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Thread: I need help with creating a flat pattern for a truncated cone

  1. #1
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    I need help with creating a flat pattern for a truncated cone

    Every website I've tried has failed to give me the proper frustum. When I print it out, it's been 2 or 3 times the size it should be. Here is my 2D diagram:

    I need help with creating a flat pattern for a truncated cone-truncated-cone.png
    I've input just the whole number into these calculators, but invariably get a truncated cone that's 450mm across; the best I've done is one about 300mm. The distance across the bottom of the finished paper cone SHOULD be just around 200mm, and the distance across the top should be 160mm, while the height is 80mm. However, I have yet to accomplish this. I need my paper cone the EXACT size of the real-life physical solid cone I will be 3D printing, so that I can draw various shapes on its face using the paper cone as a template.

    Can anyone help with this??
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    Re: I need help with creating a flat pattern for a truncated cone

    Quote Originally Posted by TheWebExpert View Post
    Every website I've tried has failed to give me the proper frustum. When I print it out, it's been 2 or 3 times the size it should be. Here is my 2D diagram:

    Click image for larger version. 

Name:	Truncated Cone.png 
Views:	16 
Size:	115.0 KB 
ID:	38494
    I've input just the whole number into these calculators, but invariably get a truncated cone that's 450mm across; the best I've done is one about 300mm. The distance across the bottom of the finished paper cone SHOULD be just around 200mm, and the distance across the top should be 160mm, while the height is 80mm. However, I have yet to accomplish this. I need my paper cone the EXACT size of the real-life physical solid cone I will be 3D printing, so that I can draw various shapes on its face using the paper cone as a template.

    Can anyone help with this??
    I just found this thread. I see it is a few months old and has no replies. If you are still here I probably can help you once I am certain what you are trying to do. Consider the following picture:
    I need help with creating a flat pattern for a truncated cone-frustrum.jpg
    Are the dimensions you need to have what I have labelled a, b, and h? Let me know if I have understood what you want and I will know you are still interested and still here.
    Last edited by Walagaster; Apr 28th 2018 at 08:41 PM.
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    Re: I need help with creating a flat pattern for a truncated cone

    I already HAVE the dimensions a, b & h; the websites, however (afaik) asked for the circumference. But either way, the frustrum comes out either WAY too big or WAY too small.
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    Re: I need help with creating a flat pattern for a truncated cone

    Quote Originally Posted by TheWebExpert View Post
    I already HAVE the dimensions a, b & h; the websites, however (afaik) asked for the circumference. But either way, the frustrum comes out either WAY too big or WAY too small.
    so I understand

    you have a truncated cone

    the base diameter you want to be 200mm

    the top diameter you want to be 160mm

    the height from base to top you want to be 80mm

    Ok, this is all very doable. What information is your 3D printer software after?

    You mentioned a circumference. Of what? The base? The top?

    The circumferences are just $c_{base} = 200 \pi~mm,~c_{top} = 160 \pi~mm$
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    Re: I need help with creating a flat pattern for a truncated cone

    Ok, try this which uses your a = 162.88, b= 202.76, and h = 79.99.
    Draw a circle of radius 419.135. Also draw an arc of radius 336.697.
    Make a central angle of 87.076 degrees.
    Cut out that strip and fashion your cone from it and see if it works.
    If you need different numbers or if that works and you need more explanation let me know.
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    Re: I need help with creating a flat pattern for a truncated cone

    Walagaster: I have no idea what you're talking about. I can draw circles (of varying diameters, but not arcs.
    romsek: the circumference of the base is 202.76; the circumference of the top is 162.88. That is, when you measure across from one side to the other. Radius is from the center to the edge.
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    Re: I need help with creating a flat pattern for a truncated cone

    Quote Originally Posted by TheWebExpert View Post
    Walagaster: I have no idea what you're talking about. I can draw circles (of varying diameters, but not arcs.
    OK draw two concentric circles using the two radii. Draw the central angle to the outer circle. That forms a curvy "rectangle". If my calculations are correct you can cut it out, tape the ends together and you have your frustrum. I thought that is what you were trying to do.
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    Re: I need help with creating a flat pattern for a truncated cone

    Quote Originally Posted by TheWebExpert View Post
    romsek: the circumference of the base is 202.76; the circumference of the top is 162.88. That is, when you measure across from one side to the other. Radius is from the center to the edge.
    I thought you told me those are your b and a dimensions in my post #2, which are not circumferences, they are diameters. Please clarify.
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    Re: I need help with creating a flat pattern for a truncated cone

    Measured across (whatever that's called) is 16 1/2 on my ruler. I'm guessing that works out to 165 mm.I need help with creating a flat pattern for a truncated cone-frustrum.png

    When I lay out the circles (as you specified) & put the angle, this is what I get. Obviously, this is wrong. The height is only about 19mm, not 90. This is one of many problems I've had with this. I finally just ended up "guestimating" the pattern by printing & reprinting & reprinting until I got close. My finished physical model isn't perfect, but it's close enough for jazz. I do, however, wish I knew how to get this precisely right.
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  10. #10
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    Re: I need help with creating a flat pattern for a truncated cone

    I'm not sure where the trouble is so I have a new picture for you:
    I need help with creating a flat pattern for a truncated cone-arcs.jpg (I haven't figured out how to make the figure larger, sorry. I guess you have to click on it).
    For this picture I used a=16, b=20, and h = 8. The picture is drawn to scale. The smaller radius is 32.98 and the larger is 41.23. The angle is 87.31 degrees.

    Notice the difference in the radii of the two circles is slightly more than 8 as the slanted distance between the top and bottom circles of the folded frustrum is a bit
    more than the vertical distance.

    if you multiply the numbers a, b, and h by 10 you have your 160,200,80 input and multiply the answers by 10 (except for the angle). This figure is correct and if you still disagree there is some misunderstanding about the problem.
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    Re: I need help with creating a flat pattern for a truncated cone

    I recreated the drawing you made. It produces a figure that's 21 mm x 20mm... a very, VERY small pie slice shape. How is this thing supposed to come out to 240 cm across and 80cm high?
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  12. #12
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    Re: I need help with creating a flat pattern for a truncated cone

    The drawing is to scale. If you want your frustrum to be 80 cm high, multiply the numbers by 10 and draw it on paper at about 450 cm across. So your x and y axes would be a bit over 40 cm.
    Last edited by Walagaster; Apr 30th 2018 at 03:53 PM.
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    Re: I need help with creating a flat pattern for a truncated cone

    That last 40 cm should be 410 cm.
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    Re: I need help with creating a flat pattern for a truncated cone

    I need help with creating a flat pattern for a truncated cone-frustrum.png
    Ok, here's the updated image. It might LOOK good - but the thing is only about 40mm high, not 80.
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    Re: I need help with creating a flat pattern for a truncated cone

    Here's an image of the one I figured out by sheer guessing:
    I need help with creating a flat pattern for a truncated cone-frustrum.png
    What I'm after is the PROPER way to calculate this shape - and to be able to calculate the PRECISE shape I want, rather than a guesstimate.
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