http://www.americanspeedster.com/http://www.stevproj.com/FAPToys.htmlthe site these pictures came from seems to be down at present. http://www.thenorwoodhome.com/2008/09/building-an-mg-tc-pedal-car-introduction/
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Start with a childs size bicycle, salvage the pedals and drive chain, reroute them to run a rear wheel in a 3 (2 on front) wheeler.
That's probably how I'd do it. If you don't want gearing (which, for age 3, you might not), there's always the Big Wheels approach of just putting the pedals directly on the front axle, perhaps by bending the front axle into a crankshaft shape (with or without actual pedals).
There's a dedicated forum: http://www.pedalcars.info/forum/default.asp This could be scaled down: http://www.pvcplans.com/kartcross.htm Some possible tips: http://www.s-p-i-l-l-e-r.com/pedalcar/en/