Introduction
A
differential is a device, usually, but not necessarily, employing gears, which
is connected to the outside world by three shafts, through which it transmits
torque and rotation. The gears or other components make the three shafts rotate
in such a way that a=pb+qc, where a, b,
and c are the angular velocities of the three shafts, and p and q are
constants. Often, but not always, p and q are equal, so a is proportional to
the sum (or average) of b and c.
In
automobiles and other wheeled vehicles, a differential allows the driving road
wheels to rotate at different speeds. This is necessary when the vehicle turns,
making the wheel that is travelling around the outside of the turning curve
roll farther and faster than the other. The engine is connected to the shaft
rotating at angular velocity a. The driving wheels are connected to the other
two shafts, and p and q are equal. If the engine is running at a constant
speed, the rotational speed of each driving wheel can vary, but the sum (or
average) of the two wheels' speeds cannot change. An increase in the speed of
one wheel must be balanced by an equal decrease in the speed of the other.
