The fundamental problem with terrestrial locomotion is that tetrapods are not buoyant in air like fish are in water. Consequently, we need to have a musculoskeletal and behavioral design that can support our weight. A bigger problem than weight support is how to deal with the transfer of energy when our body impacts the ground when we walk, run, jump, dance, fall, etc. This kinetic energy (KE) is eqal to 0.5MV^2, where M is mass and V is the velocity of the body part at impact, and the ^2 is V raised to the second power (or squared). If KE is greater than what the skeleton can absorb and release, the result is a broken body. Read this essay by JBS Haldane and think about these two sentences "You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes." Here is an explanation why.
Small, slow tetrapods like red backed salamanders do not need a musculoskeletal design to deal with the transfer of huge amounts of energy. But much of the history of tetrapods in many different lineages is a history of increasing size and speed and these animals need mechanisms to absorb and release this energy.
The primitive condition for tetrapods is a sprawling posture, in which the stylopodal segment of the limb (humerus or femur) points to the side of the body and the zeugopodal segment (radius/ulna or tibia/fibula) is at right angles to this and points to the ground. This is ok if you are a small and/or slow animal like a redbacked salamander or a marine iguana but it places huge bending loads on the limbs if you are large and fast. Consequently, larger, faster tetrapods tend to have a much more upright posture, in which the stylopodal segment is rotated under the body. Dinosaurs and mammals have very upright postures. Some lizards and especially crocodylians have various levels of semi-upright posture.
Terrestrial locomotion involves swinging a limb from some caudal position to some cranial position. The distance swung is the stride length and posture constrains the way animals swing this limb and increase stride length. In sprawling gaits, stride length is a function of three distinct movements: (1) lateral axial undulation, (2) rotation at the shoulder and hip, and (3) rotation of the humerus or femur about their long axis. In upright gaits, stride length is a function of (1) dorsoventral axial undulation and (2) rotation at the shoulder or hip. Really fast mammals have a flexible back (allowed by the shapes of the intervertebral joints and the material disign of the ligaments) that allows large dorsoventral extension and flexion. The cheetah is the posterboy for this movement but I don't have a movie of this. Here is a pretty good example from a greyhound.
In general, a single gait may not be optimal for moving at different speeds and many animals change gaits to move at higher speeds. For example, many groups of lizards use a bipedal gait to run. This bipedal gait has allowed basilisk (Jesus Christ) lizards to run across water! (As the foot pushes down into the surface of the water, surface tension allows a large dimple to develop. As long as this dimple doesn't collapse on itself, the water provides enough resistance to act like a solid, but very compliant, surface. A popular question in mammal biology has been "why do mammals change gaits?" Megan is doing a nice poster on this question.
What are the components of the skeleton and how does the design of these components influence their function?
The skeleton is composed of tendon, ligament, cartilage and bone.
Tendon is high in collagen which gives it good tensile strength
cartilage is high in water and proteoglycans. The proteoglycan ground substance holds the water because it is hydrophilic. It is the water that makes cartilage stiff in compression, just like it is the water in a hot water bottle or a very full water baloon that makes these only marginally compressable. A sponge also holds water but is still very compressable because compressing it simply squeezes the water out. Unlike a sponge, compression of cartilage doesn't squeeze out the water because of the bonding with the proteoglycans.
bone has a large amount of mineral and a moderate amount of collagen. Since the mineral gives bone great compressive strength, why isn't bone more mineralized? The answer is that highly mineralized bone is brittle - that is, it fractures with very little energy input. The collagen makes the bone much more tough, or resistant to fracturing.
stiff - a stiff material deforms very little when loaded. The opposite is compliant. Steel is stiff while bubble gum is compliant.brittle - a brittle material breaks with very little energy input. The opposite is tough. Chalk is stiff but brittle. Kevlar is tough.
So the composition of the femur and other skeletal structures differs among tetrapods depending on that element is typically loaded (remember, we use the term "load" when we say that a pressure (or force) is being exerted on an object).
Interestingly, repeated loading of a bone seems to weaken it, which is bad if you are a large, fast, active tetrapod. Consequently, fast, active tetrapods (mammals and birds) are constantly remodeling their bone, that is, osteoclasts are removing bone matrix and osteoblasts are laying down new bone matrix. This remodeled bone results in haversian systems (remodeled, concentric columns of bone with a central artery). Haversian bone in dinosaurs (pic1, pic2) suggest high, non reptile-like, activity in these animals.
The essay by JBS Haldane is good reading but this is Mandatory Reading: Michael LaBarbera's The Strange Laboratory of Dr. LaBarbera, a witty, technically accurate account of the effects of scaling that was written for the University of Chicago alumni magazine. It goes into non-vertebrate things since LaBarbera works on invertebrates but he discusses most of the things I talked about in lecture.
One good strategy for being fast is having longer limbs since this increases stride length and speed is stride length * frequency (of limb oscillation). But longer limbs are more likely to break unless the cross-sectional area also increases and a major question in comparative vertebrate morphology is, how much should limb length and cross-sectional area increase in size as animals get bigger. That is, how do length, L, and area, A, scale with mass, M? Let's focus on Area. As tetrapods get bigger, their mass increases and it is this mass (or the energy associated with this mass) that loads the bones and causes them to break. If bones scale isometrically, that is, they stay the same shape regardless of size, then the bones of large tetrapods have to support relatively more mass, per cross sectional area of bone, than small tetrapods. Go here to see why. So we might expect that bigger tetrapods would have relatively larger cross-sectional areas (that is, Area scales with positive allometry) to support their weight. In mammals, at least, this isn't true, bone dimensions seem to scale isometrically, at least between mouse and horse size animals (really large mammals like elephants do have disproportionately large bone dimensions).
So it would seem that small mammals are either really overdesigned (that is their bones have large safety factors) or large mammals are underdesigned and will die off any moment. But if we look at mammals we see that the posture of small mammals (crouched but not sprawling as in salamanders) and large mammals (upright) is very different and this loads the skeleton very differently. That is, the effective mechanical advantage (EMA) of their limb design is larger in large mammals because of their upright posture. The strain on the bones will be dependendent on this EMA. Bigger mammals should have larger strains becuase of their relatively skinny bones but the bigger EMA reduces this. In other words, it appears that strains are relatively constant across mammals from mouse to horse.
Think of a column whose length, L, is 10 cm and has a cross-sectional radius of 1 cm. Its cross sectional area, A, is 2*pi*1 = 6.28 cm^2. Its volume is L*A=62.8 cm^3. Give the density of the material 1g/cm^3. The mass then is 62.8 g. The mass/area ratio is 10. Now make the bone twice as long and the cross-sectional radius twice as long, so the bone stays the same shape (this is called isometric scaling). The new cross-sectional area is 2*pi*2=12.56 cm^2 and the new volume is 12.56cm^2 * 20 cm = 251.2 cm^3 and the new mass is 251.2 g. What is the new mass/area ratio? 251.2/12.56 = 20. So the mass/area ratio has increased by a factor of 2, the same as the lengths, in other words M/A is proportional to L.
KE=0.5MV^2. The mass in the equation is not so important, initially. Its the V^2. There are two forces on a falling object: its weight, which makes it fall faster and faster and drag, which makes it fall slower and slower. Weight is constant because its just mass x gravity and both of these are constant. Drag is proportional to V^2, and so is zero at the start of the fall but increases pretty quickly. At some point, Drag catches up to Weight and the object reaches its terminal velocity; it is still falling but at a constant speed (instead of falling faster and faster). Drag is proportional to area while Weight is proportional to volume. Since Volume/Area ratios get bigger as objects get bigger (see above), larger objects have to travel relatively faster to reach terminal velocity. So big animals have even bigger terminal velocities. And since KE is proportional to V^2, big, falling animals have really, really, big KE. When a horse reaches the bottome of a mine shaft, the KE has to go somewhere. Most of it goes into exploding the horse.
