What does a Hexapod gallop sound like? (1)

Click to enlarge; copyright Gert van Dijk

 The image above represents one of the very first Furaha images ever, painted way back in the previous century. The planet did not even have a name yet, and I certainly had not thought much about biomechanics. I just tried to paint an interesting and pleasing picture. These primal hexapods were fairly insect-like, with a stiff-looking body. The details where the legs join the body suggest exoskeletal parts as much as they could represent skin flaps. I can show the painting here, as it will not feature in The Book: it doesn't fit anymore. 

But I still like the scene very much. In my minds' eye, I can see a large herd of these impressive animals ('handlebars' or 'handlebar-horns') enter the scene from the left, advancing towards the right, until they turn towards the camera, wheeling like cavalry. That scene deserves to be done again, with new and updated handlebars. The update does not only require revising their anatomy, as part of the Great Hexapod Revision, but their gait as well. After all, if you paint a fast-moving hexapod, you should have an idea how its legs should be positioned. Imagining six-legged walks is apparently not something that comes naturally to all illustrators: many, including brilliant artists, fell back on on four-legged locomotion patterns, and simply added additional pairs of identical hind legs until the required number of legs was reached (see here, here, here and here). I never liked that, even though I realise that doing otherwise asks a lot of an artist who may not be familiar with the gaits of insects and other invertebrates. 

Perhaps I am being too difficult about this; after all, the viewers are likely to accept the result anyway. When you looked at the handlebar painting, did you think 'I wonder whether that gait is correct?' My guess is you did not, but I still wanted to do better. I like to think that a fairly thorough biomechanical background is a selling point of Furahan fauna; I also do not think I could let it slip anyway... 

Click to enlarge; copyright Gert van Dijk

I therefore wrote a suite of programmes to help me design decent hexapod gaits. In fact, I wrote them again, as I had done so once before, in 'BBC Basic' on an Acorn Archimedes. There are still a few animations on the main Furaha website that survived the transition to other operating systems. The programmes did not. This time, I wanted to do better, meaning that the programme should find out how to fold a leg by itself, rather than requiring me to control each minute limb movement by hand. I thought that that would be tricky, and it was... I had to settle for limbs with three main segments, as I could not yet add a fourth one the position of which looked convincing enough. You will just have to imagine the feet. I will use the program as background material to design paintings, and I can add details myself. The programme does allow body position to adapt to the chosen gait, so that part works. 

 

Here is an example of such a three-segment limb. The programme uses segment length, built-in movement restrictions of the joints, and the phase of the movement cycle to control the thigh angle. The other bit of information is where the foot should end up on its motion path. Together, that is enough. The movement is a bit uneven, because the programme chooses from an array of possibilities, and I should have increased the number of possible solutions. 

 

This shows what happens when you vary the choice which joint should 'stick out' the most. The further a joint is from the vertical, the more energy is needed to keep it in that position. You can see here that making life easier for one joint makes it more difficult for another. The middle position looks like it provides a nice middle ground in that respect. In biology, an optimum usually represents a compromise that minimises the overall energy required. 

Click to enlarge; copyright Gert van Dijk

 

The basic hexapod anatomy these days consists of six fairly similar legs that all have 'zagzigzag' pattern, (see here , here and here), meaning the most proximal segment ('coxae' or thighs) generally point backwards. I chose that as I could not find a convincing argument to state whether zigzagzig or zagzigzag was better. The legs are not identical, though, and future hexapods will see more pronounced differences. In the pattern shown here, the middle pair of legs is stouter than the front and hind pairs, and their feet are placed wider apart. That latter bit of information is only visible if you look at the 'support diagram' under the beastie. Placing some feet wider apart is a trick to avoid leg collisions, although it is not strictly necessary: Earth tetrapods manage to avoid collisions just fine with similar distances between pairs of limbs. 

 

And here is one complete hexapod in a slow walk. The sounds were taken from sound recordings of horse hoof beats, because I had to use something; it doesn't mean the animal has hooves! Keen observers may well deduce some as yet undescribed anatomical information from the animation. 

So how about the gallop sound? Next post!

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.