Odd walkers II

Last year I discussed possible gait patterns for animals that walk on an odd number of legs, including various tripod walkers. Around the same time I was contacted by a reader who asked me to help him visualise a gait design. I will not go into details, but the idea was to have an animal, the tiborou, that was to have two paired legs in front and a third unpaired leg in the midline towards the back of the animal.

At that point I thought that this would be similar to the tripod walks discussed in my post, and that all their gaits could be summed up by defining the phase differences between legs. The legs of a walking human have a phase difference of half a cycle or 180 degrees. The hind legs of a hopping kangaroo move together, so the difference is 0 degrees. Back to a tripod walk: a straightforward pattern would be to have legs at 120 degree intervals (there is an animation of that on my old post). Other 'logical' patterns would be to have two legs move together (0 degrees) while the remaining one has an 180 degree difference.

But that was not at all what the reader, Metalraptor, had in mind. He asked for something I at first found very hard to visualise. All the gaits just mentioned have one thing in common, and that is that the walking cycle lasts equally long for all legs. When you think about it, that is how all Earth animals walk, regardless of how many legs they have. The gait of the tiborou had to depart radically from this idea, by having the hind leg go through two cycles in the time it took a front leg to move through one. Now just try to see visualise that...

In the end I thought I should write a small computer programme to illustrate the gait. The following reasoning helped to define its characteristics. Instead of imagining an animal moving over the ground, imagine it staying in place and having its feet slide beneath it (as if it is walking on a treadmill). Now make a film and look at individual frames: when a leg is on the ground its foot will move a certain distance between successive frames. If two legs are on the ground at the same time, that distance between frames must be the same for all legs. If not, one foot will be slipping over the surface. This must be true for any walking gait, and so holds for the tiborou as well. So: the hind leg moves the same distance over the ground between frames as a front leg, and yet moves through two cycles while the front legs move through one. There is only one way out: short steps.

Unfortunately I did not have a handy routine for a lateral view of a leg walking cycle, so I more or less let the matter lie. But later I found out that gaits with different cycle lengths actually occur on Earth! Well, to be precise, I know of just one. I discussed it in my post on brachiation. which showed monkeys that use their tail to grip branches at twice the frequency of the arms.




That knowledge put me back on track and I wrote a rough program to show what such a gait could look like. It is shown above. Please note that the animation makes no attempt at showing feet and it is otherwise also quite unrefined. The white dots are the points where the end of legs end up during a walking cycle.



Here is the animal once more; this time it moves across the surface. That makes it easier to see that the feet of the front and hind limbs do not move relative to one another when on the ground. You can also see that the steps of the hind leg are short, both in time and distance.

Seeing that gaits in which different legs have different cycle frequencies are not just a fictional invention but also something that occurs on Earth, they probably deserves a name. Perhaps it is time for another Furahan neologism, following centaurism and cernuation: how about a 'harmonic gait'? 'Harmonic', when dealing with frequencies, is often used to describe frequencies that differ from one another by multiplying or dividing them by a whole number. That is the case here, as the hind legs moves at twice the frequency of the other ones.

Oh dear... That thought immediately suggests that there could be 'inharmonic' gaits in which different legs have different cycle frequencies, but not related through whole numbers. They probably make little biological sense, but having thought of it I cannot get rid of the concept. I am trying to visualise an animal walking with such a gait right now, and it feels like the insulation of my brain is overheating...