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I have heard certain AWD cars have an epicyclic center differential that provides more torque to the rear axles than the front axles. I have watched a video by KYLE.ENGINEERS
(link https://youtu.be/BRmwHEjEyVM),
and he says it can do this torque split with no relative rotation between any of the gears.

How can it give more torque to the rear axles with no relative rotation between the gears? In order to multiply torque, doesn't there have to be relative rotation between the gears?

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The presenter says there is no relative motion in a steady straight line. The engine is driving the planetary cage, and in steady state conditions the planet cage input, the sun output and the annulus output all have the same rotational speed.

The torque split is achieved by the different gear ratio beween planets/sun and planets/annulus. The torque transmitted is porportional to the gear ratio, and is independent of the rotational speed. No matter what that ratio is, it is possible to have the whole epicyclic unit rotating as one.

It is only when a differential rotation speed is needed (driven by demand from the front or rear) that there is any relative motion between the three components.

This is similar to the conventional differential, when under steady conditions there is no rotation of its internal bevel gears, although the torque split is 1:1.

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