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

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

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

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

I get 109.47°

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

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.

Good explanation, DC31K

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.

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

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"

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

Don

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

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.

I did it in CAD by using the Mirror tool.

Martin.

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