So for a thought experiment I came up with the idea of a species that uses wheels for locomotion, sort of inspired by a species shown in His Dark Materials. Under what circumstances would such a species develop, and what would they look like? And more importantly, how would a creature with wheels work physiologically?
When designing a wheeled animal, there are three problems you must overcome:
- How to have a wheel as a body part without it being separate from the body.
- How to propel oneself
- Smooth roads; if you spend energy making them, that can be exploited by peers and is thus not a viable evolutionary solution.
His Dark Materials tackles all of those problems excellently with its mulefa race.
Rather than having their wheels as an organ, the mulefa have entered a symbiosis with the seedpods of local plants. These disc-shaped seed pods fit onto spurs on their legs, allowing the mulefa to travel speedily. Meanwhile, the grinding against the ground cracks open the pods, spreading the plants' seeds.
The mulefa evolved very differently from the real world's chordates; rather than a spine, they have a diamond-shaped skeleton with legs on each corner. While the back and front legs are used for attaching the seedpods two, the middle pair of legs serve as limbs to push when the rolling slows down.
Lastly; The Amber Spyglass' parallel Earth features formations of volcanic rock, smooth strands of basalt. These serve as perfectly good roads and are evolutionarily viable because the mulefa expend no energy in constructing them.
Under what circumstances would such a species develop, and what would they look like?
I imagine that your creatures' ancestors would start out by learning to roll on the already disc-shaped seed pods (many real seed pods are disc-shaped), consequently cracking them open on the rock and unknowingly helping the plants spread their offspring.
The creatures would get further on more round, smooth pods, so the plants which bore rounder smoother ones would have a selective advantage (since, the further the creatures ride the pods, the more likely they are to open).
This trend of specialization would continue until the seedpods were very well-designed for rolling and the animals for utilizing them.
And more importantly, how would a creature with wheels work physiologically?
They would probably be adapted for speed, and if they had those diamond-shaped skeletons their internal organs would probably be configured differently. Other than that, I cannot foresee any major physiological considerations, except those which you are free to make up yourself.
I'd posit an alternative scenario: even here on Earth we find cases of parallel specialisation in which two species effectively co-evolve - we refer to them as symbionts. Mostly, these tend to be cases in which the symbiont is microscopic relative to the host (think gut boita, skin biota et al) but we do see macroscopic, macros-fauna examples - birds (Egyptian Plover) which clean crocodile teeth, fish which clean parasites and dead skin from larger fish's skin, and so on.
Let's imagine a species pair which gets this done.
How about we take one of the elements of Morris the Cat's answer - and posit a critter whose whole body is wheel-like, but in our case when actively curled up like a pangolin or armadillo, and then posit a chassis critter which then cares for (feeds, cleans, protects) four wheelie critters, and whose terminal claws are hook-shaped (thank to Philip Pullman) but whose highly-motile lips (giraffes, horses) allow for a wide range of cleaning activities... let's further posit that the wheelie critters are typically slow-moving and heavily-armoured (therefore don't travel far) and so their selective pressure advantage to this is being widely spread and fed, which allows them to structurally support the weight of their host. The host evolved from an arborial species which brachiated quickly under branches, hence the long back-curved hooked claws (sloth-like but faster and more flexible) and so they too gain huge travel advantages from this symbiosis.
If you're not stuck with Earth-based skeletal systems, go for six-limbed to distribute the weight between more of the wheelie critters.
I think this could work - the wheelies are then also almost pets - companionable, cared-for, and of course, in situations of total extremis, as a last ditch, they are edible.
As it happens, this has been done before. A species in David Brin's Uplift series of novels uses wheels for locomotion.
G'Kek (ab-Drooli) - The first of seven races to illegally settle on the fallow planet Jijo, the G'Kek have since become extinct elsewhere in the galaxy, due to a campaign of persecution which the Jijoan exiles sought to escape. Physically, they are wheeled creatures with magnetically-driven axles and a pair of short "pusher" legs, possessing a compact trunk with two arms ending in weak, feathery hands, and topped by four highly sensitive eyes on stalks. Most of their emotive expression is produced by these eyestalks; twining two stalks together is equivalent to a shrug, while having all four eyes stare into each other connotes introspection.
The critical factor here relevant to your question is that this didn't evolve naturally. The G'kek's wheeled locomotion was deliberately designed into them by a more advanced race. There really isn't any realistic way that a wheel/axle structure could evolve naturally, so your species would have to be at least partially artificially evolved by someone else.
The only alternative I can think of would be for the species entire BODY to be the 'wheel' and they just roll around. You could have manipulator limbs and sensory organs and so forth attached to the 'hub', but they would have to operate like an owl's neck does, once every rotation of the 'wheel' they'd have to spin a turn in the opposite direction to avoid overstressing the joint where they attach.
A creature with biological wheels is pretty unlikely to evolve naturally, as there are few (if any) reasons why a half-evolved wheel would outperform a half-evolved leg. However, a creature that evolved to behave like a wheel is definitely reasonable: For their origins in the shallow reefs of your world this hypothetical creature, the 'armawheelo', evolved a unique defense mechanism to dissuade predators and travel in comfort.
The armawheelo's back skin consisted of tough, slippery, streamlined scales, and when a predator approached not only would curl into a ball to protect its vulnerable underbelly, but it would use it's flippers to spin itself as fast as it could. Predators struggled to get a grip on the spinning armawheelos, giving them enough time to bolt into the safety of sharp coral and rock where the armawheelo made its home.
As the armawheelos began to move onto land, their curling and spinning found a new use. The cliffs beside their watery homes were bountiful, but dangerous. To escape predators, the armawheelos would curl into their trademark ball and use their flippers to propel themselves down the cliffs, rolling and bouncing to safety. The armawheelos who could predict the smoothest, safest slopes back to the water had the best chance of escape.
As the armawheelos with the best understanding of slopes moved from their coastal origins and onto the rolling plains, they finally find a purely locomotive use for their curling prowess. They waddle to the top of the nearest hill, scout out a promising area for the best grubs around, and roll their way towards it in a way that's faster and less tiring on their stubby legs. They need not fear birds who cannot pierce their scaly rolling hide, and their propensity for careful observation of hill and dale helps them avoid any would-be predator.
Expanding from @Morris The Cat answer, I think the best idea is a creature that can roll on its entire body.
My idea is a kind of shellfish, who has an almost spherical shell. They can breath for a small time out of water and protrude the head and the tentacles from an opening in the shell, but can also completely seal themselves inside it.
They live near the coast, in a place with high sloping rocky reefs and strong tides. When the tide rises, they reach the top of the reefs, maybe because they've adapted to integrate their diet with some kind of vegetables the live over there. But at some point, during the low tide it can become too dry for them to survive (or staying there too long would attract birds and be dangerous), so they must quickly reach the sea. The quickest to reach are the most likely to survive.
So, in the millennia, some shellfish started to roll on their shell along the sloped reefs to reach the sea. In even longer times, it is possible to forecast that they would learn to move also on flat ground, developing some methods to give themslves momentum and direction. For instance they could give themslves impetus using the tentacles (like somebody giving himself impetus on a scooter), or - even better - contracting their muscles to continuously move ahead their center of gravity.
Probably they would move only for short paths (because they have no way to check direction while rolling), or could evolve small holes in their shell, under which they have light-sensing tissue or rudimental eyes.
This could be possible even with radial-simmetry animals, like starfishes, which could roll on their sides (think of their arms as the radia of the wheel). They have more than five arms (better rolling this way), and moving them they can gain momentum and steer. They could see the direction by having eyes (or less fragile light sensing organs) on the point of their arms, so that at every time at least one eye is looking ahead.
Despite what others have suggested, I think that wheel/axles could evolve naturally. Many systems that we have may have originally evolved for one reason and then was co-opted for another. It has been suggested that bones first evolved as a way to control calcium concentrations, but have since been used as a structural element.
Our creature first develops several bony shield-like appendages as a defense against predators. These appendages develop a smooth round form, which makes it hard for its predators to grab onto, which have sharp claws. The creature begins to secrete an oily substance around the shell that makes it even harder to grab onto. This appendage protects it against most predators, but the shield is heavy and makes the creature slow because it has to lift the shield or drag it. The creature than evolves a mechanism to release the shell and run away, which can later regrow. The shell grows much like an antler—it is immobile and covered in living tissue during a part of the season, but becomes dead and detachable during the rest of the year.
The creature lives on a planet where the surface becomes molten during the summer (this is the season where the creature hibernates in deep caves and regrows its shields). During the rest of the year, the surface of the planet is quite flat and smooth. Hence, we have all the ingredients for the creature to evolve wheels. One of these creatures is born with shields that don't detach well, but start to spin along the ground on the joint (using the lubrication the creature is already producing). This allows the creature to run around more quickly without lifting or dragging its shields. This creature's offspring very quickly evolve appendages that act less and less like shields and more and more like wheels.
Now the creature runs on legs and uses the wheels for more efficient travel on the flat surface of the planet (like a skateboard). Subsequently, the creature develops a week electrical system that allows it to apply force to the wheels. You see, the creature is able to deposit metal on the wheels (this isn't too crazy since bacteria form metal nanoparticles). Maybe this metal strengthened the shields or wheels. This metal develops by chance has a coil-like structure that allows it to respond to magnetic pulses produced by electric currents in the nervous system in axle. This coil evolves toward a efficient AC induction motor design, allowing the wheels to be directly driven. The legs, now mostly being dead weight, become smaller and smaller until the creature drives on motorized legs alone.
I have for kicks designed a biological wheels system in class once. The problem with any of these wheel systems is that it needs to evolve rather than be engineered. Somewhere during that evolution you have half a wheel. How useful is it? How does half a wheel that probably cant even turn, start becomming a full wheel that can? How does the bloodsupply and nervous system evolve?
One thing I did run up against is that even my designed bio-wheels would have a limited time they can function. During rotation bloodsupply will be greatly limited to the wheel part. You could offset most movement to the "hip" where the wheel it attached and basically allow several appandages to turn the wheel, but the skin, bone and flesh will eventually need blood again. Operations on your arms can happen while all the blood is out and it takes several hours before permanent damage happens so it could work for most trips.