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# Mathematics of flat-pack box design and assembly

Does anyone know if there a name for the subject of flat-pack box design, and what is/are the corresponding mathematical methods applied for modelling the assembly from 2D (flat) to 3D (assembled)? Presumably these are used in box design processes.

Background: I'm trying to design a certain type of box, and slowly coming to the conclusion that I may need a more analytical approach.

Thanks for your input!

Background: I'm trying to design a certain type of box, and slowly coming to the conclusion that I may need a more analytical approach.

Thanks for your input!

ASKER

Thanks. I googled the "packing problem" and it seems this is about how to pack known objects into a known space. What I need is more subtle I think, to design the object itself based on constraints such as how it will be assembled.

I suspect I might start with a set of equations defining the constraints, using trigonometry at least. The term "phase space" jumps to mind, not sure if relevant. eg take a simple example of a square piece of card folded in half... what equations define the possible movement of the card? there are two planes which intersect along a line, the angle between the planes can vary by any amount, so this is probably straightforward.

But presumably complexity increases substantially as cuts and folds are added...

I suspect I might start with a set of equations defining the constraints, using trigonometry at least. The term "phase space" jumps to mind, not sure if relevant. eg take a simple example of a square piece of card folded in half... what equations define the possible movement of the card? there are two planes which intersect along a line, the angle between the planes can vary by any amount, so this is probably straightforward.

But presumably complexity increases substantially as cuts and folds are added...

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I think this is probably more art than science.

You might want to look here for some examples:

https://www.google.com/search?q=box+assembly&tbm=isch&imgil=zgu6nZ7ZASnqZM%253A%253BgEzKK3-RjR256M%253Bhttp%25253A%25252F%25252Fwww.contestboxes.com%25252Fpage%25252Fpage%25252F1837491.htm&source=iu&pf=m&fir=zgu6nZ7ZASnqZM%253A%252CgEzKK3-RjR256M%252C_&biw=1536&bih=707&usg=___zmA0j8Gv8dr2wwoXPPpSC0QOoU%3D&ved=0CCoQyjc&ei=vCidVe6VLYaqsgHu8aPoDg#tbm=isch&q=cardboard+box+assembly

This one is pretty interesting

http://cdn2.bigcommerce.com/n-d57o0b/hintl/products/676/images/1911/medium_gift_box_graphite__67174.1407505444.1280.1280.jpg?c=2

You might want to look here for some examples:

https://www.google.com/search?q=box+assembly&tbm=isch&imgil=zgu6nZ7ZASnqZM%253A%253BgEzKK3-RjR256M%253Bhttp%25253A%25252F%25252Fwww.contestboxes.com%25252Fpage%25252Fpage%25252F1837491.htm&source=iu&pf=m&fir=zgu6nZ7ZASnqZM%253A%252CgEzKK3-RjR256M%252C_&biw=1536&bih=707&usg=___zmA0j8Gv8dr2wwoXPPpSC0QOoU%3D&ved=0CCoQyjc&ei=vCidVe6VLYaqsgHu8aPoDg#tbm=isch&q=cardboard+box+assembly

This one is pretty interesting

http://cdn2.bigcommerce.com/n-d57o0b/hintl/products/676/images/1911/medium_gift_box_graphite__67174.1407505444.1280.1280.jpg?c=2

ASKER

hi Ozo, thanks for that link it looks like the way to go. Leads to some interesting demos eg http://demonstrations.wolfram.com/OrigamiFlangedPots/

Mathematica software is probably what i would need on the technical side.

Agree with d-glitch it's probably more art than science, but then again on the front-line isn't it all art ;-)

Mathematica software is probably what i would need on the technical side.

Agree with d-glitch it's probably more art than science, but then again on the front-line isn't it all art ;-)

It sounds a tough assignment.