A bandsaw is a continuous saw blade stretched between two rotating spools. A deck provides a level feeding surface while a fence, perpendicular to the deck, provides guidance.
Bandsaws can be any size and cut at nearly any speed. There are bandsaws that you can clamp to a table and use to cut baseboard; most of these are worth their weight in non-functional bandsaws. There are bandsaws large enough to have foundations poured specifically for them. These accept whole trees at a rate comparable to second gear in your car.
FIRST ATTEMPTED
Today's bandsaws are preceded by a shocking number of prototypes.
The bare idea was patented in England in 1809 by William Newberry. In practice the saws were impractical, because a) the metal then was incapable of flexing at high speed, and b) the welding then was incapable of tolerating load.
Unfazed, Benjamin Barker of Ellsworth, Maine filed the first American patent on the same concept in January 1836. His patent application would probably not have passed review, being that it contained obvious prior art (as in, maybe from England probably). Review would not be introduced to the patent process until July of that year. Barker's bandsaw had wheels five useless feet across and a blade 34 useless feet long.
William Cary patented the bandsaw a month later in Poughkeepsie, using similar machinery with an extremely wide blade.
Other fruitless designs attempted to redistribute the pressure placed on the blade. Lemuel Hedge patented two semi-normal designs, one of which featured a set of guides on the upper wheel. In 1851 he patented a saw that incorporated several small wheels and a driving belt, to tension only the section of blade under load. Well attempted! Others, patented by others, involved hinged plates, chainsaw blades, hand cranks.
FIRST COMPLETED
The breakthrough came in 1846, when Anne Paulin Crepin developed a welding technique that produced blades that could cope with load. A. Perin & Company, based in Paris, soon bought rights to Crepin's work and applied it to improved alloys. Thus materialized the modern band saw blade.
The first commercially-available bandsaw was from Pryibil in New York, whose first ad appeared in the April 20, 1867 issue of Scientific American:
IMPROVED PATENTED ENDLESS OR
band saw machine; can be worked Faster than any
other in use ; they work smoother by an adjustable gate,
and Saw Breaking !! entirely prevented.
Molding Machines, Shafting, and Pulleys constantly on
hand.
And it was good.
It's a graceful thing, the Pryibil. Abandoned, thanks mostly to improved metalworking, was the Wile. E. Coyote wood-drums-and-paddles quality of earlier designs.
By 1876 there were eleven different bandsaws on the market, eight of them associated with Pryibil. In the United States they were unavailable anywhere west of New York nor south of New York. Most were cast iron and four-footed; most were of the C-Frame design demonstrated by the external link. Some were of flanged frame design, which (broadly) involved enclosing the spools in wood paneling.
USE/SAFETY
Bandsaws you can readily buy today fall into two categories: vertical and horizontal. The blade in a vertical bandsaw runs vertically, etc.
Vertical bandsaws are favored by woodworkers. Because a bandsaw blade travels in only one direction, it produces a very clean, precise cut. Vertical bandsaws are often built without fences to allow free movement of work material. They can be intimidating at first, mostly because they are quite a bit more dangerous than horizontal saws. The bandsaws in some furniture factories, for example, expose six feet of blade. The blade travels down so as to pin the material to the deck as it cuts.
So, safety.
Vertical bandsaws require much more attention to your fingers. Keep those close together and check often on where they are (I do). You want your elbows as far out as you can hold them while still performing the cut, so that the arc of your hand tends to be away from the blade. Stand with feet at shoulder width. Breathe slowly. Try to come out of the cut without pinching the blade--fan both hands away at the same time, like you're making snow angels. Go nice and slow, always. Don't be pissed off; don't be scared; calm produces good work. Use push bars for small pieces. Do not wear gloves--those catch.
Horizontal bandsaws are primarily used to cut metal stock--pipe, bar, and the like. Because they require the work to be clamped in place, they lend themselves to more precise, square cuts. The spools and blade are on an assembly that pivots down onto the material. Lubricating/washing fluid waits in a reservoir and travels through valved tubing to the site of the cut. The speed of the descent is usually controlled by a hydraulic piston and fine-tuned by a large adjustable spring attached to the pivot point.
In either case, the blade is tightened by moving the spools further apart. The mechanism for this varies from machine to machine; expect either a large bolt/screw or a hand-turned wheel. A blade that's too loose will slide, and most likely run off the spool. A blade that's too tight will snap with just-over-normal stress. A good rule of thumb is to tighten your screw or turn your wheel as much as you can, then back off a quarter-turn.
Always clamp your material to the fence on a horizontal saw before starting your cut. Double-check that; with long material, it can be a rude goddamn surprise when the blade snags and nothing's clamped. As with any saw, the type of material you're cutting should dictate the speed of the blade. Softer material allows a faster-moving blade. If you hear whining, slow your descent or your blade speed, or tighten your spring. Always take the beginning of your cut more slowly to establish a controlled path.
Fine metal cutting typically involves a steady flow of oil or water over the material. If you see smoke, increase fluid supply and/or, better yet, slow down.
Unplug every tool ever before switching out anything--blade, cover, screw, anything. I don't care where you are, or how much you paid; switches fail.
Sources
Experience.
Jeff Joslin, "Pre History Of Band Saws."
http://wiki.vintagemachinery.org/Pre%20History%20Of%20Band%20Saws.ashx
Raymond McInnis, "Glossary Bandsaw."
http://www.woodworkinghistory.com/glossary_bandsaw.htm
Philip Marshall, "Band saws."
http://www.philipmarshall.net/hs/techniques/systems/wood/machinery/band_saws.htm
Wikipedia. "Bandsaw."
http://en.wikipedia.org/wiki/Bandsaw