I will make an effort to demystify one of the most persistent myths in online forums about inverting the rear truck. It is assumed that something uncanny happens when the truck is inverted, just because the axle rotates the other way than usual.
What I’ll try to show is that an inverted truck is simply a truck with a negative pivot axis angle. If by dewedging the truck we could lower our angle below 0° (which is actually possible under certain conditions, but let’s not focus on this now), then in effect we would have inverted it. I’ll start by examining all the possible configurations between front and rear truck angles.
Let rear pivot axis angle be rpaa, front pivot axis angle be fpaa. (A reminder of the meaning of the absolute value might be needed.)
A) As long as the rear truck turns less than the front truck (|rpaa| < |fpaa|), then the front of the deck will turn towards where the rider leans, as usual (see image).
B) The same is true when rpaa > fpaa, but that makes the skateboard almost uncontrollable, because the rear is too maneuverable.
C) If the two trucks turned the same but with the rear inverted (rpaa=-fpaa), then the board would just move in parallel lines in the same direction.
D) If and only if the rear axle turned in absolute terms more than the front one, but with the truck inverted (|rpaa| > |fpaa| and rpaa < 0°), then the board would indeed follow the opposite direction of the where it’s tilted.
Inverting the rear truck works quite predictably, because when the rider leans towards the turn and pushes against the board (i.e., a pump), the board tends to move towards the turn (i.e., the inside of the curve), where the center of mass is. Nothing eerie or singular happens at 0°. It’s an ordinary continuum. Inverting is “de-wedging,” nothing more, nothing less.
If any of the above gives you trouble, please let me know to edit it for clarity. As everything else in this blog, it is not information I ask you to just accept, but an idea I want you to understand.