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!