whale in the lab -- but we do what we can. Real preserved creatures get studied which intensifies experience and insight.

Drawing is an important part of the labs. But when it is so easy to take a picture why draw? Because drawing forces you to look – really look and see the part under study. By trying to capture shape manually you are helped to understand how it might transmit force.

Lastly you should make yourself increasingly comfortable with the names given to larger groupings of animals and plants, i.e., grow your taxonomic vocabulary. You already know the common names of a great number of organisms: lions, tigers and bears among them. But you should broaden your understanding of how these 'common names' get grouped together by learning taxonomic names such as cetacean, chiropteran, ungulate, angiosperm (flowering plant) etc. It's important to know that a lion, tiger and a bear are all vertebrates and that they are not arthropods, and that both Vertebrata and Arthropoda etc. are metameric. You should know that a dandelion is a flowering plant that differs from a basidomycete by having seeds not spores, etc. Theoretically some Introductory Biology course has already taken care of these taxonomic needs. But everyone's taxonomic vocabulary can grow and the web offers an excellent means of reminder.


Ennos, Roland 2012. Solid Biomechanics. Princeton Univ. Press, Princeton, N.J.

Thompson, D'Arcy 1961. On Growth and Form. Cambridge Univ. Press, London. Abridged edition Bonner, J.T. (Ed.)

Gordon, J.E. 1978. Structures of Why Things Don't Fall Down. Penguin Books, England.

Gordon, J.E. 1976. The New Science of Strong Materials. Princeton Science Library, Princeton Univ. Press, Princeton, N.J.

Marking Scheme

Midterm test (in lecture February 3) . . . . . . 10%
Labwork (drawings, quizzes) first half. . . . . .5%
Labwork Bellringer first half . . . . . . . . . . . . 10%
Labwork (drawings, quizzes) second half. . . 5%
Labwork Bellringer overall . . . . . . . . . . . . . 20%
Final Exam . . . . . . . . . . . . . . . . . . . . . . . . . 50%