Showing posts with label locomotion. Show all posts
Showing posts with label locomotion. Show all posts

Monday, 13 July 2026

How many legs should animals in speculative biology projects have?

By Sigmund Nastrarruzzo and Biblaridion

We recently published the first of two posts in response to comments on Biblaridion’s YouTube review of Sigmund/Gert’s book ‘Wildlife on the planet Furaha’. The number of legs of Furahan creatures evoked many comments, in particular Furahan scalates. Scalates are animals with some similarities to Earth vertebrates, such as a comparable size range and bilateral symmetry. But the six legs of Scalates urged some people to argue that larger animals should always have at most four legs. The previous post dealt with limits posed by a Bauplan: the genetic building plan that defines an animal’s main anatomical features. In this post, we start with discussing Bauplan effects some more and then try to work out what effects the number of legs may have on animals. 

Bauplan limitations 

The odd thing about a Bauplan is that its contents are largely locked and cannot be modified through evolution, and yet that same Bauplan can only have come into being because its contents were at one point highly malleable! If the number of legs is locked in a Bauplan, that number stays fixed. The four limbs of Earth vertebrates are locked, so vertebrates will not have offspring in which the basic pattern jumps to two, six, or eight legs. There are three major lessons here. 

  1. The fact that ‘four legs’ is part of the vertebrate Bauplan does not mean that this number works significantly better or worse than another number; all we can conclude from the long history of vertebrates is that four legs work well enough. 
  2. The number of legs does not have to be locked in a Bauplan in each and every animal clade! The number is in fact variable in Earth millipedes, and speculative biology creators can use that fact to decide whether the number of legs in their creations is fixed or malleable (it is variable in Furahan rusps). 
  3. The basic instruction ‘make four limbs’ still allows anatomical modification of those four limbs. Evolution can find other purposes than walking for front legs, a principle baptised ‘centaurism’ in this blog; examples are the front legs of mantises, wings in birds, the hands of primates and theropods, and mouth parts in just about any arthropod. The result is that the animal gains new functionality at the cost of a pair of walking legs. Such centauric evolutionary changes probably starts with animals using their front legs both for walking and for a new purpose, and over time the new function takes over completely, so the walking role is lost. Some commenters on Biblaridion’s video felt that many-legged animals would lose legs until they arrived at four legs, without a new function. But in an evolutionary process each step has to bring an advantage. To make their scenario work, animals would have to start using only four of their six legs even though all six were fully functional; we see no clear advantage in that, and evolution is not driven by future goals, but by advantages here and now. 

Building costs 

If a leg is only a weight-bearing cylinder, then each leg can be more slender the more legs there are. But what is the total mass of many slender legs, compared to that of a few stout ones? The calculations on that question (here and here) showed less total weight with fewer legs, with the least mass for just one leg! But you only have to think about how fatiguing it is to hop on one leg to realise that building costs cannot be the only consideration. In evolution, many factors usually play a role, and the best solution then is a compromise between conflicting demands. For example, factors such as stability and surviving harm may outweigh saving weight. 

Surviving harm

If a one-legged or two-legged animal breaks a leg, it will be unable to eat or drink, and will quickly become someone’s dinner. Four-legged animals are probably also doomed (dogs and cats can adapt in amazing ways, probably because humans help them through the critical phase). A six-legged animal can probably limp away after the loss of one leg, and the consequences of injury become less severe with a larger number of legs. Do millipedes even walk slower after losing a leg? In short, multiple legs allow better chances of surviving injury than four or fewer legs. 

Speed 

Animals that walk fast use four principles to speed up. The first three are simple: steps become longer, step frequency increases, and the fraction of time a leg is in the air increases, while time on the ground decreases. The fourth factor is gait, meaning phase differences between legs. During a slow walk, the body has to be supported at all times, which is best done by having all legs move at different times, so no two legs move in synchrony. For slow walks, this works best with four or more legs. However, fast running works best if the gait contains jumps, meaning periods in which all legs are off the ground at the same time. To achieve that, leg movements have to be synchronised to a degree, which can -in principle- be done regardless of the number of legs. For instance, take a Furahan rusp with 24 legs. When such animals run, all right-sided legs move in unison, and so do the left-sided legs, but exactly 50% out of phase. 

Bipedal running cockroach; click to enlarge. From Full and Tu 1991
 

However, that is not how many-legged animals run on Earth. Cockroaches, crabs and lizards may use just two legs when running fast. Why do they not use all their legs and run like rusps? Well, rusps have their feet close to the midline, which makes it easier to support the body with legs on one side only; cockroaches, crabs and lizards have splayed legs, which makes one-sided support difficult. Another part of the answer appears to be that the preferred legs for bipedal running in cockroaches and lizards are longer than other legs, so the other legs are less useful for speed. Note that, even though crabs may need only two legs for maximum speed, this hasn’t resulted in crabs with only two legs! The other legs are useful at other speeds. For instance, crabs need good stability when walking slowly, helped by having more legs, and their life may depend on their ability to cling to a rock using all legs in heavy surf. 

For large animals, it is less likely that one pair of legs provides enough power for maximum speed, so they need more legs to achieve that. Perhaps another factor weighs in too, such as the animal not achieving stability with only two legs while running. 

Stability and size 

We will use ‘stability’ essentially as the likelihood of not falling, while standing or walking. Animal size is extremely important here, because the effects of gravity are relatively much more important for large than for small animals. In contrast, sideways forces such as wind and water currents are more important for small animals.  

Gravity always presses large animals firmly to the ground, so their feet do not have to cling to the ground or grasp it. Stability primarily means keeping the centre of gravity over the area defined by where the feet touch the ground (a support diagram), and secondarily being able to keep the body orientation the same. 

Small animals, say insect size, do need to cling to or grasp whichever surface they reach, regardless of whether that is vertical (as in the illustrations below), horizontal or even upside-down. For them, stability is keeping the body position and orientation stable regardless of where the footholds are. 

What happens to stability and position for large and small animals when the number or legs increases?

Click to enlarge; copyright Gert van Dijk

  • One leg allows a large animal to stand and to hop, with gravity ensuring it always returns to the ground. One-legged standing and hopping amounts to a continuous balancing act, which in turn needs very sophisticated nervous and muscular systems. Animals that are just learning to walk on dry land will not yet have evolved such sophisticated systems, so it is doubtful that one-legged animals could even begin to evolve the skill of walking. For a one-legged small animal, hanging from its one leg, life is simple: if it relinquishes its grip, it falls away from its support surface; not a good idea. 
Click to enlarge; copyright Gert van Dijk
  • Two legs means fewer directions to fall in, which helps. Birds, some other dinosaurs and people all walk well with two legs. It is not easy though: faster walking requires dynamic stability, meaning the centre of gravity needs to kept over a continuously changing support diagram. To do that, you will again need exquisite control, so we advise bipedal animals that aim to become terrestrial walkers, but cannot do so yet, to not bother. Very small two-legged animals could theoretically hang from one leg while moving the other, but it would be very difficult to prevent the body from just hanging down from one leg: not a good idea. 

 

Click to enlarge; copyright Gert van Dijk

  • Three legs, for larger animals, allow a neat support triangle; that is all you need to stand still, and you do not need complex control for that either. But walking with three legs will require excellent control. Very small animals can hang from two legs, but it will still be difficult to control body position

 

Click to enlarge; copyright Gert van Dijk

  • Four legs, in larger animals, do not make standing easier than with three legs, except when there are strong sideways forces such as water currents or strong winds. If there are, it helps to have a leg sticking out in the direction of that force. Walking with four legs offers a fundamental advantage over walking with three legs: you can lift one leg and still remain stably supported by the other three. This is still not exactly easy: tortoises, moving slowly, have stability problems, as they tend to fall in the direction of the lifted leg. It takes a specific order of moving the legs to prevent that, so here’s that neural control again. Small animals with four legs can maintain their body position using three legs, while one limb moves to a new foothold. 

 

Click to enlarge; copyright Gert van Dijk

Click to enlarge; copyright Gert van Dijk
  • Five and more legs will not improve stability much, for large standing or walking animals. This probably holds for small animals too: with many legs, they can choose which ones grab a surface and which ones move to the next foothold, all while nicely keeping the body in position. However, many legs may help to grasp objects better: the eight legs of crabs may act as fingers, making a crab a sort of hand to grab rocks with; insects walking uphill may keep more feet on the ground than they do on a horizontal surface; the many legs of millipedes may help them bulldoze through dead leaves or soil. 

Stability becomes easier with more legs, at least up to a point; we guess that stability will not increase much beyond, say, six or eight legs. We suspect that ‘beginner walkers’, animals that are just learning the art of moving on dry land, will find the task easier if they have more legs, say six or more. If you are just learning to walk and have only four legs, don’t expect to be able to lift the body at all times at first! Start by crawling on your belly, and only try to lift the body when your control system can guarantee stability. However, if you start with six or more legs, you’ll learn to walk in no time! 

Planetary effects 

Many of these effects will depend on local gravity. On a planet with low gravity all legs can be spindly, and falling won’t hurt as easily. With a very strong gravity, legs have to be very strong and as many legs should be on the ground for as long as possible, which is easier the more legs there are. With a high gravity a lifestyle clinging to branches and twigs is asking for trouble, unless there are always lots of legs keeping a secure grip. 

Conclusion 

The number of legs plays a role in stability, building costs, surviving harm, locomotor efficacy and probably factors we didn’t consider. The number is restrained by evolutionary aspects and may be locked genetically. Whenever there are many factors determining an outcome in biology, it is usually impossible to identify one factor as the sole determinant of success or failure. We think that this holds for the number of legs too. The optimum number of legs is like most biological optima: a summation of many functions with lots of compromises. 

However, this can only be true if the number of legs can in fact vary freely, in which case evolution can modify the number as the outcome of such a summation. But if the number is locked, which seems more likely, then evolution has to work with what it was given. The number may then constrain evolution: for instance, an animal with just two legs would find it difficult to combine flying with walking. 

With all these factors weighing in, we do not think it likely that all large animals in the universe must have four legs (or six, for that matter). There are too many variables at play, so we expect the usual evolutionary mixture of Bauplan constraints and many factors weighing in. That seems to be how biology works, and for that reason speculative biology should work that way too. Are we certain of that? No, we aren't; it’s all speculation, remember? 

 

Short reading list


  • Büschges, Ache. Motor control on the move: from insights in insects to general mechanisms. Physiol Rev 2025; 105: 975–1031
  • Full RJ, Tu MS. Mechanics of a rapid running insect: two-, four-and six-legged locomotion. Journal of Experimental Biology. 1991; 156: 215-231
  • R McNeill Alexander. Optima for animals, Revised edition. Princeton 1996 
  • R McNeill Alexander. Principles of animal locomotion, Princeton, 2003
  • Riiska CA, Harrison JS, Thompson RD, Nina JQ, Gallice GR, Rieser JM, Bhamla S. Katydids shift to higher-stability gaits when climbing inclined substrates. Integrative and Comparative Biology. 2025 Dec;65(6):1667-77. 
  • Weihmann T. The smooth transition from many-legged to bipedal locomotion—Gradual leg force reduction and its impact on total ground reaction forces, body dynamics and gait transitions. Frontiers in Bioengineering and Biotechnology. 2022; 9: 769684  

Sunday, 21 November 2021

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!