So the basic principle behind continuously variable transmissions are nothing new, and have been used successfully in snowmobiles and various cars over the years. So why not simplify it and apply it to a bike, which doesn't have nearly the torque requirements?

The basic variator mechanism consists of two cones (which act as the gears) connected by a belt. In order to change the input:output ratio you just need to slide the belt laterally along the cones.

In order to make sure that the change in gear ratio corresponds with the change in the bike's speed, have a spring-tensioned centrifugal-governor style system so that as the rear wheel increases its rpm, flyout weights linked to the two cones automatically adjust their position.

Ideally, you'd be able to pedal at a consistant rate and the variable gearing would automatically do all the work for you.