There are quite a number of types of wheels; I've been able to come up with five types:
- Free-motion wheels: these are round wheels with no driving force of their own. Instead, the wheel spins freely on a fixed axle. The rear wheels on a front-wheel-drive vehicle are like these. Multiple wheels would spin independently.
- Locked wheels: like the free-motion wheels, these have no driving force, but rather than spinning on a locked axle, these wheels are directly connected to the axle, which spins freely. Many children's toys have a system like this. Multiple wheels on a single axle would all turn at the same rate.
- Axle-drive wheels: these are the driven version of the locked wheels. Rotational force (torsion) from the axle causes the wheel(s) to turn.
- Direct-drive wheels: each individual wheel has a drive system internally. Thus, each wheel moves completely independently of other wheels. Large earth-moving equipment often has wheels like this.
- Treads: rather than a fixed round shape, trades are a flexible strip which is "pushed" by an internal drive system, usually wheels.
Free-motion wheels
This option is fairly possible, though would result in some strange creatures (see diagram). The actual drive system could be legs, claws, or even a slithering motion; the wheels would simply reduce sliding friction, and possibly remove the creature from a dangerous environment, like caustic or hot surfaces.
The creature would need a fixed bone that protrudes from each side. The bone would terminate in a sphere. An organ just above the bone would excrete a cementing substance, similar to the oyster's pearl-forming system. It would coat the sphere, gradually growing larger. The sphere (and attached bone) would excrete a lubricating liquid that would also keep the area clean.
Here is a creature, viewed from the front (so cute!):
___ ___ ___
/ \ /o o\ / \
) O==={ _ }===O (
\___/ \/ \/ \___/
Small amounts of damage would be repaired, while large damage would result in the wheel breaking off and being reformed.
Locked wheels
This may be even easier to design; a creature with a soft, slippery underbelly would find round branches, rocks, or anything else shaped like a cylinder. It would lay on top of the object, pinching it slightly, and excrete a slippery substance. As it dragged itself forward, the cylinder would roll on the ground. These wheels would allow the creature to have a small, low-energy means of propulsion, but still grow quite large; it could also float, assuming it uses trees rather than rocks. Of course, it doesn't work well on land that isn't terribly flat.
_/
/,\ _________________
|_ \___/ __ __ \
\ ____// \\___// \\__/
// \__/ \__/
As it grew, it would have to find bigger and bigger cylinders, which may limit growth. Then again, a few well-placed fallen trees, and this creature may end up the size of a house!
Axle-drive wheels
This was the drive method I had the most trouble with. The best I can come up with is a system like the locked wheels above, except that the "feet" that push the creature along push on the center of the wheel, instead of simply sliding. That would allow the creature to have tiny feet and a flabby body, but still get around with ease.
_ _______ ________
/o\/ ____ V ____ \
> |||||| |||||| \
\__// \\___// \\__/
\__/ \__/
Direct-drive wheels
These are actually pretty easy to imagine; a slug-like creature finds (or builds) a large hollow cylinder. It then climbs inside and "walks", pushing the wheels forward. The wheel not only protects it against predators, it also allows it to achieve very high speeds going down hills!
====
// \\
// _\\
|| i_ | ||
||/ \_/ ||
\\ //
\\====//
Treads
Similar to the direct-drive wheels, this creature is fairly slug-like. It excretes a thin, slippery lubricant. When it has no wheel around it, the lubricant dries into a sticky, rubbery film. As the slug moves, it pulls the film from its back, across its front, and underneath itself. The film picks up rocks, sticks, and other debris as it is pushed onto the ground. At the read end of the slug, it flips the film up, where if sticks and becomes a rubbery tread. The slugs can use this tread for protection, both from enemies and from a hostile environment (hot or dry ground, salt or other traps, etc.).
/#########\
|#/,\_/ \#\
\#\_____/\__\#\
\############/
Would it work?
The biggest disadvantage to wheels in nature is that wheels sink, get stuck, or otherwise slow you down. Wheel are terrible for climbing. Walking, slithering, and burrowing are all more reliable means of transportation. If wheeled creatures "won out," there would need to be a good reason. Large, flat spaces, with ample materials and good reason to have wheels. Of those I listed, the slug-in-a-tube is most likely the best possibility. It's not hard to tunnel out a branch or wrap a leaf into a tube, and if it protects its inhabitant, all the better!