Servos to fold paper Cubes & Origami

Ok so i’m trying to get these paper origami cubes to fold. They fold from top to bottom and fold vertically down to like a square. Imagine you had a cube but wanted to shrink its height basically. I will put a servo inside each cube that will cause the cube to either collapse down to a square or expand back to a cube. They will be placed in a 5 x 5 x 5 grid And the arduino will control the entire configuration of them so i can manually tell which ones i want to fold or unfold. Obviously there will still be a little thickness because of the servo so it won't fold completely flat, however if i can get it to be 1/5 of its original height that will work fine. I originally was going to use nitinol wires for actuation, however nitinol is extremely sensitive to current and temperature so decided it would be much easier to use servos instead.

The problem is i cannot figure out the appropriate use of the servo to achieve the folding and unfolding of the cube. I have a piece of 0.5mm galvanized steel wire that i am attaching to the arm of the servo and am threading within the paper of the cube. The servo rotates 90 degrees, which in theory would pull on the wire that is threaded within the paper and cause the cube to fold right? but so far it's not folding the way i want it to. It seems to bend the entire paper cube to whatever way the servo rotates and is not folding to the crease lines. It would be ideal to use linear motion to cause the cubes to collapse, but all of the linear actuators i’ve seen are slow and clunky. We have to find the best use of the rotation of the servo to cause the cube to fold and unfold. Do you have any suggestions? Where to place the servo, where to thread the paper, or perhaps an entirely different suggestion. Any feedback will be appreciated thx

I got my idea to use servos instead from this origami robotics video as they use servos in their robots.

https://www.youtube.com/watch?v=zfU6KPzmNUU

This is what kinda what i’m trying to only i’m not using nitinol actuators and the cube won’t fold in a twisting motion.

https://www.youtube.com/watch?v=4cti_npMzrI&t=18s

Here is some photos of my servo trying to get a cube to fold. The entire cube isn’t fully folded but i’m just testing out the sides to see if I can get the servo to make one correct folding actuation. Like i said above, it moves the entire cube, and the cube doesn’t fold to the crease lines. I thought that by adding some pressure from the servo it would cause the cube to “snap” to a fold because of the two faces of the paper being within close proximity to each other , it would naturally fold but this isn’t the case. (I tried to make it a video but it seems i'm not able to)

Previous posts by the OP on this same topic:

I'm adapting my original design. What's wrong with reposting?

No "wrong" mentioned, suggested or implied.

well do you have any ideas on how to make it work with the use of a servo? Do you have anything that will help me out?

I doubt there is enough information in your post for anyone to have a very clear idea of how you are trying to implement the transformation, or why it failed.

So, if someone IS interested, the relevant background may be helpful.

Good luck with your project, and by the way, did you every write to the authors of the paper you cited, as I suggested?

The cube will fold like this. It folds straight up and down How to Flatten a Cube – Mad Art Lab

A servo is placed inside of it. Now how can the servo be configured so that when it rotates the cube folds flat or unfolds back to its original size. Is this clear enough?

The cube can never fold flat with a servo in it

I know but as long as it is 1/5 of its original height that is fine. There will obviously be some thickness with the servo

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