First, a quick disclaimer about the design: Since there is a lot of variation between different bikes and small engines, this design will likely need to be adapted to fit your equipment. Itís important to figure out what you have before you commit to an engine or bike since some types wonít work very well.
The design was constrained most by the motors available to me at the time and my lack of welding capabilities. I wanted to use my all-terrain style 12 inch tire scooter along with a clutch but I couldnít come up with the necessary equipment. My searches of local (and on trip that was not so local) yard sales and eBay returned few useful motors. Mounting the motor without welding also posed a challenge since that was the efficient and obvious way to fix everything together.
When I couldnít get a motor with a clutch, I got frustrated enough to haul off and improvise a spindle driven design for my bike from 5th grade. The bike is quite small for me, but still allows pedal starts and has coater brakes which frees the handle bars for the gas and kill switch. I decided to make it front wheel drive for ease of construction: thereís a lot more free room up front.
For the engine, I used a small 26cc McCullough engine which came from a hand-held leaf-blower. It is a half shaft motor (only one side of the crankshaft is supported) without a clutch, but it had a threaded shaft which allowed for easy attachment of the spindle so I was happy.
I initially went very simple with the design: just make some brackets and bolt it on. That worked for a few miles when the engine mounts loosened up and the spindle stopped transferring power. I eventually modified the bike to include a spring tensioning system to keep the motor firmly on the tire.