From erect dinosaurs to pivoting fly feet (Frustrating feet 2)

This post is long, fairly complicated and rambles along a bit, so do not say I did not warn you. We are so used to seeing big mammals that most ‘alien’ legs in drawings and films are just mammal legs. One thing you will find in many books is that a key feature of mammal locomotion is that the legs are 'erect'. 

 

Click to enlarge. From Box 4.3 in: Fastovsky & Weishampel. Dinosurs A concise natural history. Fourth Edition Cambridge University Press 2021

 

The image above shows such a scheme, making the point that dinosaurs legs are as erect as mammal legs, using a human as an example. I have always felt that the legs of the dinosaur in the picture are not really 'erect', while the human's leg both are less erect than they usually are in a standing human. 

Click to enlarge; copyright Gert van Dijk

Let's explore this further. Above, you see the species Disniformis inexpectus and on the left its cousin, D. expectus. The elbows and knees of D. inexpectus stick out sideways, while those of D. expectus do not. Which animal stands in the most energy-efficient way, and which is the most 'erect'?

 <pause to think>

Many readers may feel that D. expectus wins on both accounts. But have a closer look: in both animals the feet are placed precisely underneath the hips, and the leg segments are tilted in opposite directions as you move down. Because the joints are angled, energy has to be spent to keep these joints from bending further under the influence of gravity. How much energy depends on the angle of the joints and how far these joints are situated from the vertical line connecting hips and feet. Guess what: the legs and joints angles are exactly the same. The legs were just rotated, except for the feet, so exactly the same amount of energy is needed to keep the joints stable.

Personally, I would call a leg fully 'erect' only if the segments are all vertical, as they largely are in standing elephants (and standing people!). If all segments are fully erect, the feet must end up directly underneath the hips. In the dinosaurs and both species of Disniformis, the feet are also placed directly underneath the hips, and it seems some authors use the word 'erect' to mean only that aspect. The opposite of 'feet underneath hips' (FUH) must be 'feet away from hips' (FAFH). If the feet are placed well to the side of the animal, you get a sprawling stance, like salamanders and insects use.         

Perhaps you feel that all this changes when the species start to walk, and then we will see that D. inexpectus can only plod along while D. expectus trots elegantly out of sight. Not so! The legs of both species can extend to the same length and the joints move through the same arcs. This means that  elbows and knees can be kept close to the centre of the animal regardless of whether they deviate to the inside, outside, back or front.

 

Click to enlarge; copyright Gert van Dijk

Still, D. expectus will have a gait advantage in that its joints can be designed much simpler than in D. inexpectus. The dinosaur drawing and the reworked D. expectus above show simple hinge joints that allow the legs to move only in a fore-and-aft direction. That save energy; nice, right?

It would be nice if animals were like trains, only moving along predefined linear tracks. But they also need to turn and to step sideways and do other things beside walking in a straight line. An animal must be able to move its feet fore and aft, but also to the side, and must also be able to turn toes in or out. This requires rotation along all three axes. You can be creative and appoint different movements to different joints, but iff you wish to obtain the largest reach for the foot, you should give the hip joint the most freedom. That is probably the reason mammal hips have ball joints (and dinosaur hips too, as far as I know). My guess is that the most proximal joints (hips/shoulders) in alien animals will also have three axes of rotation. Mind you, the three axes do not have to be used to the same degree in daily life (fore-aft movements will see more use than toe in/out movement).

The ankle joint should allow the foot to adapt to uneven ground, so the joint must allow a toe up/down rotation and also a thumb up/down rotation. That is two axes already; we will get back to the third axis. This leaves joints in between, and these need only have one direction of rotation, like mammal knees (that need not be universal though and is probably something for another post).

 

Click to enlarge; copyright Gert van Dijk

We are now getting to something that has vexed me for years. Above is an image from a post from 2010, showing D. salamandris. This is what I wrote at the time: "To get a movement suitable for walking, its foot should move in a straight line from front to aft … But ensuring that the foot always points forwards also requires that there is a way to rotate some of the bones around a longitudinal axis."

It is the need for that third rotational movement in animals with FAFH ('sprawling') legs that vexes me. Humans are very good at this movement, called pronation and supination (if you hold your arm in front of you, turning the palm down is pronation and turning it up is supination). But I couldn’t find good discussions on this type of movement in the prototypical sprawlers: arthropods. If readers know about such studies, please let me know.

I looked at some internet videos of walking insects to see whether their feet remained fixed to the surface while the leg rotated; if so, these insects had pro- and supination. I would expect the tarsus to allow that movement, even though the text I found previously said that the tarsus only allowed flexion and extension. If the foot would rotate along with the leg, it would pivot over the ground, something hardly compatible with a firm grip.

There weren't that many videos that allowed such close scrutiny, but here is one, showing a fly walking across glass. The foot stays in largely the same position and does not rotate along with the leg. To allow it to that while the hip is moving forward, something has to 'bend'. The tarsus indeed seems to bend a bit, but not much. In fact, the tarsus keeps on pointing in the same direction all the time. 

 

Click to enlarge; copyright Gert van Dijk

I thought of a possible explanation, and it involves a different kind of hip movement. Above are two spidrids. The first has a typical vertical axis of rotation through the hip; that's a normal spidrid. The rest of the leg lies in a plane, and the movement is shown by two 'ghost legs' (this is typically how crabs move). The second image has another hip, with the axis horizontal. The animal can still reach fore and aft, but the results looks different.

 

Here is what the differences amount in an animated view: first a typical spidrid movement with a vertical axis. The gray structures indicate the planes in which the legs move.

 

And now a Neospidrid with a horizontal axis (the model caters for intermediate angles too).

An thay means we can get back to flies; in a textbook of arthropod anatomy (Manton 1977) I found indications that insects hips have an added 'rocking' movement that would indeed allow some rotation around a horizontal axis. But there's a rub. With such an axis, you still need pro- and supination to keep the insect's 'palm' against the surface. I still do not know how insects solve the need for this longitudinal foot movements. Crabs are probably easier, as they have no feet in the common sense, so they can just pivot on the tips of their legs. 

I confess that designing alien animals is sometimes easier than studying Earth animals. In particular when it comes to feet!                    

 

 

Feet are frustrating! (Feet I)

A long time ago, I promised I would write about feet or toes, but it took ages to find my footing (sorry). Why? Well, animal feet proved to be very complex. My first associations included shock absorption, weight distribution, pivoting, friction, toes or no toes, walking upside down on the ceiling, walking on water, feet as attack weapons or digging instruments, etc. All that did not immediately suggest one simple theme. Moreover, this blog is about speculative biology, but as Wikipedia has no entry 'Feet across the universe', I found myself in uncharted territory, once more. Other speculative biology projects do not help much either: there is the usual tendency to copy Earth's vertebrate or arthropod legs. I think I will have to write more than one post on foot design' because the subject is too large. I must warn you that the result may be quite speculative.

I thought to start with foot anatomy of various Earth animals, reasoning that a comparison of independently evolved foot designs should help detect universal foot design elements, if there are any. The first rule I thought of (I was making up these rules as I went along) was to limit the discussion to walking on land, so I would not have study specialisations for walking on ceilings or climbing vertical walls. I will disregard microscopic and very small animals and will not discuss walking with tentacles (it's been done; start here and search the blog for tentacles). Wikipedia says that eleven animal phyla invaded the land, but omitting legless animals and overly small groups left only vertebrates and arthropods.

To start with vertebrates, various fish lineages crawl onto land, but as they haven't become completely terrestrial, they did not count. Tetrapod vertebrates are monophyletic as far as I can tell, so they all count as having one basic foot design anyway.

As for arthropods, at least six groups seem to have left the water on their own: arachnids, insects, myriapods, woodlice, some sandhoppers and crabs. However, if some or all of these had a common aquatic ancestor with fully formed legs, shouldn't they count as one design? Then again, these animal groups had a very long time to evolve different feet, so perhaps they should all count? In the end, I selected arachnid, insect and crab legs to add to vertebrate legs, giving me four largely independent foot designs to talk about. I had a look at robot feet too as a possible source of designs.  

Scheme of tetrapod limbs. The point is that the hand or foot ('autopod') consists of a number of parallel radiating elemets: fingers or toes. From Young et al 

Tetrapod feet
The basic tetrapod foot or hand has five radiating toes. Early tetrapods may have had more toes, which  did not necessarily all have to radiate from the same spot. Instead, they may have radiated sequentially, meaning one toe at a time branched off if you moved along the leg in the direction of its end. (see here how that 'Devonian pattern' shaped the feet of Furahan Scalates/Hexapods). During evolution, some toes became completely separated, such as those of predatory dinosaurs and birds, while others are encased in a common hull, such as those of elephants and sauropods. Some animals developed additional pseudotoes (panda's and elephants), while horses reduced the toes to just one. In many walking tetrapods the toes all point forwards and make a front-to-back excursion while walking, but I am not yet certain whether that should be a Foot Law or not, so a future post will ask whether backward-pointing toes or sideways toes impair walking. In any case, tetrapod feet consist of multiple segments: in human hands, for instance, fingers start with metacarpal bones in the middle of your hand leading to the three phalanges in your fingers (two in thumbs).  

Obviously, tetrapods are generally large than the other animals to be discussed, and that means that physical circumstances make their world quite different from that of insects and spiders. That definitely affects foot anatomy, and perhaps that merits another post.  

 

Typical spider leg. From: Nentwig et al. All you need to know about spiders. Springer 2022 

        
Arachnid feet
Spider (and scorpion) feet consist of a long leg segment, the tarsus, but only the end touches the ground. The end carries impressive claws and hair tufts. Why? Well, gravity presses the feet of large animals securely against the ground, but animals of insect and spider size need to deal with other forces too, such as wind: a breeze may blow them over, which is why they have splayed legs and why their legs need to hold whatever it is they walk on (the 'substrate'). That is why there are hairs, suction pads and claws to get that grip. 

 

Spider feet showing haiors and claws. From: Labarque et al

Claws are easy to understand as they simply grip the surface with friction, but pads and hairs are not as intuitively understandable: they rely on electrical Van der Waals forces as well as capillary forces to cling to the surface. This gripping has as a consequence that letting go of the surface is not a given, so they may have to peel their legs loose every step. Most spiders have two claws, but some have three, and the third one is apparently used to get a hold on the silk threads of their webs. There's a challenge other foot designs do not have to cope with.   

 

Insect leg from Wikipedia showing the tarsus

Insect feet
The insect tarsus consists of five or more segments at the end of which there is an attachment device that once again bears claws hairs or suction pads to adhere to a surface. The tarsus is segmented in insects, in contrast to that of spiders. The segments can flex, meaning the whole tarsus can curve down if a flexor muscle pulls on a single tendon that runs through the entire chain of segments. When the tendon is released, elastic forces in the exoskeleton straighten the chain again. It cannot curve upward, and the segments also cannot move sideways. 

 

Robotic insect tarsus, From Tran-Ngoc et al

The image above shows a robot foot, copied from an insect foot design. Pulling the tendon in an insect tarsus operates the claws and bends and stiffens the tarsus. This structure reminded me of human fingers that also consist of a chain of segments (phalanges) that flex in one direction only. The similarity stops there, as we use our fingers to curl around objects, whereas insect tarsi do not do that: only the claw/pad/hair assembly at the end does the touching. It is therefore not clear to me why the insect tarsus consists of many segments.   
 

Crab firmly gripping tree bark. From Wikipedia

Crab feet
Crab feet offer a surprise: there aren’t any. Of course, crab legs touch the ground, but the last limb segment, the dactyl, is slightly inwardly curved and ends in a somewhat blunted point. You can call the tarsus a foot, but if so, it is one the claws, pads, sticky hairs of smaller animals, and also without the fingers / toes of large animals. The dactyl itself resembles a claw, which made me think of a reason for the absence of additional clawy or sticky elements. Crabs, evolved in water, had to withstand the  sideways forces of flowing water. One way to avoid being swept away could have been to equip each leg with nice graspers at the end, such as fingers of claws. That would work, but only if the surface had irregularities small enough to hold with one foot's graspers. If the surface elements were larger, they cannot be held with one leg. But another solution would be to treat the entire crab as an eight-fingered hand, with each finger ending in a claw (the dactyl). This larger hand can grip on fairly large objects, provided, first, that the legs/claws clench inwards; second, that there are always few legs clenching the surface from opposite angles; third, that you have enough legs to do that. If I look at the photo of a crab hanging from a tree, I can see it as one large hand. 

A robot crab with such curved dactyls squeezing inwards did a lot better than when the dactyls did not squeeze inwards.  

In this view, instead of saying that crabs have no feet, you can instead regard the entire animal as one big grasping hand or foot.       

The robot Spot from Boston dynamics; the feet are just blobs. 

Robot feet
I guess everyone over the years has seen clips of Boston Dynamics' walking robots. The photo above shows Spot. I have always been surprised that the legs of these robots have only two segments, whereas tetrapods and arthropods have lots more. I guess the engineers felt that two segments were complex enough to start with. The robots also have no wrists or ankles and the 'feet' are just balls, probably made of a substance that provides friction. I suppose that the engineers were avoiding additional complexity. The design shows that you can get away with having no feet; well, robots can. I suspect that having feet is much better than having no feet, and that the difference lies in walking animals having sophisticated nervous systems that can easily control a large number of segments. 

There are many other examples of robot feet, but their makers used animals to base their designs on, so those do not count as aseparate designs. 

Conclusions
The various feet designs allow some rather tentative conclusions. Small animals, of insect size, apparently need feet that provide an active way to adhere to the surface while large animals may simply rely on gravity to press their feet to the ground. That's probably universal Foot Law Number One. Do you remember that my first rule was that I would look a walking only. not climbing or walking upside down? That may have been naïve, as insects seem to use the same mechanisms to stick their legs to horizontal surfaces below as they use for any other surface; in other words, the slope of the surface doesn't really matter for them. It matters for us, as large lumbering creatures hampered by gravity.

Radiating toes are a feature of tetrapods only, and tetrapods are also the only group with really large animals. The two features do not mean that all large animals must have multiple toes. After all, horses have one toe per leg, and so do crabs, in a way. I wouldn't say that multiple toes are necessary. So no Law here.

That leaves the presence of multiple segments placed one behind the other, as occur in insect tarsi and vertebrate feet. Arachnids and robots can do without, so no clear Law here either.

That's it for now. There will be more posts on Feet!