This pushes and pulls on the rotor-blade control horns,
constantly changing the pitch of the blade as it flys around in a
circle. If you tilt the dinner plates forward, the blade flys at a
lower AOA in the front 1/2 of the rotor disk than it does at the back
1/2. Since its producing more lift in the back 1/2 than in the front
1/2, the blade flies higher in back. Stay with me here. As the blade
flies higher, its coning angle relative to the rotor head increases to
a greater angle than it does in the forward 1/2 of the rotor disk..
Therefore, its line of thrust relative to the fuselage is not vertical,
but is actually inclined forward.

Except the swash plate is not inclined forward in forward
flight. It's inclined to the right in forward flight, if the rotor
turns counterclockwise as seen from above, as in most American
'copters.
The rotor is a gyroscope, and trying to tilt one edge of it
will result instead in tilting the edge 90 degrees away in the
direction of rotation, like any other gyro. The rotor blades reach
their maximum pitch on the left side of the machine, and the blades
reach their maximum flap at the rear, tilting the disc forward. The
advancing blade on the right has minimum pitch and the front of the
disc is lowest.This is a happy coincidence, since we also need a lot
more AOA on the retreating blade to partly make up for its much lower
airspeed through the air compared to the advancing blade on the right.
Assymetrical lift has to be dealt with or the machine will roll over as
soon as it move forward, so the retreating blade's higher pitched AOA,
the blade's small downward flap approaching the retreating side and
rising flap approaching the advancing side also contributes to AOA
changes, and the lead/lag hinges on many rotors allow the blades to
accellerate on the retrating side and decellerate on the advancing side
at and therefore reduce some of the airspeed difference. Symmetrical
airfoils are used to minimize vibration caused by center of pressure
changes with AOA changes.
Helicopters are a lot more complex than they seem.

Dan