Sunday, 24 December 2017

Run, rusp, run!

I keep coming back to rusps because their basic centipede shape allows me to play with gaits and movements more than I thought at the start. So far, I have only shown very large rusps, 'megarusps', having a mass equalling or surpassing that of sauropods. If you need to brush up on your crambology (yes, I invented a word to describe the knowledge of rusps), start with some earlier posts: one, two, three and four (there are more, but these will do). Of course, you can also learn about rusp gaits on the main Furaha page.  

Now, megarusps are immense, and you should not expect them to hop and jump around a place like a rabbit on speed. Instead, expect them to move ponderously and solemnly. Still, megarusps must have evolved from smaller ancestors, and that by itself suggests there could be lots of medium and small rusp species, and indeed there are. And then I wondered whether their multilegged nature might keep them from running fast?

Click to enlarge; copyright Gert van Dijk

Here is my earliest sketch of small rusps again. I have not done any full paintings of such minirusps yet, but I do envision a fruitful adaptive radiation, including arboreal and burrowing species.  I have finished two paintings showing metriorusps ('metrio-' indicates medium-sized), and to do so I had to think about their gaits and in which way these would differ from those of megarusps.

Digging rusp. Click to enlarge; copyright Gert van Dijk
Varkrusp. Click to enlarge; copyright Gert van Dijk
 Here are some sketches of metriorusps, that did not make it to 'evolved' status. I played with the idea of differential leg development, so I could have digging species. That design has not made it to a painting, but running and armoured rusps did make the 'evolved' status, though.     

Millipedes and centipedes on Earth can move pretty fast, but they do not really run. Can rusps run?  The answer lies in what exactly is meant by 'running'. On the one hand you can simply interpret the word as 'walking quickly', but there are more complex biological connotations too.
  Walking consists of cyclical strides, and each stride consists of two phases. In the stance phase, a leg is pushed down onto the ground and backwards, providing upwards and forwards force. In the swing phase, the leg is lifted and moves forwards so it will be ready for the next stance phase. During the lift phase the animal should not fall, and preventing that is usually accomplished by having other legs on the ground at that time. To walk more quickly there are few options: increase stride frequency and increase stride length. The latter can be done by having long legs and by swinging it over the largest distance possible, and to get that working, the time a leg is on the ground will have to be shortened.

copyright Gert van Dijk
 This is precisely what happens on Earth. Here is an old animations of mine showing a horse walking. When walking, each leg is on the ground for more than half the time, so there are likely to be multiple legs on the ground at any one time. The slower an animal moves, the more the situation resembles standing still, and for an animal standing still its centre of gravity must fall within the area described by the feet: that is static stability. The stars in the animations represent the corners of that area. The order in which the leg moves ensures that the area has the shape of a triangle under the body.
copyright Gert van Dijk

For a galloping horse, each leg only touches the ground for a short fraction of its movement cycle. The result is that the chances are low that many legs will touch the ground at any time. In fact, there may well be no legs on the ground at all at some times, so the animal is in fact making a series of jumps. At high speeds static stability gives way to dynamic stability, meaning the animal is kept from falling through inertia and a footfall at the correct time and place.

Running is regularly defined as walking with each leg touching the ground for less than half a walking cycle. On earth, all really fast animals use these principles. Having said that, it is time to go back to centipedes and rusps. Centipedes do not run: their stance phase typically lasts much longer than their swing phases. This increases the chance that there are many legs on the ground at any one time, and, seeing how many legs rusps have, this is almost a certainty. This adds up to there being no jump phases, which seems a bad idea if we want a fast rusp.


The answer, I thought, would lie in the gait. The animation above shows a rusp with a slow gait: each foot is on the ground more than half the time. In real life, the animation may have to be sped up for a more realistic effect, but at least the movements are well visible. To support the body well, no region of the long rusp body should be unsupported for a long time, and that is achieved by choosing specific phase differences between the legs. In this case, these seem to work reasonably well. Mind you, rusps have typical 'zigzagzig' legs (see here, here and here for what that means).

The next step, above, is to equip the rusp with a different movement cycle for its legs; the legs now swing further and touch the ground less than half the time. I kept the phase differences the same for comparison. Fortunately for this rusp, its legs do not kick one another with this setting, so the result is not at all bad. There are always legs on the ground though, and that may limit a further increase in speed.

So the gait is the next parameter to tweak. Here, the phase difference between successive legs is much less than before, so the legs on one side move almost in unison. Still, at the moment the last leg on one side leaves the ground, there is already a leg just touching the ground on the other side.            

That can easily be amended. Now the phase differences are almost gone, and there are two periods in the movement cycle when there is no foot on the ground at all. Again, you will have to imagine a proper film speed. This rusp is going so fast, its feet hardly touch the ground!  

So yes, I think there are ways to have rusps run. Actually, they might be able to change phase differences very subtly and continuously, giving them a 'continuously variable transmission', unlike Earth's large mammals, that typically have up to three gaits to choose from (walk, trot and gallop), each with a specific preferred speed.  But that will also depend on energy requirements, something I haven't studied in any detail. 

Click to enlarge; copyright Gert van Dijk

So here is the scale diagram of the runrusp, one of the metriorusps that has already been painted. To close with, it may be interesting to know that I leave hexpods for last, because I am not fully satisfied with the animation of their middle legs yet. But I must say that exploring all the nonhexapod lineages on Furaha is perhaps not a bad idea: it gives more attention to designs that are least Earth-like.  


Andrew Broeker said...

Long ago you promised an explanation of the biomechanical value of toes. Will that ever happen?

Sigmund Nastrazzurro said...

Andrew: Acually, two thirds of that post had already been written when I started doubthing the validity of my reasoning, and then I shelved it. I did not expect to be sidetracked this long, but your question now made me think about it again. I think I have the answer now. If not, I can at least present a reasoning that readers can choose to follow or not. When will I publish it? I do not know yet...

Petr said...

I can't believe I've missed two posts already!

Rusps have instantly become my favourites, although I do admit sawjaws and marshwallows are charming creatures as well. (Charming to watch from a safe distance, that is :D).

The medium-sized rusp really has some legs on him, doesn't he? I looped the videos so I can watch the walk cycle in more detail and pay better attention to it.

I really enjoyed the post, I really wouldn't think a truly running rusp would be feasable but it really doesn't look out of its element at all. :)

Anonymous said...

Even with their smaller body sizes, don't the metriorusps have too much armor weighing them down, for them to go at much of a speed?

-Anthony Docimo

Sigmund Nastrazzurro said...

Petr: A running rusp indeed? Who would have thought it possible? And yet, here they are ;-)

Anthony: good point. The page on metriorusps starts by asking how small and medium rusps rusps survive without the advantages of enormous size. The answer is by having other strong points in their favour. Do not expect armoured metriorusps to run; instead, while you try to work though their armour, they'll have a go at you with their thagomizers.
As for runrusps, they do without thick, heavy armour. Their speed is part of their protection, and if that fails, their whips are equipped with stinging quills (have a look at the sketch of small rusps: the tufts on the whips aren't to make it look pretty, but are venomous to a degree.
The basic rusp design is a bag of tricks...

Petr said...

Although... What is a rusp's run to the flight of a bumblebee... :)

Keavan Ѳ said...

It's funny to me that, though your blog brought to my attention the biomechanical flaws with "doubling" legs, one of your creations, the runrusp is an example of doubling taken to the extreme, with even a similar gait.

Theoretically speaking, do you think "middle centaurisation" would be viable for any organism, eg, a rusp with legs highly specialised for defending it's middle, for example.

Do the number of limbs vary between species of rusp'? And do any gain or lose them as they age? They seem to have at least somewhat of an endoskeleton, and the only organisms I can think of that have wildly varying numbers of segments/limbs are invertebrates.

Anonymous said...

well, there is at least one clade with middle centaurization:


Sigmund Nastrazzurro said...

Keavan: there is indeed irony in the running pattern of runrusps, as you can indeed see them as an extreme example of 'doubling' legs (see the posts of May 5, 2012 and February 11, 2010). But I criticised 'doubling' as used in those posts as a way to animate multi-legged walking animals because they did not make mechanical sense. In contrast, the runrusp has a synchronised gait because it does make sense -to me at least-...

It is interesting that you should ask about the actual number of legs. Let me quote from the concept text I have written so far: "The number of pairs of legs varies between species, and can in fact even vary within a species. Crambologists first thought that this was due to a genetic mishap, but studies failed to show anything wrong with individuals with a lower than expected number of legs (‘oligopods’) of with a higher number (‘polypods’). The number of legs can in fact easily change up or down in successive generations. Biologists had taken it for granted that something like the number of legs would be an immutable feature of an animal’s Bauplan. Violating that is as if it would be normal for the number of fingers in humans to be anything between four and seven. And yet, this is normal for rusps." I am not certain I will keep this though.

Regarding 'middle centaurism', my first guess would be that I could not think of any examples. I then thought of Amblypygi (see post of March 8, 2009): these are arthropods that have 'raptorial pedipalps' at front, and the next pair of limbs are long feelers. If you count the pedipalps as legs, then the feelers are the second pair of legs, so they may count as middle centaurism. Then again, if you consider mouth parts as well as pedipalps as modified legs, then you can argue that all these are still 'frontal centaurism', which then becomes 'successive recruitment of legs from the front'. Congratulations to Anthony for finding the Ricinulei. The Wikipedia text seems to suggest that it considers the pedipalps as the first pair of legs.
Perhaps 'middle centaurism' should be reserved for animals in which limbs in the middle evolve to do something new while there still are functional walking legs in front and behind; doesn't speculaitive biology lead towards surrealistic ideas? ;-)
That is an interesting idea. The legs should probably do something more that just sit there as a thick immobile shield, because it is probably easier to derive such a simple use from the skin anyway. So this should probably concern mobile limbs, recruited for a defensize purpose. Hmm....

Anonymous said...

well, given that millipedes are appearantly born with a single pair of legs, and gain more pairs as they grow...could that be a possible reason for variable leg count in rusps? (or would it be a red herring some researchers might pursue, and maybe/maybe-not find out the real reason later)


Sigmund Nastrazzurro said...

Anthony: I did not know about millipedes starting life with fewer legs than they have as adults; fascinating. I thought that equipping runrusps with a varianble number of legs would bge an original concept. There is also the possibility that I had read about this millipede fact at one time but no longer have a conscious recollection of this, and that my memory came up with the association, now packaged as an 'original' idea. Memory can perform tricks like that.

Anyway, reading the wikipedia entry on milipedes also provided a real-life example of 'middle centaurism': "...In all other millipede groups, males possess one or two pairs of modified legs called gonopods which are used to transfer sperm to the female during copulation. The location of the gonopods differs between groups: the Helminthomorpha... they are located on the seventh body segment."

Evan Black said...

There's something that seems... off to me about the running rusp. It seems, and correct me if I'm wrong, that the legs on one side of a rusp hit the ground more or less at once, then after a brief jump period, the legs on the other side follow suit. Would the rusp experience quite a bit of site to side "rocking" as a result of this gait, and could that prove problematic?

Secondly, what is the functional difference here between the rusp's gait and that of a running biped? If such is the case, then is this case of rusps "pretending" to have two legs distinct from your detailed analysis of the creatures of Cameron's Avatar "pretending" to have four legs?

Keavan Ѳ said...

I didn't mean to imply that I thought there was some inconsistency or hypocrisy in your part, if that's how my comment about doubling. I just absolutely love that the seemingly inefficient strategy of doubling, when taken to what can be seen as its unreasonable extreme, what with 8/ish sets of legs, as Evan put it, all "pretending" to be only two legs, can yield a seemingly functional gait.

The reason I was wondering if the number of legs varied over the course of an individual rusp's lifespan is because, like mentioned above, millipedes do. I was curious because millipedes have an exoskeleton unlike rusps, which seemingly is better suited to radically changing body plans. Would new limbs slowly grow out at the front or back, initially useless, until they're long enough to reach the ground, and the body has grown another full "segment"? If I remember correctly, both vertebrates and arthropod are segmented, though those segment are much, much clearer in arthropods.

I could imagine a particularly long, slow species of rusp having repurposed some of their central limbs as further defensive weapons, to deter from attacks on their middle, too far from either whip.

Now I find myself wondering about rusp anatomy. Do they have a highly centralised nervous system, like a mammal, or do their legs act on their own, like a cephalopod? Or maybe even more extreme, like a cockroach, able to walk, reproduce, and survival for days without their head.

Decentralised nervous systems seem to be advantageous to certain species. I remember watching a TED talk on what engineering and robotics can learn from biology, and one of the most interesting points brought up was that the brain or computer doesn't have to handle everything, the body can coordinate itself. The example given was the salamander, which tells it's body to move by sending simple pulses down its spine, the speed of which being the determining factor in whether it walks or swims. It can smoothly transition from the snake-like side-to-side oscillations of walking, to the side-to-side thrashing of swimming, as the frequency of the pulses increases.

Sigmund Nastrazzurro said...

Evan: You are abolutely correct. An animal with lots of legs on the ground can place the legs directly under the hips, or displeced outwards, such as arthropods do. This helps to broaden the support polygon, meaning the area on the gorund defined by which feet are on the ground at any moment. As long as the centre of gravity lies above this polygon, the animal is stable. As you increase speed there wil typically be fewer feet on the ground at any time, and if these feet are on one side of the body only, the centre of gravity cannot lie above the polygon (which shrinks to a line or even a point). Then it helps to place the footfalls close to the midline of the body, which is what animals tend to do. To do the runrusp justice I should have ensired that the footfalls are placed closer to the midline the faster the aninmals runs, but I didn't ( I was lazy...)
As for the runrusp pretending to have two legs only, well, that's what Keavan Theta asked as well. I think that the 'doubling solution' as used in Avatar did not make mechanical sense, whereas the runrups's gait does -to me at least-.

Keavan Theta: It was a fair criticism and no offense was taken at all.
No, the number of legs of runrusps does not alter during the life of the animal. I had not consider4ed the matter, but it would be impratical for the reasons you describe. I suppose that it can only work in animals that moult: a new pair of legs could form inside the body of the animal, and when it moults the new pair is inflated and its skeleton hardens forming an useful leg (I assume that that is how it works).
Having defensive legs in the middle of the animal is intriguing. I'll think about it but can already feel the Rusp Bauplan in my mind starting to shapeshift a bit, but I did not plan on doing more rusp paintings that the five spreads that they already have, so they may be stuck where they are.
I do not think that equipping rusp legs with separate brains would help much, as their effectiveness relies on coordinating their actions with legs around them. That is not a very complicated task, though. I envisage rusp nervous systems as having started from a rope ladder nervous system. Walking is done by distributed computing with minor input from the frontal ganglia. For a discussion on how walking in animals can be controlled,m see 'central pattern generators':
In contrast, whip movement is controlled by head ganglia exclusively, with limited interconnections between front and aft.

Petr said...

Did I hear you say five spreads about rusps? :D

Sigmund Nastrazzurro said...

Petr: yes. One showing the brontorusp, one showing various other megarusps, one showing rusp gait and snout features (a bit technical), one showing two metriorusp species and one in which the text is about humanbs, band the image shows a mega rusp and a human alongside. The first four are ready, the last one, is about 90% done.

I am thinking about showing the last one in a post. after all, in aprilk the blog will exist 10 years (!) and I am considering a post a week in April, including one on toes. Perhaps one will be about the "Drake Equation", which I assume you know, and its variant that you cannot know: the "Nastrazzurro Equation".

Petr said...

Oh my gosh! So many exciting things lie ahead! :)

As always, thanks for keeping this blog going for all this time, it has always been both exciting and informative/educational.

mote said...

Hello, I have read your blog for a while now but as I know very little about biomechanics I have not yet commented. Your blog has been really valuable for me though as a resource for my own project!

I would like to send you an email if possible so I can send you the World Editor for my WIP game. You might find it interesting because with a bit of work, you should be able to model Fuhara and its solar system in a lot of detail including climate, terrain etc. Right now I am just looking for feedback so I can improve it!

If you are interested, please get in touch. I use gmail and my address starts with hcrofton@...

The Eurypterid said...

Ooh, I like the animations. Question, though- assuming that at least some rusps are flexible dorsoventrally, would it make sense to move the legs in rough pairs instead of one side at a time? That might let them add some whole-body motion to their run cycle, in turn giving them a better stride length and helping them run.

Sigmund Nastrazzurro said...

Eurypterid: let me check whether I understand you correctly: do mean that the body should arch in the way running cats arch their backs, i.e. to increase stride length?

L13B3 14641 said...

Well, cats aren't the only animals to do so; I believe dogs do so too, and so do caterpillars.