As long as it's coplanar, don't worry about cross products, just draw the free body diagram.
A point that gets missed: linear motion into an anchored brace point will only produce rotation if the linear motion of the center of mass is off center.
But the brace point is not necessarily anchored in 2D.
You really like word salad don't you?
I know what you meant to say, The brace has nothing to do with what you are describing. If you accelerated a disc from it COM, it won't spin. Because the force is applied as torque, it must spin.
The brace allows you to maximize the force applied due to the kinetic chain.