I have been racking my brain on how to develop a rear coaster brake system for a pedal go kart for a while now and it dawned on me the other day that I was making it too complicated.
It does however require two bicycle rear ends to complete the task but in reality it is quite simple.
The way it works is that the coaster brake rear end from one bicycle is made to drive a solid drive axel.
The wheel hub will need to be de-spoked. A sprocket will then need to be welded onto the wheel hub. This sprocket then will drive the rear axle.
The lower rear section of the bicycle should be retained and mounted into the framework the go kart. It is important to maintain a workable drive ratio, and typically 1 to 1 drive will work best for the weight involved on the cart.
Ideally the most robust drive uses the bike frame work (cut back of course) because it has metal frame work. If you cannot afford to use the bike frame work, then metal plates are the next best option. The metal plates are fixed into the frame work using sheet metal screws or lag screws.
When using a bike coaster system, a basic understanding is needed. The way it works is that the hub drives the wheel and the inside of the hub acts as brake. So in action (as many of us grew up with) the pedals cause the bike hub to turn in one direction, coast in the other and then brake when the pedals are reversed.
The important note in all this is that there is a brake arm that hangs off the opposite end of the drive hub. This brake arm needs to be fixed to the frame work; otherwise the brake will not work. What will occur if the brake arm is not fixed is that the brake arm will tend to rotate when the brake is applied. So fixing it is important.
As you have been guessing, at least two bike systems are needed to make this drive system work. The reason I say that, is because the drive ratio of 1 to 1 is needed, and in order to attain this a large sprocket in the rear is needed. This large sprocket will be removed from a pedal system off of another similar bike. Then this sprocket will be attached to the smaller drive sprocket on the coaster brake system. Because of the forces associated with the pedal go kart (mainly how heavy it is) a ratio of 1 to 1 or even higher is needed.