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jeric_synergy
08-19-2016, 06:42 PM
Hey, math types:

I need to make a physical template that describes HALF of a conical bucket's sides, but truncated such that:
the bottom of the bucket is 5.25" in diameter;
the top of the bucket is 7.5" in diameter;
a straight line from the bottom EDGE to the top EDGE is 6".

How could I construct such a template?? THANKS!


(Think "veterinary collar of shame" construction, and from a flat sheet of material.)

meshpig
08-20-2016, 01:35 AM
0.25 of an inch? The shape would be 16.4 x 23.6 x 6 inches with a 5 1/4" diameter disc cut in half :)

JoePoe
08-20-2016, 09:27 AM
I'd model it. ABF Unwrap it. Export the UV as an EPS and scale (constrain proportions) in any print/layout program. The point-to-point segment shown needs to be 6.424" (163.1674mm). If I'm thinking about it right....

134118

jeric_synergy
08-20-2016, 10:10 AM
I'd model it. ABF Unwrap it. Export the UV as an EPS and scale (constrain proportions) in any print/layout program. The point-to-point segment shown needs to be 6.424" (163.1674mm). If I'm thinking about it right....
134118
That's pretty much it, if I could be certain the proportions remained correct.

I had a reasonably clever guy last night insisting the circles needed to be concentric, even while I showed him the physical 'bucket' (actually, a lampshade-- the template is to cut out a scrim to fit inside). My counter examples of a tube and a cone did not convince him........ :stumped: :(

I'm pretty sure olde schoole draftsmen and sheet metal workers have some truly slick (2D) way to do this....


Thanks! :thumbsup:
+++++++++++
I don't think I communicated one dimension correctly: the point to point distance shown, as do all the radial lines, should measure 6".

JoePoe
08-20-2016, 10:16 AM
They are concentric. All of those individual point-to-point segments are the same length :hey:.

edit for your edit: So, then model it that way. It'll still work :).

jeric_synergy
08-20-2016, 11:01 AM
In 3d: from a 2d sheet they are not.

JoePoe
08-20-2016, 12:12 PM
Oh, you mean bending in LW from flat. Yeah, There's going to be a lot of stretching/skewing (i think...aflw). You can bend manually step by step around each "spine" axis. That'll work, but what a pain.
Maybe there's a non-stretch layout solution too.

jeric_synergy
08-20-2016, 12:24 PM
Actually, I mean bending in the Real World (RW).

pinkmouse
08-20-2016, 01:19 PM
It really is basic trigonometry. Here's a hint, look at it as a triangle in 2D space first, using pi and the measurements you've given you can calculate the top and bottom of the truncated cone, then extend those side angles up to get the origin/apex. The rest is just playing with a big set of compasses.

RebelHill
08-20-2016, 01:22 PM
^ yep. So easy.

pinkmouse
08-20-2016, 01:24 PM
My "0" level in Technical Drawing does come in useful every now and again. :)

JoePoe
08-20-2016, 05:28 PM
Actually, I mean bending in the Real World (RW).

I'd like to see that! I think I'm with the "reasonably clever guy" :D.

jeric_synergy
08-20-2016, 05:51 PM
I'd like to see that! I think I'm with the "reasonably clever guy" :D.
,,,,,.... oh, I remember this feeling.... it's me failing at geometry, again.....

OK, I'm wrong, but what shape is defined if you move (in 2d) the smaller circle away from the larger circle so they're not concentric, cut it out and roll it up?

RebelHill
08-20-2016, 07:05 PM
what shape is defined if you move (in 2d) the smaller circle away from the larger circle so they're not concentric, cut it out and roll it up?

An oblique cone ofc.