Sunday 13 January 2013

Monopods: getting off on the wrong foot?

How many legs can animals have? That is a subject that has been discussed more than once in this blog and its comments. A first gross division of 'leggedness' could be whether the number of legs is even or odd (for odd numbers see here and here), and a second one whether the overall pattern is one of radial or bilateral symmetry. Last week Petr commented on the Xenohox Gazelle, an animal on the doubly odd side of this classification, in that in combines a radial design with an odd number of legs. For those of you who are well-versed in such things, the difference between the radial design of animals such as my tetropters and the Xenohox gazelle is that the axis of symmetry is vertical in the former and horizontal in the latter.

 Fragment from The Future is Wild

Getting back to the topic at hand, Petr asked what I thought of animals with just one leg. I realised that I had omitted walking with one leg or with no legs at all (whether the latter is possible may be a matter of semantics, but there are aspects of moving without legs that resemble those of true walking). Are there many such beasts in speculative fiction? The first one to come to mind is the 'desert hopper', an animal evolved from snails in 'The future is wild'. The DVD is easily available. There is also the Eponan springcroc; there are undoubtedly more.

What should be the proper term for this mode of locomotion? There is a choice between  Greek and Latin equivalents. Examples are the Greek 'tetrapod' and the Latin 'quadruped'. For one-leggers, the words could be 'uniped' (Latin) or 'monopod' (Greek). I prefer the rhythm of the Greek one, so let's stick to that one.      

Monopods have biomechanical problems. The first can be demonstrated easily by hopping on one leg. You will it fatiguing. One reason, but not a major one, is that one set of muscles does the work normally done by two. Fair enough, but the bigger problem has gravity as its cause. Any walk cycle has a stance phase in which the leg pushes against the ground and a swing phase in which thee leg swings forwards, free from the ground. During that swing phase the body will of course fall down, unless another leg supports it. Monopod animals, not having another leg, must deal with the tendency of the body to fall. Do not underestimate this: a normal human biped walk cycle lasts about 1 second, and each leg is off the ground for about 40% of the cycle, meaning about 0.4 seconds. In that time the other leg s supports the body, but what if there wasn't one? Under Earth gravity a time of 0.4 seconds is long enough time to fall 78 cm, much too far to catch up easily with the next step. That unsupported phase should therefore be as short as possible: for 03 second the fall will be 44 cm, for 0.2 seconds it will be 20 cm, and for 0.1 second it will be a mere 5 cm.

During running there are periods in which no leg touches the ground, resembling the monopod problem. Still, our bodies do not move down a long way during the unsupported phase: the unsupported phase does not last long because we do have two legs and because the rate of cycling is much higher than during walking; also we actually jump up enough to combat the falling tendency.
Let's turn the biped human into a monopod human. If you keep the leg moving at the same rate as if you were walking with two legs, the unsupported phase will be about 0.4 seconds as shown above. The only way not to fall 80 cm during that time would be to jump up in each step. This is a sizable jump, costing lots of energy. Of course, speeding up the rate of movement helps, but that calls for high acceleration and deceleration, also costing lots of energy. There is probably an optimal balance in there, minimizing the energy for forward movement. The balance would, as holds for any gait with any number of legs, depend on speed. Monopod animals might not be good at low speeds, because gravity does not allow for a slow jump.

A monopod animal is like a human on a pogo stick. 'Pogoing' (we need a verb) would cost less on a low-gravity world, so perhaps they should be sought there. There is probably an optimal mass for pogoing animals. Jumping is not a good idea for animals with a large mass, because they then need disproportionately heavy skeletons. There would be lower limits too: you might think that falling is irrelevant for animals as small as insects, as they would not hurt themselves much by doing so. Then again, the short distance means that there is no time to break the fall, and whatever your size, during a fall control of the body is lost, never a good idea.

Click to enlarge; copyright Gert van Dijk
Another big problem for a monopod would be stability, as shown above. Standing on three legs or more is easy, because there is little skill involved in holding the centre of gravity over the support area on the ground, defined by the points where the feet touch the ground. Bipeds can only stand upright with a sophisticated neural control system. For a monopod such as 'Unipes disneyi', on the left,  the support area is small, requiring an even more sophisticated control system. Sideways forces would pose a very large problem for monopods. Wind is more likely to blow very small animals over than larger ones, and for insects and the like it pays to splay their legs: it produces a large support area. So, alien monopods perhaps should probably not live on planets with very dense atmospheres. The obvious way to solve that problem would be to have long toes sticking out in all directions: the middle monopod in the illustration. They would have to be very strong to counter a tendency of the body to move. In this respect the toes would probably be inferior to legs that stick out towards the same points on the ground but starting from the body, shown on the right. But if the starting point is one leg, the toes would probably be the answer. I do wonder about the body scheme of an animal with just one leg; would that preclude the presence of other paired limbs or organs?        

Finally, having one leg results in no redundancy whatsoever: a monopod with a leg injury is probably doomed, whereas a biped might limp away, and a millipede would simply continue on its way.

Click to enlarge; copyright Gert van Dijk
Are there workarounds? I am tempted to think so. Take the large-toed animal at the left above and make it stand on the tips of its toes. Evolve it a bit to get the animal at the right: the toes get bigger and the upper part of the leg shrinks. Now that animal could just swing one toe forwards while keeping the other ones on the ground. By repeating this movement for the other toes it would no longer need to jump up. But what that does, obviously, is upgrading the status of the toes to that of legs, and then the animal is no longer a monopod but a secondary tetrapod. And a very silly one at that.   


Petr said...

Wow this is unexpected, but very insightful! Thank you for taking the time to discuss this! =)

Luciano N. Ribeiro said...

Very interesting post. I think to understand monopods we could perhaps look at bipeds which move with the two limbs simultaneously (kangaroos and passerine birds and others). They pretty much have the same set of advantages and disadvantages, minus the stability problem. Overall I think the Desert Hopper is a pretty plausible beastie. Hoping my disproportionate love for snails is not clouding my judgement XD

Petr said...

@Luciano - I beg to differ on the plausibility of the desert hopper. it's a snail living in the desert, and it somehow manages to be quite large and hop without having any bones whatsoever. I think the creators of TFIW put it there as a joke. ;)

Sigmund Nastrazzurro said...

Luciano & Petr: You are right in that kangaroos and the like prove that hopping by itself is not necessarily inferior to other gaits (in fact, the movement need not even cost more in energy terms). Of course, the stability issue remains.
As for how plausible the desert hoppers are, I too have my doubts about the internal arrangement of the foot. Without a proper skeleton, you might consider a purely muscular design (a 'hydrostat'), or perhaps there is a stiff but elastic plate in there, serving as a spring. As far as I remember no such information was provided. I also do not know enough about snail biochemistry to determine whether they could afford such a lifestyle. But purely from a design point of view I have always liked them.

Jan said...

It is interesting how many fictional animals walk on widely splitted fingers, but it seems to me a bit improbable. What if monopod rests on the front part of the body and there gradually evolves something like legs, similar to flamboyant cuttlefish?

kopout said...

What If the Monopod had some kind of supports for when it came down? say for example it has an exoskeleton and the underside has long spikes that hold the body off the ground while the single leg moves into position to push off again?

Petr said...

@kopout - so let's say one leg in the back and two struts in the front. we've basically given this animal crutches to walk with, but then again, isn't this crutching animal basically a tripod? that's the same problem as the monopod who elevated its digits to function as four separate legs, but then the animal is no longer a monopod functionally, but a very silly tetrapod instead, just like gert said in this article =)

Now I have another wuestion for Gert:
What about bipeds with legs in tandem? I am not talking about the gyrosprinter from Expedition of which I am aware you aren't in favour of, and I share this view with you, mainly because it would never be advantageous for an originaly tetrapodal animal to fuse its forelegs and hindlegs together, but legitimately bipedal animals with legs in tandem. what are your thoughts on that? =)

I got mainly inspired by this video: where the dog seems to be coping well even though it's coping with noth being anatomically complete any more, I am guessing an animal who would be like this naturally would have even fwer problems than that dog.
On a completely unrelated note, what abour some asymetrical animals? It there was an ancetral animal with a row of legs on the belly, and its descendants would move these legs zig-zag to left and right to be more stable, can you imagine terrestrial vertebrate analogues with similar asymetrical leg arrangement? what would it look like if there were two legss on the left and three legs on the right? could that work?

Ronan said...

Honestly, the desert hopper is one of the more plausible monopods I can think of. It's derived from a critter that already has one "foot," of sorts, that needs a way of getting around fairly quickly. Hopping snails already exist today, for that matter (, and presumably evolved for similar reasons. That said, I'm not sure if the snail in the video quite qualifies as a pure monopod; instead of resting on its foot it seems to use its shell as a landing prop of sorts, so in a way it sort of functions as a serial (rather than parallel) biped.

Petr said...

@Ronan - thanks for the interesting video, but there are a few things that need to be mentionned. The snail hops in water, not in air and it's a small snail. I don't know how big the desert hopper was, but it was much much bigger than that. it stood erect on a purely muscular foot (there was no mention of any solid internal limb structure in TFIF) which is simply not possible. No "documentary" like this should be taken too seriously, it's made for the audience's amusement so they are trying to make cool creatures for the sake of looking cool and not worrying bout plausibility that much.
P.S. that was some heavy-looking shell of the desert hopper, quite an unnecessary weight IMHO, when armadillos and pangolins start to hop like kangaroos, I will consider it a needless weight which makes the hopper less efficient than if it had a smaller shell or no shell at all. ;)

Edward Ott said...

Fantastic article. may i ask what program did you use to do your pictures?

Sigmund Nastrazzurro said...

Kopout: I see what you mean: the 'crutches', as Petr calls them, would mean that the animal would not have to spend much energy in jumping up, as it would be resting passively on the crutches. For slow movements that would work. It reminds me of slow-moving kangaroos: they rest their weight on the tail and fore legs, while the giant hind legs are swung forwards. It seems awkward (but, then again, so do slow-moving kangaroos...)

Petr: legs in tandem would at least cut the 'air time' of monopods in half, but still have the disadvantage of lateral instability, compared to animals with bilateral symmetry.
As for asymmetry, that is a difficult question. Not because it would be impossible to design a gait, but because my instincts all start yelling 'No! Don't!'. Perhaps they need rewiring.

Ronan & Petr. I read TFIW again, and the desert hopper is about 30 cm high (the book says a 'foot', but feet, being anatomical units, should not be confused with measurement units ;-)
I agree that the shell seems like too heavy a burden. But make the hopper smaller, drop the shell, give it an elastic plate in its foot, and then, why not?

Edward: Thank you. I use Vue Infinite from e-on software for such simple schematic illustrations. I think that there is a free entry-level version.

Anonymous said...

What if a monopod had a tail for counter balance?

Also, have you ever heard of Wayne Barlowe's Gyrosprinter? It has only two legs (the forefront are fused as well as the back) and it sports a set of halteres to keep balance. Here's a link for more info:
I'm just curious what you think of it. I'm not sure I find it too plausible.

Anonymous said...

This was a very insightful post awesome stuff as always. You should do a post on tripeds, front and back oriented both. I'm trying to figure out if they're too awkward (esp the ones with one front leg) when moving at slower speeds.