Man this is hard to describe.
Here is what Im doing in a nutshell.
3D Text layer swings like a hinge from its anchor point which has been moved to the top of the text layer.
I duplicate this text layer and move it below the first one and am trying to parent the anchor point of the new text with the BOTTOM of the swinging text. They will look like they are swining independently but are "hinged" together at the bottom.
Here is an example:
Notice how the first 3 words that pop up in the animation are "hinged" together.
I have been thinking how to do this and for the life of me cant come up with any ideas.
Just use the anchor point tool to set the anchor point of each layer of text on the hinge point, then set some keyframes. The kinetic movement, the swinging back and forth, is easier to do with an expression than to keyframe by hand, but the positioning is easy. The expressions are right there in your example so that part is easy.
Start by setting your type layers in their final position after the hinge unfolds. Enabling the grid or setting some guides will help you accurately position the anchor point. then add a couple of keyframes for position and rotation and the expression and you should be done. Parenting will only help a group of layers to move together. I would have the second layer parented to the first, the third layer parented to the second. Then you add rotation keyframes by hand.
BTW, the HTML code on vimeo causes a bunch of extra characters to be added to the expressions so I would select the expression text in vimeo and then hold down Ctrl+Alt+Shift+V on a Mac or Ctrl + Shift + V on a PC to paste the expression to a simple text editor first, then copy and paste again in AE to avoid errors.
Here are the expressions as effects presets. Just apply and then adjust the position and rotation keyframes to fit your project.
The last rotation keyframes are set to 0, the values you see in the screenshot are the result of the bounce expression.