This is the first version of a bicycle where when you pedal forward the bike moves forward and when you pedal backward the bike still moves forward, but in a different gear. No gear shifter or derailleur is necessary. Although the basic mechanism works in this version, it is not practical for an actual bicycle because of the high torques involved.
Step 1: Designing the Hub
Simplified schematic of hub. Roller chain transfers torque to the sproket. During forward pedaling, the roller-pin clutch on the left catches and rotates with the sproket. Torque is also transfered through the gears (not shown) in the gear box to the "anti-sprocket," which moves in the opposite direction of the sprocket. During backward pedaling, the clutch on the right catches and rotates with the anti-sprocket. Regardless of pedaling direction, one clutch catches while the other is free to rotate. By connecting the clutches to the spokes of the wheel, we have a wheel that moves forward regardless of pedaling direction.