"At each Tai Chi move, the center of the body will be shifted. In order to stay in balance, the center must be reestablished each time."
To this statement I say...
This is a difficult concept to teach but...
I have a method that actually works quite well, a little something called "Pole Shifting".
What is it? Good question, glad you asked.
Take a pole, any pole will do but it works better if you use one that is slightly taller then you are, at least shoulder level though because any shorter than that and it gets a bit hard to feel what you should be feeling, and place the butt of the pole on the ground directly in between your legs and hold is straight up between your eyes in Preparation Form (I will be using the Yang style form names for this, they correlate to the other styles form names though so just replace those with yours and all will be good).
In PF you are standing with 50/50 weight distribution so this line is your "center", the pole correlates to that. During "Opening" the butt of the pole will stay centered by staying right where it is as you don't "shift weight" to either side, the top of the pole will move though both forwards and back slightly as you shift your weight to perform the movement, then return to center when you reach the end of the movement.
I'm hoping you now can see that the pole will be following your center during this exercise, though it does need a little help from time to time as they stubbornly refuse to move themselves.
The next thing that every style I know does is to shift weight. Doesn't matter what side you go to, the method is the same, but I'm going to stick with Yang posture names so...
"Shift weight to the left", to begin the transition into Grasp the Birds Tail/Ward Off Left.
To do this I teach hip wigglin'. Those of you who groan every time I mention that may do so now.
Wow! That was loud...
Use whatever method you use but none of them are ever going to equal hip wigglin', up to you though.
OK, while you wiggle your hips to make this shift your hands move the pole (I told you it wouldn't move on its own, why are you so surprised?). The butt gets placed into the inner arch of your left foot, the pole goes as straight up and down as you can make it as it presses lightly into the side of your bent knee, then up through the inguinal crease at your hip, and then up through the inner crease at your shoulder.
This is now your new "center of movement", the "pivot" you are going to turn around to make the whole body turn to the right.
That pole should stay upright for this and the top should not oscillate very much. This will take practice, don't beat yourself up when it does oscillate because it will, just work towards keeping that to a minimum over time. My pole still oscillates a little, I imagine Grand Masters poles wouldn't move the width of a hair but I'm not a GM so... It does a little.
That's the method.
What? You thought this was going to be hard?
Sorry to disappoint but it's just that easy.
Every time you "shift weight" you move the pole to the other side, it stays just like I described above.
The butt of the pole against the ground represents your root, it sticks to the ground like it's glued there until you shift to the other side, then you move it to the other side.
The top of the pole will follow your upper body direction, leaning with you in any direction.
This method works to teach this concept quite well.
Not only does it work it works the first time, right out of the chute.
I've been using this method to teach for decades. It's never failed me.
I have heard other methods that are very similar, one Master I know of uses wrapping paper rolls instead of poles and only teaches the bit between the hip and shoulder.
Bob Bu Hao (and how!)