Skeletons and levers

Every animal that walks, runs, swims or flies is a machine built from three kinds of part: bones that hold their shape, joints that let them turn, and muscles that supply the force. Put them together and you get a set of levers. Once you can read a limb as a lever, a cheetah's leg, a mole's paw and your own arm all start to make sense.

Muscles only pull. A muscle gets shorter when it is switched on, and that is all it can do. It cannot push. To move a joint in both directions, the body uses antagonist pairs: two muscles on opposite sides of a joint. In your upper arm the biceps bends the elbow and the triceps straightens it. When one pulls, the other relaxes.

A muscle is attached to bone by a tendon, a tough cord of fibres. When the muscle shortens it pulls the tendon, the tendon pulls the bone, and the bone turns about the joint.

The lever rule. A turning effect is called a moment: force multiplied by its perpendicular distance from the joint. A limb that is holding still has equal and opposite moments:

F_muscle × d_muscle = F_load × d_load

The mechanical advantage is MA = d_muscle / d_load. Most muscles attach very close to the joint, so d_muscle is small and MA is less than 1. That means the muscle must pull harder than the load it holds.

Worked example (simplified). Hold a 2 kg bag in your hand with your forearm level. The load is 2 kg × 9.81 m/s² ≈ 19.6 N. Assume the biceps pulls at 4 cm from the elbow and the bag is 32 cm from the elbow. Then F_muscle = 19.6 N × 0.32 m / 0.04 m ≈ 157 N. The muscle pulls about eight times the weight of the bag. (We ignored the weight of the forearm itself, so a real muscle pulls a little more.)

What you give up and what you gain. The same short attachment that costs force buys speed and range. When the biceps shortens by 1 cm, the hand moves 8 cm. The hand is eight times farther from the elbow than the tendon is, so it sweeps eight times as far, in the same time, eight times as fast.

So animals face a trade-off. A limb with a short muscle arm and a long load arm is fast but weak. A limb with a long muscle arm and a short load arm is slow but strong. Evolution tunes this ratio for the job:

• A runner such as a horse or a gazelle has a long, light lower leg. The foot sweeps a long way for every bit of muscle shortening: speed.
• A digger such as a mole or an armadillo has a long lever for the muscle (a long bony projection at the elbow, where the big triceps attaches) and short, stout bones in the paw. It trades range for force.

Same plan, different jobs. Look inside a human arm, a bat's wing, a whale's flipper and a horse's leg. In each you find the same sequence of bones: one long bone in the upper limb (the humerus), two in the lower (radius and ulna), small wrist bones, and bones for the hand and fingers. This is the pentadactyl limb ('five-fingered'). The details differ: the horse has one long toe, the bat has very long fingers, the whale's fingers are inside a flipper. Biologists call bones that share an origin, whatever their job, homologous structures. They are evidence that these animals descend from a common ancestor.

Be careful with a look-alike idea. A bird's wing and an insect's wing do the same job, but they are built from completely different parts. They are analogous, not homologous.