## Sunday, 18 October 2009

### Odd walkers

Even the title is odd! (And yes, that was an intended pun.) I cannot help but be fascinated by how animals walk, hop or otherwise move around. This time we go for a somewhat bizarre approach: is it possible to walk with odd numbers of legs, such as three or five?

Why not? To obtain a first look of how a pentapod (five legged) animal might possibly look like, I adapted the Matlab program I had used to animate the octapods on my site. (you will find them on my site: go to it here, chose the yellow 'land' icon, and then go to the 'walking with...' icon). It was simple job to change the number of legs to five. Obviously, there is gait to consider: what should the phase differences between the various legs be? The first choice would be to have a 'skipped walk' , in which one leg is at 0 degrees (the same as 360), and the others are at 72, 144, 216 and 288 degrees. It's just a question of assigning a phase to a particular leg. Anyway, there it is.

I then thought I would experiment with legs moving in pairs as well. Of course, there will be one left to move on its own, so what you get might be two pairs and a single. So here we go:

Odd? Indeed. There is an animal on Furaha with a similar gait pattern. I do not remember mentioning 'secondary bilaterally symmetrical neospidrids' before, even though they are quite common. What happened is that some spidrids, octapods and therefore without a left/right symmetry axis, started lifting some of their legs to catch prey. They used three legs for this purpose, so these three 'raptorial appendages' are an example of centaurism. This leaves them with 5 to stand on. This induced bilateral symmetry, but with the plane of symmetry going through one leg!. This leg is in the median plane, and is noticeably bigger and stronger then the others. It is the neospidrids' jumping leg, providing most of the force of its jump. The adjacent legs help with propulsion and with steering the animal while jumping. In slow walks you get a gait more or less as shown above.

You might think that no animal on Earth walks like this, but you would be wrong. True, there are no animals with five locomotory legs, but there are several using five appendages for locomotion. The following video, from YouTube, shows one. Have a look at the adult kangaroo. Moving slowly presents kangaroos with a odd problem: their legs aren't exactly designed for that, and for some reason they do not alternate the movements of their hind legs. These move in a pair, and so do the front legs. It is the tail that does the trick. Look very carefully: when the hind legs are swung forwards, the kangaroo rests on a tripod formed by its tail and the two front legs. This tripod alternates with a phase in which the tail and front legs move forwards while the animal rests on the stable area formed by the large feet. A pentapod on Earth!

And to make it even more wonderful, consider the tail. It is of course a stack of vertebrae, but it must take some strength to keep it from buckling. Isn't this an example of 'walking on tentacles', in particular the Mark II Walking Tentacle?

Now it is time to reduce the number of legs to three. Quadruped animals lose a leg if unlucky, and there are many videos to be found on the internet of dogs and cats who seem to manage quite well as three-legged animals. But I know of no animal on Earth that uses three similar legs for walking, and for once there seem to be nu Furahan alternatives either, or at least they have not been discovered yet. So I whittled down my 'octapod' design to only three legs, and introduced a phase difference of 120 degrees so the legs are not in phase. Here it comes:

Could it walk? Certainly not as shown here. This model was designed for octapods in which there are always legs on the ground, which means the legs can be placed wide apart. If you have just two legs, or three for that matter, the feet should be placed much closer to where the centre of gravity projects on the ground. Just try to walk with your feet at least 60 cm apart and see where that lands you. I could adapt the program, and may, but that will take time.

The only recourse left are the worlds of science fiction and of mechanics. In SF a 'tripod walk' can only be associated with one thing: Well's War of the Worlds, and the tripod mechanical marvels in which the Martians strode around eradicating anything human. For good engineers they were remarkably poor biologists, but never mind that. So how did the tripods actually walk? Somewhat to my surprise I could not easily find clips of the Spielberg movie. Why is this? Aren't there any? Surely Spielberg's computer people solved the problem of having them walk in a believable fashion? I did find a very entertaining video made by 'mrgrotey' of a tripod as shown in Jeff Wayne's adaptation of War of the Worlds. Its original location on YouTube is here, but there is a more elaborate website as well. Have a look:

Before the tripod starts to dance, you will see it walk. Note that it moves with 120 degree phase differences between its legs. Is that they only way to move with three legs? Not really. You could have two legs moving as a pai with the other one as the odd man out, or have all of them move together. Someone has already worked that out. On Peter Balch' site I found three animation showing just that, and here I will only show one, so you will be tempted to pay his site a closer look. The support diagrams are very nicely done.

Note that the feet are planted very close to the midline, so there should be no problems with keeling over, or at least none that cannot be solved by a suitable brain, biological or otherwise. It seems to be the only design in which the legs are not attached to the body in a triangular pattern but along a line.

Finally, you may wonder whether someone has built a machine that walks on there legs. In fact, one such has been shown earlier on this blog, but I have found another. Here is where I found it. Unfortunately, I can't seem to copy it for you here, so you should follow the link. . You can see that the designer chose to have the legs wide apart, so for the beast not to fall it has to move the projection of its centre of gravity close to the legs that remain on the ground. Only then can it afford to move the third leg. The only other solution would be to actually build something like the tripod animation above, but I am certain that taking care of what an animal brain does naturally (sensing, adapting and correcting) is extraordinarily difficult to do with a computer. So the little machine shown through the link is quite brilliant: it is a walking tripod machine!

Anonymous said...

This helps confirm the form of locomotion for the life of my own project.

Unknown said...

Hi Anonymous,

I remember that you wrote about a tripod design. If I may quote you "It supported the majority of its weight on its front two legs, and had a third in the back. When it ran, it used this third leg to push itself forward, leading to its movement resembling a galloping mammal, or maybe a weird rabbit. When it walked, the third leg only took a half-step for each full step of the forelimb, allowing the hind limb to keep up."

The first statement sounds like a 'bound', but could you say more about the half-step of the third leg? Do you have drawings or anything similar?

Anonymous said...

Maybe you're thinking of another 'Anonymous'. I don't remember writing that...

j. w. bjerk said...

Wow, that tripod robot looks extremely awkward.

Of course, bipod robots generally look pretty awkward too, so it doesn't necessarily condemn that tripod gait.

BTW, i really appreciate this blog. It's not very easy to find theoretically biology that tries to make mechanical sense.

sidney-the-aussiedude said...

Wow, never realized the bizarre implications of a kangaroo's unique gait before! Having lived in Australia most my life and seeing them all the time, it's easy to forget just how much evolution messed around with this familiar marsupial.