According to this tutorial over here: http://commons.wikimedia.org/wiki/User:Phys1csf4n
It is stated that $a_A + a_B + 2a_C = 0$
But I don't understand the logic used. Is there any way to prove this mathematically, instead of logically?
It holds true for the two cases presented, but how do I know that it holds true for every single case? I can not think of the solution for some reason. I do know that $T_4 = T_3 = T_1 + T_2$ and $T_1 = T_2$, but there is no way to relate the acceleration because the masses are different.