Free Body Diagram of Simple Inverted Pendulum

interesting. Good suggestion. GA, Ky.

The reason that B is correct and A is not, is because the forces are applied at Point O. There is no force applied at M.

To balance the system in the vertical, at the point if origin, by most efficient means, the initial Fx will be negative (to the left), and the Fz will be negative (down) at point O. This should set up a 'fall' with respect to Mg in the positive x direction. The Fx & Fz will then switch to positive, carrying the system back to the Point of Origin. Hope I didn't dumb it down too much there. The power profile will be elliptical.

The faster you wish to return to 'balanced' in the vertical the greater are the initial and final forces (ellipse). If you think about controlling the energy of the system, you will be on your way to understanding the balancing of the system when other forces are applied ...

Now imagine that Point M were a human knee ... then A would be correct. And of course the rod would only be semi-rigid and have some nominal weight.

Try this link to inverted pendulum control ... It might make things intuitively clearer. And some cool video. http://www.sc.ctrl.titech.ac.jp/SCHP/research/index.php?lang=e&page=InvertedPendulum

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Kirk tells Scotti to let the Dell's cat out the bag. Scotti says 'Aye Aye Captain ... Full Impulse power ... But it's gonna take a moment. '

I should have said, if it were a human knee, FBD1 would be correct, instead of A.

Because Fx and Fz are reactions to torque Tq and weight Mg.

that means we will have Tq and Mg at bob end and Fx and Fz as reactions to them at fix point O. we need not to have reactions Fx and Fz at bob. that is why B is correct , A is incorect.

O is not a fixed point. See the link I posted above.