This question is a continuation of the question How to calculate variable pitch propeller parameters? mentioned before.
Actually, the theory described as an answer on the question above is the exact one i am using at the moment. However at the current stage, i want to make the calculations only for a 2D sectional symmetric airfoil, supposing a rectangular-shaped blade and not considering any twist. Also i forgot to mention before that my idea is to attach a rod on the root of the blade, set in an offset of the aerodynamic centre Xa.c (variable) and place a gear on it to connect with the opposite blade and synchronizing it. Also counterweights will be attached on the rod for balancing purposes but this is for later studies.
In this case i have ended up with the following formula for the pitching moments:
dM = dMa.c - dL*Xa.c
As can be seen here dM and dL are correlated there are two unknown there which are the lift coefficient Cl and angle of attack α.
from literature i found that Cl can be expressed as Cl0 + Cla* α and then to 2π*α (from thin airfoil theory), as well as Cm = 0 for symmetric airfoils.
Using these assumptions and moment equilibrium i end up on α=0 which doesn't make sense.