# Car Differential With Spur Gears

Yellow and violet gears have the same tooth number.
Rotary axes of grey case, blue and green shafts are in line.
The blue and green shaft carry car wheels.
This mechanism maintains equation n1 = (n2 + n3)/2.
n1: velocity of grey gear and case (fixed together).
n2 and n3: velocities of blue and green shafts respectively.
The mechanism has 2 degrees of freedom. Two input motions in this video are n1 and n2. The video shows three stages of the blue shaft:
1. n2 = n1
2. n2 is larger than n1
3. n2 is smaller than n1
Yellow and violet gears roll on each other only when n2 differs from n1.
Assembly condition: when axes of blue, yellow, violet and green shafts are in a plane, axes of cross holes on the blue and green shafts must be parallel. If not, velocity of the green shaft will be irregular when n2 differs from n1.
The space around yellow and violet gears is filled with oil. Rooms of two sides of the contact teeth are connected via a spring valve. Thus friction torque is created when the two gears roll on each other to prevent the slipping once one wheel losses traction. Complete closing the valve will lock two wheel together.

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