With Java animations by Bill Casselman

Proofs 1. Choose a coordinate system moving with the green rack. In that coordinate system, the top rack moves with speed a-b. Instantaneously, the top of the pinion is moving with speed a-b, the bottom is moving with speed 0. It follows that the center is moving with speed (a-b)/2. In a stationary coordinate system, the bottom rack moves with speed 0+b=b, the top rack with speed a-b+b=a and the pinion and slider with speed (a-b)/2+b=(a+b)/2. Back to 2. The straight-line differential.

• 1. What is a differential gear?

• 2. The straight-line differential

• 3. Elementary rotary differential

• 4. The differential in the Antikythera Mechanism

• 5. The differential in your car

• 6. Starley's 1877 differential