Rigging for Popup Book

Question

I've struggled with rigging a simple popup-book example; I don't even know if it's possible. A simple example:

This shows three states of a popup-book. The top state is the "open book" state. The book (green pages) lies open. It has a popup (blue) attached to the pages and starts perpendicular to the book.

The middle state shows the book partially closed. Closing the book causes the popup to rotate inwards and downwards.

The lower state shows the book halfway closed. The popup rotates even more. Note: The perspective is deceptive -- the topmost edge of the popup is lower than the attached edge.

I would like a rigging that allows me to animate opening/closing the book, and the popup rotates accordingly. I haven't figured out whether there is a working combination of forward/inverse kinetics, connected/unconnected bones, and constraints that would make this work.

Any advice is welcome!

Answer 1

I found a way to do this with a simple rig (see attached blend file).

There are two armatures, one for the book, the other for the popup.

The book armature (yellow bones) above controls opening/closing the book:

1. Each page (L and R) has two bones; the innermost bone controls opening/closing via simple rotation. The outermost ones are there only for targeting the IK constraints in the popup armature.
2. The tails of the inner bones (Page_L and Page_R) are positioned so they are attachment points of the popup.
3. A rotation constraint on Page_L and Page_R makes the book open on axis for the book binding.
4. Rotate Page_L to open/close the book.
5. It only needs forward kinetics for opening/closing -- no IK constraints.

This image shows the Popup armature (orange bones):

1. The Popup_Center bone is the root bone; its head is where the popup middle is attached to the book and its head is where the popup apex is attached.
2. The Popup_L and Popup_R bones extend to the book attachment points.
3. IK constraints keep the popup attached to the book pages:
   • Popup_L IK constraint targets Page.001_L of the Book armature
   • Popup_R IK constraint targets Page.001_R

By rotating Page_L to close the book, Popup_L is pushed, due to the IK constraint.

Popup_L pushes on Popup_Center, forcing it to rotate towards the book.

Popup_R also pushes on Popup_Center due to its IK constraint.

Some additional notes:

1. I probably could have gotten away with using only a single armature. With two armatures, I could modularize multiple popups.
2. A control bone for managing the rotation of Page_L would have been nice, but I don't know how to do that.
3. I probably could have been more flexible with the bone placements, using offsets, but I haven't learned yet how to do that.
4. Blender is amazing. What I thought would be difficult or impossible is actually easy, once I learned how IK targets work.
5. I would have liked to make an animated gif of how this works in a 3d viewport, but I don't know how do that (advice, anyone?)

Here is an updated blend file: