Go 5 axis.
I've got (what I think) is an odd & difficult design ? for ya.
Looking at Bathsheba Grossman's designs with ProMetal Direct metal 3d printing, I thought up something I'd like to make.
I am still a total amateur when it comes to CAD design, but I have an idea. It involves a spherical shell, with a continuous cut-out design covering the entire thing, like latticework. If you're wondering what it's for, it's a custom censer (I burn a lot of incense, it helps me design).
The idea is to somehow wrap a flat, tiled design around a sphere completely, and there are 2 parts to the tiled design, a positive & a negative. The positive obviously stays behind, and makes up the skeletal "shell" of the sphere. The negative is just that- cut out. Simple, right?
Here's the hard part- the design is based of a simple, traditional Japanese folk pattern called "sayagata". See attachments. I have analyzed the design, and come up with the single part that tiles to create the pattern, and defined it mathematically by proportions, so that I can create this design at any size, by simply tiling the single drawn main shape.
Basically, you'll understand what I want to make by seeing the 2nd attachment, Example. I want a lace-like metal shell where the green-marble looking part in that picture would be. The inside is hollow. Just a spherical, lace-like shell.
I'd like to put the center of one of the "X" points both at the top & bottom centers of my sphere.
That's my design. I'd cut it in half, and mount gimbals inside for the incense holder. I want all the negative space (the white in the design, between the black lines) to be the same width all around the sphere on the OUTSIDE.
MY QUESTION IS: how the hell do I make this? I have 2 ideas:
1. Somehow "wrap" this design into a sphere shape, and send it to be printed by ProMetal. I don't think it's a physically impossible shape.
2. Make a simple die shape out of the main pattern, and a negative block to hold it in (with the bottom of the block contoured to a sphere the diameter I will use), then hand press this against a hard wax shell I could make around a craft foam sphere. I gradually stamp through the wax, into the sphere underneath, and when I'm done, I use a special chemical to eat away the foam sphere underneath, leaving my spherical lace shell behind. I then send the hard shell out *CAREFULLY* to be lost-wax cast in metal, no CAD involved.
Any ideas? It seems so simple as an idea, but the route to MAKING the damn thing is confusing the hell out of me. Also, can the flat design really be wrapped in any way around a sphere without distorting the sizes of it's design parts?? I'm thinking it can't..
I know this is a strange question, but look at guilloche nested spheres that old craft turners have made- some others have done similar things, just not with a linear pattern like mine.
Go 5 axis.
Try taking the drawing on a piece of paper and wrapping it around the sphere. You can't do that without crumpling or stretching the paper. The way you described the constraints (the widths of the white spaces are all the same), you would have to vary the widths of the black spaces. How do you think that would look?
If you eliminated the constraint, there are lot's of partial solutions to your problem. The inverse problem is to take a sphere and map it to a plane. Cartographers have been addressing that problem for hundreds of years.
Some of the projections used preserve directions; others preserve areas. None of them work over an entire sphere.
I don't think there is a solution to your problem.
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Maybe this is a good idea of what I'm going for?
His positive lines that make up the shell are all the same width or abouts. I'm not sure how that would look if you took the design to a plane, but it is spaced properly on the sphere.
So I'm thinking this could be done. Only the width of the lines need apply on the outer side, I know that they would taper a bit towards each other the thicker I cut the pattern through a thicker shell. The shell I wanna make is only several mm thick though.
Oh, I forgot to mention I thought of the wrapping the paper around the sphere idea. I know from studying geodesic domes that you can approximate a sphere with what is essentially a flat surface, verticied by many triangles. I already tried scoring a few hundred small triangles into a sheet of paper by using a ruler parallel at 60 degree angles, and folding it over a ball, but it didn't work very well. Theoretically it should have, but maybe I wasn't exact enough.
Here's a museum piece I saw from Syria that gave me the inspiration for this, kinda. It's a different design, though.
You can easily make 1 sphere in 2 halves them using a diferant material make another sphere to fit over the first. Attach the sphere together witha good epoxy them put them on a 4th axis and machine the desired shape into the outer sphere. You could make the inner sphere lock together for machining then, un screw it after. The outer sphere would have to have a foot on it that would be removed after or act as the base for it to sit on.
I am not sure of the material is that you are using, but lets say the inned sphere is aluminum and the outer sphere is another type of machinable material. You can use a sacraficial material for the inner sphere and make a 2 piece outer sphere and attach it to the inner sphere by heating up the inner sphere and appling a layer of bees wax, then you attach the outer sphere. when it cools it will lock the 2 together for machining. After it is done just warm up the part and it will come apart. The apply the outer and inner to make up the sphere. I hope this makes some sence to you if not just delete it