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Geometry question: What is the angle between two 45 chamfers, after the two connecting surfaces have been 'flattened'?

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Donald MacDonald 120/03/2022 23:59:25
50 forum posts

Hi

Geometry question:


If you start with a box, and then put two 45° chamfers onto the box, whilst making sure that the chamfers touch each other... (i.e. see surfaces "A." and "B." in this diagram):

If we now take just the two connecting surfaces ("A." and "B." ) , and imagine that they are made out of a single thin sheet of paper, that has been creased to get around the corner...


If we now flatten the paper, what would be the angle between the two areas? (A. and B.)

 

Thanks!

Don
 

PS By experiment it seems to be something like 19° off straight ( i.e. 161° in my diagram). Does that seem about correct?

 

Edited By Donald MacDonald 1 on 21/03/2022 00:19:36

Michael Cooper 521/03/2022 02:43:56
16 forum posts

I’m getting 109.5 deg, for your 161 .Definitely try it on paper before you take my word for it lol.Good luck Don

not done it yet21/03/2022 07:08:48
6812 forum posts
20 photos

You know the dimensions of the parts. A bit of trigonometry would provide you with the proper value.

Gary Wooding21/03/2022 07:13:16
983 forum posts
254 photos

I get 109.47°

JasonB21/03/2022 07:15:50
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Moderator
22751 forum posts
2653 photos
1 articles

yes 109.5 approx

Measure the 4 edges of the chamfered face off your CAD model and draw that "flat" then measure the angle, easier than trig

geometry.jpg

DC31k21/03/2022 07:24:29
686 forum posts
2 photos

Assuming that the chamfer is 45 degrees and the corner of the block is 90 degrees, you only need the chamfer distance to calculate this:

In either a side or end view of the part (does not matter because the chamfer is 45 and the corner is 90), you see the vertical height of the chamfer (top to bottom) as a true length (1). This is the chamfer distance.

In a plan view of the chamfer, you see the base length as a true length. It is the hypoteneuse of a 45 degree right triangle with side length = chamfer distance (2) .

Those two lengths allow you to calculate the true length of the intersection slope (the vertex of your unfolded pattern) (3).

The side or end view gives you the true length of the chamfer (the sloping bit) (4).

(3) and (4) allow you to calculate the half angle.

Using the same reasoning, you can write a general formula where the inputs are: chamfer angle, a characteristic chamfer distance (either vertical or horizontal) and corner angle.

A good place to start is an old technical drawing book, where you learn how to draw a view of something such that a particular feature is shown as its true length and its angle to a plane is a true angle.

Michael Gilligan21/03/2022 08:32:52
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20183 forum posts
1053 photos

Good explanation, DC31K yes

It’s also worth noting that Builders have been doing this stuff for millennia … so a visit to ‘Builder Bill’ is quite informative: **LINK**

http://www.builderbill-diy-help.com/roofing-angles.html

MichaelG.

Hopper21/03/2022 10:48:37
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6404 forum posts
334 photos

Sheet-metalworkers handbooks have all that information too. They use it for making ducting etc. I suppose these days there would be sheetie websites and calculators that would do it for you like the builders site MG posted above.

Pipefitters handbooks/websites have all the same kind of info for circular forms (pipes) and cones etc.if you ever need it.

How's the invention going?

Edited By Hopper on 21/03/2022 10:50:32

Donald MacDonald 121/03/2022 11:11:22
50 forum posts

Thanks everyone. 


Meanwhile you have inspired me to draw a sketch on the chamfer surface in my CAD (OnShape) and the internal angle measured "54.7356103deg", which for my purposes needs to be doubled, which gets me to "109.4712206 deg" smileyyes

 

...Just in case anyone else might need all those decimal places!

Don

 

Edited By Donald MacDonald 1 on 21/03/2022 11:15:19

Paul Lousick21/03/2022 12:47:24
2043 forum posts
722 photos

CAD software that has a sheet metal module can produce a flat pattern that is used for bending.

It is first modeled as a solid 3D part to the final shape. Then the software converts it into a part that is made from sheet metal. This part can then be flattened and dimensions added. Lines for bending are also shown.

flat plate.jpg

blowlamp21/03/2022 14:30:48
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1617 forum posts
105 photos

I did it in CAD by using the Mirror tool.

Martin.

old mart21/03/2022 17:44:00
3775 forum posts
233 photos

Paul Lousick has the answer with 19.47 degrees, (19-28-12".

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