## Saturday, 7 November 2009

### Walking machines III: the abiological ones

A while ago, I discussed walking machines, and found that most inventors opted for stability by designing six-legged machines. There was one design that really resembled an animal in the way it moved. That was Big Dog, a four legged machine designed for military purposes. The reason it looks so biological, in my opinion, is not that it has four legs, but that it obviously has a very flexible control to allow it to cope with uneven terrain, a slipping leg, and even an unkind human 'master' that kicks the poor beast, eh, robot.

In other words, neural control is probably the prime difference between animal locomotion and man-made machinery. 'Control' goes much further than just standing upright or thinking of where you are going. It also affects leg design to a very important degree. Have a look at the following graph.

This is the result of one of my Matlab programs to animate fairly simple legs. First suppose that a leg is suspended, so when it moves its hip will stay in place and the foot will described a movement in the air. The blue dots show 100 points of just such a cycle: in this case, 50 points describe how the foot moves forward (to the left) through the air, and the bottom 50 points describe the part where the foot is supposed to go over the ground. In that section, the foot has to move the exact same distance from dot to dot, and the movement should be in a perfect straight line (anyway, if you do it this way the animation is much easier). The brown lines show a variety of ways how you could position a leg with just three 'bones' in it (thigh, leg and ankles) to link up the same hip and foot positions. Obviously, there is an infinite choice here, and in biology the nervous system decides on the best one, taking into account anatomy, gravity, lengths of bones, etc.

If you haven't got a brain, such as holds for mechanical designs, but you want a walking leg nevertheless, you will have to find a way to get the leg to move through a similar movement arc as shown in the figure above. In short, the degrees of freedom a nervous system can easily deal with must be abolished altogether. The trick is therefore to start with a defined movement provided by a motor, such as a rotary movement, and to devise a system of links and levers to end up with a foot moving though a suitable path. Some people actually solved that problem. Let's have a look.

One of the first must be the Russian engineer Chebishev, brought to my attention by Pavel Volkov (thanks Pavel!). Pavel also pointed me towards the video shown above, an animation of how the system was supposed to work. Here it is in its YouTube home if you prefer that. I have no idea of how this engine was supposed to be powered.

The impressive machine ambling along on the video above is a strandbeest. Theo Jansen's 'strandbeesten' (which is Dutch for 'beach beasts') must be the most famous of this type of walking machine. His designs are marvels of engineering as artistic wonders as well. They have to be seen to be believed (before anyone asks, no, I have never seen them with my own eyes, which is something I should rectify one day).

Personally, I have found that I had to watch it, and others like it, quite a few times before I began to understand how the legs move. Apparently Mr Jansen made use of an evolutionary approach to work towards the optimal proportions of all the struts and links that make the legs behave as necessary. If you type 'Jansen linkage' into Google, you will find that many people are equally fascinated, so the 'Jansen linkage' seems, like any good meme, to be spreading and evolving. If you wish to se it in more detail, have a look at this site, where you can even play with design to see if you can improve the output. His devices have been copied in wood, cardboard, and other materials. There are Lego examples as well.

The one shown above is made from wood. It has a very clever gear system that ensures that only one leg is off the ground at any time. The YouTube text says that this is a stop-motion animation. Its website is here.

There are other approaches as well, such as the Klann linkage. It results in a more spidery walk, as can be seen by a direct comparison of the two linkage systems. This system has spawned several large mechanised walkers, to be found through Google or through the Klann site.

Do these designs lend themselves to 'biologification'? In other words, could I or someone else use them for a fictional animal? I can think of no reason why it should be impossible to have a pantograph-like leg. But why would you want a leg that can describe only one movement? All adaptability and all flexibility are thrown out of the window. If you throw in a fairly decent nervous system instead, you can solve the walking problem and do much more besides. So no, I do not think that this is a mechanical design that would work well in biology.

But that doesn't stop me admiring and enjoying the ingenuity of designs such as the strandbeesten!

j. w. bjerk said...

These are cool.

I agree that a life-form is much better off with legs that it can use to do useful things like change direction, or walk over bumps.

But i think one could find specific edge cases where something like these might be practical.

Like what about seed pods in an environment with negligible wind, and perhaps no animals. Simple mechanical "legs" might carry it beyond the parent plant... powered by some pressurized gas perhaps? It wouldn't matter than most get stuck and fall over.

It does seem far fetched, but so does earth life too sometimes.

Anonymous said...

Unless, of course, said "organisms" are highly derived robots. But then again there is no reason why one could not just program a computer brain to calculate all the motions.

Sigmund Nastrazzurro said...

I think there might actually be one or two 'pantograph'style skeletal constructions in nature, in fishes' jaws and perhaps some bird wings. I would have to find proof of that though...

Anonymous: quite right. The 'Big Dog' is a good example of a robot with a 'nervous system'. What I meant was the type of mechanical device that is still the norm: less of a nervous system than a worm...