That's, the rotation spider gear of a differential.
basically the wheel rotate in two direction, which mean it I universal joint.
the wheel are connect to a point on the surface of the wheel.
it is hard to explain graphical by mathematically is very easy to see how the equation of a differentia work. this is how.
a differential gear has two degree of freedoms, one os the rotation around the crown axis and the other around its own axis
in the lack space of the we can represent that as a vector
W = (Wx, Wy, 0)
now imagine two point on the surface of the gear. but with symmetry alone one axis only
let the point attached to left wheel be
pl (-xl, yl, 0)
and point attached to the right be
pl (xl, yl, 0)
now the linear velocity of each one of those points is give the cross product, of the distance to the cog.
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vl = cross (w, pl) = (0, 0, Wx * yl + Wy * xl)
vr = cross (w, pr) = (0, 0, Wx * yl - Wy * xl)
and if we make yl and xl = 1.0 and we link the unit veleocity to a point on a tire at a radio 1.0
and this is a trivial relation joint, we get the kinematic relation for the tire angle velocity
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left_tire_omega = Wx + Wy
right_tire_omega = Wx - Wy
as you can see that instant velocity of that point is the equal to the angular velocity of one axis minos the angular velocity of the other axis. This is exactly the kinematics equation of a differential.
Now if we control Wx by plugin in to an engine (a engine body conceded by a joint acting as a transmission) while Wy is controlled by the two tires linked to the middle body.
differential behavior should emerge naturally as opposed to the nonsense of dividing the torque by half. Also notice that it is no limited to just two tires, we can plug four tires for a four wheel drive car.
It is not completed yet by I can see the emerging behavior already, I just hope the numerical errors are small enough that do not ruin the effect.
finally the object will be a null collision located and the center of the axel or the center of the vehicle, for now It an let it be there for calibration.