Friday, 8 October 2010

These legs are made for walking (Legs II)

In my last post I played with some concepts about leg design, mostly concerning whether it is better to have sprawling legs or ones that function as pillars. It turned out that there is no answer that is always correct: for large animals pillars help minimise energy expenditure in the form of muscle power, and for small animals sprawling legs provide protection against wind forces, something that gets more consequential the smaller you get. Perhaps wind is also one of the reasons why small arthropods are so good at gripping surfaces tightly: I had thought that that was mainly a neat feature to cling to vertical surfaces or even to land on a ceiling, but perhaps simply keeping put where you are if there is a strong wind weighs in too. What do insects do when there is a real gale out there? Does anyone know?

There are still enough problems to play with. I took the Disneius species that had just evolved last time and decided to take its legs one step further, i.e., I tried to simplify their design some more. The reasoning was that legs largely have to move in the body direction, rendering movements in other directions less important. The result is Disneius mechanicus:

Click to enlarge; copyright Gert van Dijk

And here it is. This has taken the idea to an ultimate form: the joints in its legs rotate purely in forwards and backwards directions. Note that this would not work in real life, as the animal would not be able to turn. In real life you would want to make the feet and at least one joint higher up more adaptable.

The legs are built in a zigzag way, like those of its predecessors. Last time I discussed that avoiding bending ‘moments’ becomes easier the nearer the joints are near the centre of gravity. Mind you, zigzagging legs in which the joints zigzag inside and outside are not necessarily worse than ones that do their zigzagging forwards and backwards. The usual explanation for the anatomy of mammal legs is that ‘vertical’ is better, but just suppose you take one of D. mechanicus’ legs and turn it by 90 degrees. If its foot was directly underneath the hip joint to start with, the rotation will not change that. The joint angles do not change either. All this leads me to conclude that ‘verticality’ in limbs depends more on having straight legs than on the direction the joints zigzag in. Legs that predominantly move forward and backwards have the advantage of allowing simpler joints, and simpler joints may allow less muscle strength to control their position: a good thing. I would expect large animals with highly evolved legs to adopt forwards and backwards bending as well. A bit boring, but that is what you get with universal laws of nature.

Luckily there are enough items left that might make alien animals more alien-looking. As you can see, the fore and aft legs of D. mechanicus are exactly alike. This is not what mammal legs look like. From a mechanical point of view fore and aft leg tend to have different effects, with aft legs providing more propulsive force than front ones. Is that also the reason why mammal knees point forwards and their elbows backwards? It seems as if, starting with a newt, its upper arms were rotated backwards and its thighs forwards to turn it into a mammal with fore-aft moving legs.

Click to enlarge

Here is a picture from this site that explains just that phenomenon. It explains why the bones in the forearm are crossed while those in the leg are not. But that is just one way to look at things. In the same newt-to-mammal trip, a third large movable segment was added to the newt's two. In the front leg the shoulder blade turned into a movable segment, and in the hind leg foot bones were recruited. If you look at the result from a functional point of view, the first large movable segment is the shoulder blade in the front limb and the thigh bone in the hind limb. Both point forwards, and from that the other segments zig backwards and then forwards. That is what D. mechanicus looks like! Based on this functional view, I feel that identical front and hind legs are theoretically quite possible. Prolonged specialisation for braking and weight carrying (front legs) and propulsion (hind legs) might change some aspects, but I see no need to ‘prescribe’ the typical mammal pattern as the only feasible one.

Click to enlarge; copyright Gert van Dijk

So here is a variant (the left one) in which the upper segments starts the zigzag by pointing backwards, not forwards, as in the righthand side one. Can this work? At present I see no reason why not. Perhaps I should do some animation studies to see if any big problems come up. But if there are none, an animal could have front legs that start with a zig and hind legs that start with a zag, or vice versa. They are in the background of the image above, but a closer look follows.

Click to enlarge; copyright Gert van Dijk

And here they are: we could make up interesting leg formulae, like ‘zigzig’for an animal in which both front and hind legs start with a forwards zig (and in which the other segments follow the lead of the first segment). ‘Zagzig’ denotes an animal with a front leg starting with a backwards zag while the hind leg starts forwards. You can think of what a ‘zigzagzig’ means for yourselves.

Click to enlarge; copyright Gert van Dijk

Just for fun here is a herd of the beasties. How many zigzags should there be? I do not know. If there is a proper foot, in which many segments touch the floor, I would expect all of them to bend backwards to promote ‘rolling’ over the ground. If just one segment touches the ground, as in hoofed mammals, I have no idea. But the majority of long segments will likely zigzag.

Click to enlarge; copyright Gert van Dijk

Here is an animal with more zigzags, along with an ancestor. The giraffomorph looks weak to me. There must be an optimum number of segments to achieve good manoeuvrability and/or good speed, but I do not dare speculate on that, or at least not now. I also do not know why the scapula in mammals is not connected by joints to the vertebral column, in contrast to the hind legs. Does it have to do with shock absorption versus propulsion? Perhaps those are good subjects for later posts.


Anonymous said...

"I also do not know why the scapula in mammals is not connected by joints to the vertebral column, in contrast to the hind legs. Does it have to do with shock absorption versus propulsion?"

It largely has to do with freeing up the mammalian scapula to act as another joint in the forelimb. There isn't really a socket for a potential scapular to spinal chord to rotate in and articulate the scapula with the torso, so instead mammals just took the "floating scapula" of tetrapods to the extreme, basically just wrapping it in a bunch of muscle to hold it on and letting it shift rather freely during lovomotion.

Interestingly the hind legs of grasshoppers would be considered zigzag.

Sigmund Nastrazzurro said...

Dear Anonymous,

I once asked McNeil Alexander the same question, and he speculated that the answer might lie in tetrapods being stuck with an original design, which, if correct, implies that the design is more dependent on contingency than on optimal mechanical properties.

Personally I would not be surprised to learn that joints can evolve secondarily. Muscles can become ligaments and those can ossify. But that is speculation.

Evan Black said...

"The giraffomorph looks weak to me."

I can't remember where I got this idea, but the more joints you have in a limb the weaker it is. Smaller life forms may be able to deal with as many joints as the griffomorph exhibits, but if you're dealing with larger life then bones may fuse together or disappear or something along those lines. Could it be possible for a life form to develop a scapula like structure from the uppermost joint, attaching muscles, ligaments, etc. from the body to the next bone in the sequence?

Jonas said...

Now, something I've speculated on is how well a limb configuration would work if the upper half was supported by a long bone (like your humerus) while the lower half was made up of a column of vertebra-like units (let's say it's 5 units). I feel now that it would be ill suited for locomotion, especially at high speeds.