There are two basic types of spinning wheels: spindle wheels and flyer-and-bobbin wheels (also called treadly wheels).
A spindle wheel is a wheel that has a spindle almost exactly like a support spindle, but it's driven by a wheel.
There are a lot of different kinds of spindle wheels. The first ones invented were in the East and where called Charkas, which is the Sanskrit word for "wheel." They were similar to this kind of a wheel: http://www.woolery.com/Store/pc/Ashford-Charkha-c105.htm
There are also small, folding charkas that fold up into a hardback book size and shape (usually called a book charka), and larger versions called brief case charkas, etc.
The spindle wheels that you'll see most often are called great wheels, walking wheels and wool wheels.
They are all basically a spindle that has support, and that is driven by a wheel that is usually turned by hand, not
by a treadle.This
is the kind of wheel that sleeping beauty ran afoul of. Spindle wheels got a lot more use than spindles did, once they were introduced, and they frequently had spindles that were metal. The amount of use that they got, over a period of time, tended to sharpen the tip of the spindle until it was really dangerous. Add that to the fact that sheep go out and play everyday in the dirt (you know, the stuff that has a lot of tetanus organisms), and it's no wonder sleeping beauty could get seriously hurt on that wheel!http://en.wikipedia.org/wiki/Spinning_wheel
Wikipedia has a whole collection of photos of different kinds of wheels and lots more information. I'm going to do more articles about treadle wheels, but you can read ahead here.
Great wheels were called that because they have a large wheel. The name walking wheel came from the fact that a spinner would have to stand, and would usually walk to spin a longer thread before she went back to wind it onto the spindle. The name wool wheel comes from the fact that the larger spindle wheels were made to spin wool, and had lower ratios, which was just what was needed to spin wool.
When a spinner refers to ratios in connection with a wheel, it tells you how many twists the wheel adds to the singles being spun for each revolution of the wheel.
Most of the charkas were built with the intention of spinning cotton, so they had higher ratios. To give you a better idea, the bottom ratio for treadle wheels will give you 3-1/2 twists per one revolution of the wheel, where the top end is more like 22:1. But some of the charkas would give you more like 36:1 to really add a lot of twist fast.
With almost every spindle wheel, you'll find a wheel with a drive cord. The drive cord will drive a whorl, and sometimes they have several whorls close together with different diameters so you can make the spindle go faster or slower to suit you by changing which whorl the drive cord is on. Some charkas have an accelerator where the wheel turns a whorl on an axle with another whorl that has a drive cord that drives the whorl on the actual spindle. This is usually called a Minor head, after the gentleman who invented it, and it's a way to get more revolutions out of the spindle for each revolution of the wheel.
Some of the book charkas and similar ones are more complicated because they have extra parts that allow them to fold, but this covers the basics of spindle wheels.