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ORIGAMI LOGIC, ? Yeah, sure, I'll try that!

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RJSV:
   Next, is shown the positioning with everything brought to maximum travel, (or some climax).
Like I've said; the fold lines have been creased so things almost go 'pancake flat'.
It's full CCW, and you can see the 'pancake' effect; where the walls of the box are offset, by the amount of the small walls.

RJSV:
For the alternate 'folding' state, (please see picture), that's a CW or clock-wise folded object.
   Mechanical advantage is from activating or pushing an arc about 6 inches, meanwhile the sliding output moves about 3/8 inch, correspondingly.
That's about 16 to 1.

RJSV:
Imagine now yourself standing, and gently rubbing hands together.   It's the act of withdrawal, or pulling a hand inward, that's the power-move.   With the paper card model discussion, there is a pairing of two flaps, still allowing sliding.
When the card model INPUT is active, there is a section, or strip that is 'folded' over a point, but also that blunt 'point' moves, so the thing is put into tension, causing withdrawal from the play field.
   So, I'm not certain if the 'mechanical advantage' is due to the length of the short wall, (of interior box shape).

RJSV:
   GOT MY BOOK  !!!
   Hello:
   My (Amazon delivered) Engineering Textbook, written by Bingim Young University Prof. Larry Howell is chock full of mathematics.

   Besides the obvious, helping myself in dealing with 'flexible' mechanisms, (like digital gates and transmission lines operating mechanically),
where I've contemplated a couple of historical trendy technology.   The particle or light 'beam' weapons (1985'ish) and the whole nanotech labled things (1995'ish) as examples.
I think some efforts around the special tech innovations occur quietly, as academia and industry maybe have less interest in sensationalism.
   One related product comes to mind; that is those single-piece plastic lids and bottle closures that closely reflect the discussion in that textbook.   So now I'm wondering at what point did that single example get introduced, present now in various retail candy containers we see on the shelves, as truly improved?

   As a short review, the Mechanical Engineering Textbook;
   Goes into matrix math, and Modulus of Elasticity.
   Solving simultaneous equations and advanced algebra manipulations, as part of the mechanics and physics analysis.
   Navigating between Sines /Cosines / Tangents and imaginary numbers.
   Concepts of virtual displacements and virtual work.

   Appendix containing data on various properties of materials and geometries of fabrication.

---------------------------------
   There are, also, some lectures by Prof Larry Howell, in directly related material (I.E. youtube).

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