#1
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Calculating the dimensions of a teardrop shape
Okay all, here's a tough one (for me). I have a periscope that is a cylinder with an overall height of 1cm and a diameter of 4.4mm. Okay yeah, small. Stick with me. The top of the scope is beveled at 45deg about half-way across. The height of the bevel is 2.5mm.
I thought I could cap it by creating an oval about twice the diameter in length. But, no prototyping shows the cap to be more of a teardrop shape. My picture of the part might be hard to see so I sketched it out. Is there a way to calculate the shape of the teardrop? I'd hate to do the trial-and-error or the trim-to-fit methods.
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Happy Crafting - Scot On the Bench: Planck and Hershcel |
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#2
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Since it is a simple oblique cut of a cilynder, I guess there are ways that involve some geometry formulas. And a bit of drawing.
But... Have you tried upscaling the part? Let's say, X10? That way you could have a much easier, faster and accurate "trim-to-fit" test, and once you have the proper shape, scan and downscale it to the original size. Takes less than 10 minutes.
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Rubén Andrés Martínez A. |
#3
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Hi Scot
If your cylinder is a perfect circular shape the shape for your flat top piece will be part of a circle and for the bevelled piece it will be part of a pure elipse. You are finding a teardrop shape because of a lack of circularity. The attached gives, in red, the developed (unfolded) shapes in 2 cases. 1) where the bevel splits the top of the cylinder in half giving a bevel height of 2.2mm. The top is a semi-circle and the bevel is half an elipse. 2) where the bevel height is 2.5mm The top is less than a semi-circle and the bevel is more than half an elipse. Hope this helps. |
#4
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Maurice's words...I was gonna say that too...only with less intelligence.
The angled slice must be an oval...or at least half an oval. Definitely not a teardrop. (If the cylinder is a tube is a cylinder) I think the teardrop shape is because your cylinder assembly is incorrectly formed at the seam. Try rolling your cylinder with two layers or use a dowel(former of some sort) to keep it nice and tubular (dude). Making a cylinder of two layers is easy. Calculate your cylinder part. Then divide its length by pi (3.1416) and minus the thickness of your card/paper. (Add 20% to the card thickness for safe margin) Now multiply that number by pi again to get the length of the interior cylinder layer that will fit perfectly. If its a straight cylinder, its simple, but if the ends are not square, its still easy. Just make a copy of your outer layer part and shrink it (length only) to the new inner dimension. Connect it to the outer layer. Angles, curves, etc will all line up. get it?
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#5
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May those links can help you...
https://www.youtube.com/watch?v=-Tgj8Yu8pIU https://i.ytimg.com/vi/TyiQdZ_KfRY/maxresdefault.jpg |
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#6
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Ahhhhh, all those who guessed that I had designed my cylinder incorrectly, give yourself a prize! I had simply cut a straight bevel on my unrolled cylinder (think trapezoid on top of a rectangle). wrong wrong wrong.
So, I now need to figure out how to draw the correctly unrolled cylinder form in MS Publisher. Or maybe a better idea will be to create it in Adobe in a larger scale and then import the shape as a gif into my publisher file. Man, I hope my mm dimensions aren't unrealistically difficult to trim out. Thanks everyone! Every part of this thread, from posts, links and math, are among the many things I love about this hobby.
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Happy Crafting - Scot On the Bench: Planck and Hershcel |
#7
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When designing paper model parts, you often have to include,
or compensate for, the thickness of the material you are using to build the part. This is especially true with rolls and cylinders that have multiple layers. The inner and outer layers will be incrementally smaller and larger based on the card thickness (and how it affects the cylinder diameter) This is why you sometimes have to design a part at its intended sale.
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#8
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Quote:
You'll end with something like this: Actually, your specific final result will be just like Maurice's drawing, because the cut doesn't go through all the diameter. it will be an oval with a straight cut on one side. Scroll down to "Truncated Circular Cylinder" here: Development Of Surfaces And a video showing the process here: https://www.youtube.com/watch?v=DqXpmfgwZsE is very easy, you'll get the hang of it in no time. You may practice the technique on a piece of paper to understand it, and then you'll be able to replicate it and adapt it in the 2D software. Sorry, I should have posted this before in my first message. But last night I was a bit tired and sleepy to search the exact technique. Again, sorry. Anyways, hope this is useful now!
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Rubén Andrés Martínez A. Last edited by Rubenandres77; 03-04-2017 at 08:21 AM. |
#9
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Rubén, thanks for that website and information on the truncated circular cylinder. I tried it out and it works great.
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~Doug~ AC010505 EAMUS CATULI! Audere est Facere THFC 19**-20** R.I.P. it up, Tear it up, Have a Ball |
#10
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Hello constructors,
in a more mathematikal way it is a sinus-curve. Look!
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