camels

A biped (such as yourself) usually has no trouble in putting his/her best foot forward. But imagine for a moment you were a quadruped; wouldn't there be two best feet and which two would they be?

Interest in animal gaits started in earnest in 1872, with a wager of $25,000 by a horse breeder named Leyland Stanford. He maintained that at certain times a horse had all its feet off the ground. To settle the question he employed Edweard Muybridge to photograph animals in motion. The series of photographs Muybridge took, with the use of trip wires, were so successful that by 1879 they were shown throughout the world. People began to question whether all four legged animals walk, jog or run in the same way. Take a camel; it does not trot but paces. A pace is quite different from a trot. It has particular symmetries, which a trot doesn't have: The two legs on the right are synchronised as are the two on the left. While the pair on the right are on the ground the pair on the left are off the ground and vice versa. So why do different animals have different gaits? The reasons are biological, but the best way to understand them is through maths. Let us start at the beginning, with the fact that each leg oscillates backwards and forwards. Neural networks in the spinal cord produce such rhythmical muscle activity.
In fact it is very similar to the motion of a pendulum. The pendulum bob swings backwards and forwards, as does the leg. It is said to oscillate. Each of the legs of an animal oscillates too. So we can model 4 legs of an animal as four oscillators.
But are the oscillators independent of each other? Symmetries in the motion imply that at least two are synchronised. So say the two oscillators corresponding to the legs on the right of the animal do the same thing. That means they must be linked or coupled together. This sounds good until we remember that any animal has more than one type of gait. A horse can walk, trot, canter and gallop. Do all these types of locomotion have the same symmetries? No, usually an increase in speed is associated with a loss of symmetry. So the couplings between the oscillators must change as the animal speeds up. In fact it is enough to allow the strength of the couplings to vary. Then, as if to justify our model, the theory of oscillators successfully predicts the change from trot to gallop etc. So a camel would find it hard to trot as it involves couplings probably not present in its neural networks. But it might be taught an asymmetrical gait like a canter.