Sunday, 24 February 2013

Sprirally slanted spidrids

Arthropod leg design seem straightforward, but there are several aspects about them that i do not understand, so I have been trying to find out more about them. Answers prove hard to find though, and so for this post I will limit myself to just one thing: why do Earth arthropods such as crabs and scorpions often walk with their legs slanted with respect to the vertical?

Click to enlarge; copyright Gert van Dijk

This image shows my prototypical spidrid. Most joints are fairly simple with just one axis of rotation. The legs turn clockwise or anticlockwise at the joint with the vertical axis near the body; let's call that the coxa, to keep the arthropod analogue going (the word means 'hip'). The other joints simply bend and straighten the leg. The result of this simple design is that each leg operates in a vertical plane. I felt that this makes sense from a construction point of view; no slanting here.

Click to enlarge; from Wikipedia
But this wonderful image of a crab shows a different pattern: the plane in which each legs lies is heavily slanted with respect to the vertical. From a point of countering gravity this design does not seem wise, but crabs are not very large, so gravity is less a constraint than it is for animals with a larger mass. Slanting must be good for something. It makes the crab flatter while the reach of the leg is not compromised. Perhaps flattening is good for animals living in crevasses. Another possible explanation might have to do with propulsion. In your typical spidrid the propulsive force of the legs at the side comes from muscles that rotate the leg clockwise or anticlockwise with regard to the body. This joint lies far from the point where the leg exerts force on the ground, which may weaken the design. The muscles that extend and flex the leg do not help much in propulsion. But slanting the legs would mean that those same muscles can now add their force to pushing against the ground. Perhaps that is it; if so, I will have to look harder for evidence.

But instead of doing so I wondered whether slanting could work for spidrids, so I played a bit with Matlab and produced some animations. My first idea was to put an angle to the vertical axis connecting the leg to the body. Doing so would slant the leg when it rotates with respect to the body, and more so the more the leg is rotated. When the leg is just sticking out from the body it would not be slanted. What you see above is the result. As you can see, the leading and trailing legs are not rotated in a clockwise or anticlockwise direction, but 'just stick out'. They do not exhibit slanting at all. The other legs are slanted when at maximal angles, and the extension muscles in them could help push the animal forward. It looks intriguing, doesn't it?

Of course, I could not resist having the legs slant the other way, but that was probably a mistake: I do not see them providing additional propulsion this way. The spidrid is not flattened, because the leading and trailing legs still lie in a vertical plane.

If flattening is needed, all legs will have to be slanted, and that idea resulted in the spidrid above. Aas far as propulsion is concerned there may be a problem. Crabs are bilaterally symmetrical, so the left and right legs can both push against the ground in the slanted position. But spidrids have radial symmetry, and that means that legs on one side can provide an additional push while the ones on the other side do not. But I am not certain that that is what slanting is for, so perhaps it is no problem. Meanwhile, I rather like the somewhat sinister aspect of this 'spirally slanted spidrid'             


mithril said...

could also be efficiency of motion. their legs are naturally kinda slanted. as a result the muscles for up/down movement also do some of the side to side movement, which ought to help reduce the amount of energy for the walking cycle.

of course it could just be as simple as the fact crabs evolved those big pincer-claws on their front limbs, and the slanted legs ensure the front of the body is kept far enough off the ground they don't hinder movement and have a wider field of movement..

Evan Black said...

I agree that the most intuitive purpose for a "slanted" gait is probably to help with propulsion, especially for higher speeds. As a leg straightens it can help push along the ground, and if you have six to eight legs working in sequence you can probably move along at a pretty good speed.

Another possible benefit for slanted legs could be traction. A spidrid with legs in an upright angle only has so much grip on the ground, but if its legs are slanted such that their tips all angle in roughly the same way, then they effectively become cleats, preventing the spidrid from sliding in that direction. This traction could be further supplemented by developing broad or blade-like "feet" that have ridges or serrations designed for greater grip.

Spugpow said...

I think the slanted legs are mainly an adaptation to living in crevices. You see the most pronounced slanting on arthropods that live in confined spaces, like whip scorpions, cockroaches, and these crabs.

Then again, cockroaches and sally lightfoot crabs are also known for their speed, so maybe quickness emerges as a secondary trait.

Dromicosuchus said...

Speaking purely from an aesthetic point of view, I find the forward-slanted and radially-slanted spidrids most appealing; the back-slanted spidrid just looks off, somehow. Also, although I share your doubts about the efficiency of the radially-slanted spidrid's gait, I have to say that I love its appearance; it'd be fascinating to see more experimentation with that mode (a rotating gait, perhaps, such that as the spidrid moves forward its body turns around its axis of symmetry?) That also has some interesting possibilities for the evolutionary history of life on Furaha; I can imagine spidrid speciation, for example, being driven by occasional switches between right and left-handed chirality.

Sigmund Nastrazzurro said...

Mithril: I doubt that efficiency is the -whole- answer. Up-down muscles might do some of the side-to-side work, but that does not mean by itself that there is less work to do (perhaps just that those muscles have to do more work). I like the originality of the lift the front approach.

Evan: that brings up the problem of friction, another one of the topics I do not find much about: why do crabs seem to walk on 'points' instead of on 'feet' with bigger surfaces. But if crabs get away with it, so can spidrids...

Spugpow: a combination of speed and flattening then...

Dromicosuchus: I agree with your feelings, and my order of preference is absolutely the same. Now, if I could just find some evidence to keep the slant in, I will split spidrids in at least two groups: slanted and 'square' ones.

All: I checked my books on Crustacea and biomechanics, but there is nothing there regarding slanted legs. I will try to find help elsewhere...

Evan Black said...

The fact that there doesn't seem to be anything out there about the angled legs makes me wonder. On the one hand, it could be that there just aren't really scientists out there looking at crab biomechanics; on the other, I can't help but think that the lack of information suggests that there's some no-brainer explanation that we just haven't hit upon yet.

Sigmund Nastrazzurro said...

I still haven't found anything specific, but may have found the answer: many crabs live in tidal zones where they are subjected to flowing water. To keep in place they have to grab the substrate firmly, keep low and generally present a small cross section to the direction of flow, i.e. horizontally. That would explain not just the slant but the flat leg cross sections as well. When I realised this I thought "how stupid of me!".

If true, crabs completely adapted to a terrestrial life would need slanting nor flattening. There are interesting consequences for spidrids. The game is afoot...

Evan Black said...

Tides! Yeah, I just slapped my forehead.

Spidrids probably don't share the same marine origins as crabs do, but it might be interesting to see what other forces, if any, might influence a "slanted" gait. Winds, perhaps? Or maybe scaling vertical surfaces such as trees or cliffs? The spidrid animation with its legs slanted toward the rear suggested to my mind a creature moving roughly downward, as if it were fighting gravity. Such a function doesn't necessarily bring about a permanent slant (since such a creature would want to climb up as well as down) but it's a plausible factor, I think.

Petr said...

and the only "unslanted" arthropods I can think of are myriapods. most insects have slanted legs, or at least jointed in such a way to provide the most efficient push for forward motion. thus, I think, slanted legs in spidrids would make them more efficient walkers/runners and that seems to be enough of a drive to adopt a slanted gait.

I do agree that the "wrongly" slanted gait looks weird, but then again, scorpions have the exact opposite slanting of legs in comparison with crabs, so maybe both are possible for different reasons. =)

and the radially slanted spidrid looks very unique, certainly very alien, and unfamiliar, but that begs the question whether spidrids with this limb orientation move like spinning tops or not, because that's what the limb arrangement would imply. =) It's also interesting to consider whether spidrids really move with two legs laying on their "longitudinal" axis, or whether the slanting would be more efficient if they walked with four legs on the left and four on the right like spiders and crabs do, but I guess you've chosen "axial leg" arrangement on purpose. =)

Sigmund Nastrazzurro said...

Petr: are you certain most insects have slanted legs? I did not define the term very precisely, but the following might do: see if all segments of a leg lie in the same plane; if so, have a look at the angle of that plane with the ground. For ants I would expect that for all three pairs of legs the planes are at right angles to the ground.

As for scorpions, you are right about the direction of the slant. Perhaps flattening is a major consideration after all. I need to find an arthropod leg expert.

The spiral spidrid indeed looks unique, and you are the second person to imply it might rotate while walking around a vertical axis. i worked that out once and it has some very peculiar effects on the legs (basically some are disabled for forward momentum).

I have been considering altering the basic angle of the legs with regard to the body. It is indeed possible to rotate legs in such a way that they end up in clusters at the 'sides' of the animal, but equally possible to bunch them up in front and behind of the direction of movement; in that way they would use their flexion/extension muscles to good effect. i am slowly working on an improved animation and will probably pick up this topic later.

Petr said...

well, I meant that if you look at insects, their forelegs are oriented to the front and the mid and hindlegs are oriented more to the back, as if the forelegs were meant to be used as a kind of grapling hooks to pull the body forward and the other legs are used for pushing the body forward. I think it's the same in spiders and kin, the front two pairs of legs would pull while the bacj legs would push. I agree that I expressed myself wrongly and that there may not really be a "slant" but there is a definite orientation of how the legs are positioned, either forwards or backwards, so they can either push or pull to provide maximal forward force, I see what you mean with the ants, but I think that the "radiality" of that body plan has to have benefits and must therefore be working good enough. maybe it's the "knees" being above the body that allows for sufficient range of movement and efficiency. also, if you look at many insects and even arachnids, you can see that the legs are variable in length. you might want to incorporate that in spidrids too to get more variety. =) some species could have generally eqal legs, which would work best for species that could fluidly decide which direction to go without actually having to "turn" but for species that are oriended for movement in one direction - like the raptorial species that i remember you've made - they could have some further specialization of the walking legs, possibly the hindlegs being the longest to provide a stronger push forward when walking, to acomodate for the legs that are now held off of the ground, or you could have some "spidhoppers" with exaggerated hindlegs and all sorts of other things =) I can't wait for another spidrid post! =)

Sigmund Nastrazzurro said...

Petr: You are of course right about te orientation of insect's legs, but I had phrased 'slanting' somewhat sloppily, hence the confusion.

I have in fact been working on giving spidrids a bit more creativity in their gaits, even without making them bilaterally symmetrical. I have also finally succeeded in rewriting the program so the spidrid can now change direction without turning, with all legs changing relative position as the animal walks. A small voice in my head says that I should make the body bob up and down and tilt a bit depending on which leg is down or up, but that is a lot of work for just a subtlety; unless I turn them into a full Vue animation... (I need at least 9 days in a week)

Anonymous said...

I like the spirally slant for spidrids. There is much less extreme three-axis motion at the shoulder.

In the top video, the spidrids shoulder requires extreme freedom of motion in both axes of the ball joint and also a great deal of rotation around the axis of the limb itself. All those large motions along disparate directions are going to require a lot of expensive muscle. That kind of joint has a lot of failure modes.

For a bilaterally symmetrical critter like a crab, a lot of movement is going to be either more or less towards something in the direction of the major sensory package(read that as 'head'), or away. So common motions are going to be in one or the other direction along the axis of symmetry. As much as possible we'll want those commonly used motions to involve readily isolated single-axis 'hinged' joints.

For less common activities, we will may need more complicated ball- or ball-and-stick joints, but those can have smaller muscle structures as long as force can be supported by less costly ligament structures in the joint most of the time.

This sort of compromise would explain why humans are subject to repetitive stress injuries when engaging in activities for which we weren't evolved...

Sigmund Nastrazzurro said...

Hello Astrographer.

There is less control needed in the top video than you might think. I drew the bit of the leg nearest to the body as a ball, but in reality it does not represent a ball and socket joint with three axes, but a short segment with perpendicular axes at either end (that is why the diagram only has those two axes and not the third one lengthwise along the first segment). The slanting is achieved by tilting the vertical axis off the vertical, towards or away from the centre of the body. I tried to put that in words, but should probably have made a diagram. In this way the control at the most proximal joint just requires two axes. In this respect they are no different than the spirally slanted spidrids' joints! In their case the vertical axis is also tilted, but now the top of the axis is tilted clockwise compared to the bottom end. Again, an image would have helped.

Anyway, this arrangement of proximal joint axes at right angles followed by a series of parallel axes is what real crabs have as well, so spidrid anatomy does not really require more power or more complex control than crabs can muster.

As for joints and forwards motion, just having a limb stick out sideways necessitates a series of fairly complex joints (and in this case I did do the diagrams ;-)

Here they are:

Petr said...

Ah, reading this again I really did misunderstand what you meant by a "slant" and used it interchangeably with "angle", but the angle the coxae are oriented with respect to the center of the cephalothorax of arachnids and crustaceans really wasn't what you were talking about in this post, but rather, that the plane of the limb itself is rotated off the vertical position inside of the individual coxal joints.

still, there are many insects which really do have slanted legs inside of their coxae, cockroaches have hindlegs with a strong backward bias in their coxal joint which allows them to run faster (some cockroaches even rear up on their hindlegs to run even faster, but that is a different topic entirely.)

Many beetles and true bugs have "backward-biased" hindlegs too, and you can see a definite slant in the legs of treehoppers as well, even hymenopterans seem to have some slant in their hindlegs if you look at their photos carefully. And in all these insects there is also a "counterbias" at the ankle to make the foot planted and provide optimal traction, but that is probably something spidrids don't need to worry about with their crab-like pointed feet.

So even though I've misunderstood you before, there still are many examples of this to be found among insects as well. :)