It turns out that cats have special wiring! The wiring travels from the brain to the muscles in the voice box, and this wiring is able to vibrate the muscles so that they act as a valve for air flowing past the voice box. The muscles work both during inhalation and exhalation, which creates the impression that cats can purr continuously. The air passes through the valve, which opens and closes rapidly to create the purring sound.
I found another link to the base mechanics of purring here: http://messybeast.com/cat_talk.htm which is a treasure trove of cat information from base care to basic colour genetics, colour patterns and genetic anomalies like curled tails and polydactylism.
Founder of the Dyslexic Clique. Dyslexics of the world - UNTIE!!