Explaining Spidrid walking

 This will be another fairly short post. In the previous post I explained that I was working on pages for The Book that explained some biomechanical tricks of Furahan lifeforms. Other such explanatory pages deal with things such as rusp snouts and gaits (done), photosynthetic spectra (done), cloakfish movements (to be done) and spidrid gaits (done).

I will not show the actual spidrid illustrations, but can show you some of the underlying thoughts by way of animations.  I used the programs -all Matlab- to produce such animations to choose a single frame, which I then rotated this way and that until I was pleased with the composition. The resulting image was then imported into Corel Painter and used as the guideline for a digital painting. But I will not show these here.

 

The first animation shows your typical run of the mill garden-variety spidrid. It is walking slowly, meaning that each leg is on the ground for one half of the walking cycle. With eight legs, it is easy to have enough legs on the ground to provide a stable support platform at all times. The ‘support diagram’ is a polygon connecting all feet that are on the ground at any one time.

The gait used here is what I call an ‘alternating ripple’. Imagine that the legs are numbered 1 to 8, going round the animal. If the phase differences are 1/8, 2/8, 3/8, up to 8/8 in the same leg order, then legs that are close in phase would also be close in space, so many legs on one side of the beast could be off the ground at the same time, so it would tipple over. So, we introduce an additional offset for even-numbered  legs: 1/8, 5/8, 2/8, 6/8, 3/8, 7/8, 4/8 and 8/8. You will probably need some graph paper to get to grips with all this...

The red lines show the path a legs traces in 3D space. Because the ‘camera’ follows the body, the tracer paths are also respective to the body. The effect is like that of the animal walking along on a treadmill.  

The second one is very similar, but the main difference is that the legs are on the ground for less than half the time. Such schemes are typical for fast movements. The animation runs at the same number of frames per second, so you cannot appreciate the speed difference. There are fewer legs on the ground at one time. The polygons of the support diagrams have now morphed into lines or even points, if there is only one leg on the ground.       

  

Now we move to a more specialised racing spidrid. The camera no longer moves along with the beastie, but is fixed in space. The animal has relatively long legs, and runs the risk of knocking them into one another. That has to be avoided by reducing stride length a bit and adapting the gait: adjacent legs should not be at opposite phases in the cycle, as they then will certainly knock into one another. This one is using the ‘slow’ leg pattern at which a foot is one the ground half the time.   

This is the same racing spidrid at high speed. Each leg is now on the ground for less than half the time, more suited to fast movements. The animal changed its gait in two ways: the first is that the phase differences between legs are smaller, and arranged in such a way that at times there is no leg on the ground at all. It is effectively jumping! The second change is that the leading leg could only contribute to forwards movement by powerful and fast flexion movement, and I decided that the flexion muscles are relatively weak, so the animal simply lifts that legs into the air. (It should really move the body up and down as well, but the animation was not designed for complete realism.)

Many of the principles here are quite common for earth animals: walking faster is often achieved by increasing cycle frequency, stride length, reducing the fraction of the cycle that a leg is on the ground and adapting gaits to achieve jumps. Most mammals and reptiles always use all four legs at all speeds, with a few exceptions (kangaroos, probably hadrosaurs; no doubt there are more). But these poor unfortunate creatures have to make do with only four legs anyway, leaving them little choice. Earth crabs do have choices, and when they speed up, they actually use fewer legs, down to just two. Spidrids, not to be outdone by Earth creatures, have similar tricks up their virtual sleeves.

Crabs as spidrids, spidrids as crabs...

I recently realised that Earth crab locomotion resembles Furahan spidrid walking more than I expected. I may have spent too much time on spidrids or not enough on crab locomotion, as there was a lot to learn about radial walking, odd as that may sound. I found a very nice paper on walking patterns of decapod crustaceans (basically crabs and lobsters) beginning with the sentence 'Most decapod crustaceans can walk in any direction they please'. 

From: Vidal-Gadea et al. Arthropod Structure & Development 2008; 37: 95–108 (adapted)

The image above is from that paper and shows leg movements of a sideways-walking crab, a forwards walking crab, and a forwards-moving lobster. The ability to move in any direction without turning the body is one of the main features of a radial walking design, something I thought did not exist on earth. Apparently crabs, particularly forwards walking ones, are quite 'radial'. In fact, the paper uses the very word 'radial' to describe leg positions for the forwards walking crab. A peculiar convergence with spidrids is that its common name is 'spider crab' (Libinia emarginata).

 Source: http://www.youtube.com/watch?v=_wZZ6N8aM3Y

While most crabs preferentially walk sideways, they can combine directions and walk diagonally if they so wish. The video above shows a crab that starts walking backwards but gradually adds a horizontal element until it ends up walking sideways only. (Click the link to see the source at a better quality).

Source: http://www.youtube.com/watch?v=uYXJ5Ww361s

And here is an example of a forward walking crab. Again, the original has better quality. If you look carefully you will see that the legs do not all point sideways: the front ones are angled to the front, and the hind ones point almost backwards. In short, they are almost placed and held radially around the body. Are spidrids crustaceoid or are crustacea spidridoid?

Click to enlarge; copyright Gert van Dijk

Spidrid legs, although the mere result of a thought exercise, are rather like real crab legs. The image above shows the simplified leg anatomy, say of a sideways-walking crab (or of a spidrid leg). The bottom part shows that the leg can turn forwards and backwards around a vertical hinge close to the body, movements labelled 'promotion' and 'remotion' in technical papers. Let's call that the 'body-leg joint'. The other joints, the 'intraleg joints', in spidrids have horizontal axes allowing the leg to be straightened and flexed (see the top part). There would be muscles for every joint, but I only showed them for one.

If the animal moves in the direction shown here the leg does not need  action of the promotor and remotor muscles: the power for movement comes from the intraleg joints.  If you rotate the direction of movement 90 degrees, muscle force for this leg has to come from the body-leg joint, meaning the promotor and remotor muscles.

Click to enlarge; Copyright Gert van Dijk

So what does all this mean for spidrids? Well, regardless of the direction it walks in, a spidrid has some legs parallel to the direction of movement and some at a right angle to it. The image above shows how that relates to the direction of movement and to the necessary range of motion. The legs parallel to the movement function as the legs in sideways-walking crabs, and  depend on intraleg flexion and extension, pulling and pushing the beastie. The legs at largely right angles to the movement depend on promotion and remotion. The leg in between simply make use of both sets of muscles to varying degrees. (Mind you, the word 'promotion' in crabs always refers towards the front end of the animal; in adapting it for spidrid use it must mean 'in the direction of movement', there being no front end.)

The next evolutionary spidrid twist stemmed from the idea that one of these two types of force production might be superior to the other. How would spidrids make use of that edge, while staying radially symmetrical? Before tackling that I realised I had never shown the spidrid's ability to change direction without turning. Solving that posed some interesting Matlab programming problems, but never mind, it works. I added height for fun and slanted the body a bit when the beastie is on a slope to make it look more natural.

 Copyright Gert van Dijk

Here it is! Finally, a spidrid that negotiates terrain and make a sharp turn. As you can see, the sharp turn calls for some interesting leg movements. With a shallow turn you would not see the changes well. So this is how real radial animals walk. By the way, should a rich Hollywood director wish to buy the concept for a film, I am available! Anyway, it is now time to adapt this standard spidrid walk to more energy-efficient gaits.

Copyright Gert van Dijk

The one above is built on the assumption that flexion/extension is more efficient than promotion/remotion. So, this species uses its promotion/remotion muscles to swing the legs as far parallel to the direction of movement as they will go. There are probably anatomical limits to this, so some legs still stick out at a right angle to the direction of movement regardless. The turn becomes odd, as some legs have to swing a long way to end up in their new position.

Copyright Gert van Dijk

But the existence of forwards-moving crabs shows that under given circumstances using promotion and remotion as the power house is feasible. The animation above has a spidrid moving its legs with a preference for positions at a right angle to the movement. This movement also calls for large leg swings when the animal changes direction. The legs bump into one another, which can be solved with phase changes, but I left it as it is for now. The anatomy of the animal is the same in all three variants, which may be unwise; I can see the last type having shorter legs to improve leverage, at the cost of stride length.

So there we are! Rampaging spidrids! What else is left for spidrid movement? An obvious additional adaptation would be to include slanting, but I will not provide an animation of that; what you see here was quite complex. Then again, I now have a program resulting in 3D coordinates for any part of a spidrid negotiating a 3D terrain. Perhaps I should go for a photorealistic animation? How about the 'Crown of Thorns' (Coruna spinea) making its way over rocks? Or the 'Blue Jester' (Fossor azureus) walking on the forest floor? The 'Lesser Strandsprab' (Nepa aranea) would do well on a beach, but the 'Hairstar' (Coma confusa) would be difficult to depict, with its hair cover. By the way, all of these appear in paintings I am working on...                    

Skitters ('Falling Skies'), spidrids and footless crabs

The previous post was devoted to spidrids, Furahan radially symmetrical walking animals. In thinking about their movement my attention was drawn more and more to Earth crabs, because the anatomy of their legs proved to resemble the anatomy I had chosen for spidrid legs. I admit that spidrid leg anatomy mostly came about because of a wish to see them walk. There are programming problems that I cannot solve myself (inverse kinematics) and I do not have any of the high-end graphics programs that can do it for me. So that is why I came up with the simple scheme I discussed before: at the hip joint there is a vertical axis of movement allowing clockwise rotation, but all other leg segments have horizontal axes enabling shortening and extension of the legs. Later, the exact same scheme proved popular with robot builders.

Last time I discussed a feature of crab (or spidrid) legs that I still do not understand well: slanting. I tried to contact arthropod experts but without luck so far. But there is another feature of crabs I do not understand: why do they not have feet? Crab legs more or less just end in rounded points. This is odd, because crabs, often living in tidal water, need to be able to get to good hold on the ground they are walking on, or else they may be swept away by the current. You would expect feet with curved claws for that. I have not found a discussion of why crabs do not have feet, just one mention of the fact that they do not. As I was considering adding feet to spidrids, I wondered whether there could be an anatomical reason for their absence. That will be discussed first, and only then will the 'skitters' of  'Falling Skies' be discussed: they have feet.

Click to enlarge; copyright Gert van Dijk

In the past I discussed the influence of leg posture on the anatomy of leg joints, and in particular how many axes are needed. The image above shows a new version of an old design (Mechanicus disneius). In the left image the leg is simply rotated forward around the vertical axis of the hip/shoulder joint: the foot ends up rotated with respect to the ground. While walking, the foot should move along a path shown as a stripe on the ground; in reality the animal moves forwards and the foot stays on the ground; it's the same relative movement. The foot should point forwards during the entire step, and that requires rotation around an axis parallel to the most distal leg segment, shown by an axis sticking out of it. The image on the right shows where the foot should be: many joint positions need to be adapted, but the one important here is the rotation of the feet around that longitudinal distal leg axis. By the way, rotate your hands palm up and palm down: what you are doing is pronation (palm down) and supination (palm up), which is just such a movement, due to the long bones in the forearm crossing and uncrossing.

The need for pronation and supination must be present for any animal with sprawling legs. That does not only include lizards and turtles, but arthropods -and spidrids and radial robots!-. I have not found any mention of how arthropods solve this problem. The robot builders just ignore it. Insects have a series of short segments at the need of their legs, the tarsus, linked through ball and socket joints. Are they how insects cope? Does the tarsus more or less flip around during a leg cycle? As said, crabs have no feet, so the end segment of their legs must turn in place during a step, rotating against the ground. Do crabs have no feet because there is no mechanism for pronation and supination? I cannot believe that. All this rotation with friction without a proper way to grab the ground seems an odd way to design a leg, and yet it seems to be there. If anyone knows an arthropod limb expert, please ask them...

Click to enlarge

What does all this have to do with the skitters of the television series 'Falling Skies'? Well, they have radial legs with feet, in an interesting example of 'convergent speculation'. A skitter is shown above, along with my simplified version to illustrate its anatomy (Disneius horrificus). Skitters have invaded an conquered Earth, but as the story unfolds it seems they did so under duress, so to speak. Their top end shows bilateral symmetry but their nether end has radial symmetry, which is odd. There are more aspects that suggest we should be well prepared to suspend disbelief (I like the series). For one, the legs are overly thick given that there are six of them. In itself that might indicate evolution in a very high gravity, but the sprawled position of the legs argues strongly against that. They can walk along vertical walls, a feature so unlikely there is little need to discuss it. They communicate through radio, an old favourite of speculative biology that seems difficult to get underway in an evolutionary sense. (All right, here is why I think so: the evolution of biological radio might well start with a primitive capability to receive radio waves, but can you see/hear with that sense? Where is the benefit?).

                            
The video fragments above show skitters in action. I have repeated the very short fragments to make it easier to see what is going on. It is clear that their nether ends are indeed fully radial, and that the feet accordingly stick out in all directions.

Above you see another fragment, one I rather like. I have repeated this one a few times as well. The skitter turns as it negotiates the path between the furniture. It must turn, as its top end has clear front and back sides: if it has to face the humans, it has to turn. With that clear preference you would expect its bottom end to have an equally clear fore to aft distinction, but that part is radially symmetrical. The one distinguishing feature of radial symmetry is that it allows movement in all directions. With such feet, a skitter might be expected to walk in any direction with equal ease, even directions in which it cannot see...  

The feet remain planted on the floor during the turn, so the legs in fact rotate around a longitudinal axis of the distal leg segment. That is nice; a pity that the anatomical mechanism is not visible. I very much like the way the animators solved the problem of how an organism with such a wide leg base negotiates the limited space between the furniture, designed for the much narrower forms of humans. The skitter behaves like an all-terrain vehicle and simply puts its legs on the furniture where needed, evening out the differences in height between its feet as it goes. That is very well done, I think.

But still... Leaving spidrids with leg points that pirouette against the ground at every step is very unsatisfying. The feeling is a bit like when you are unable to solve a puzzle, the answer of which must be staring you in the face. I think I will equip spidrids with feet, if only to end the irritation. That still leaves crabs, presenting the same puzzle...