topic Re: Diamond lead pattern, how to draw this in AutoCAD Forum

AutoCAD - Diamond lead pattern, how to draw this

tromekhimself — Thu, 22 Sep 2022 08:35:38 GMT

I am pretty enew to autocad, and I found very difficult to draw a diamond lead glass pattern.

I got so much difficulty calculating diamond sizes so I wanted to ask if theres any way of doing this.

Lets say we got a glass size 1195 x 403 like below:

And I want 3 diamonds in the width and 6 diamonds in the height with 12mm thickness. How to calculate them sizes? I would really appreciate any help with this.

Many thanks

[ The subject line of this post has been edited to include the product name by @handjonathan ]

Re: Diamond lead pattern, how to draw this

imadHabash — Thu, 22 Sep 2022 08:38:39 GMT

Hi,

As much as i understand your issue ..

By DIVIDE command .. make your needed parts ( 3x6 ) as i did ( Red blips ) .
draw lines between those blips .. then draw diamond shape with PLINE command .
Now use ARRAY ( Rect ) command .

Click on below image to see how it works .

Re: Diamond lead pattern, how to draw this

tromekhimself — Thu, 22 Sep 2022 08:47:48 GMT

Thank you for replying.

The issue is, that all the diamonds need to be 12mm thick and fit into the frame. It suppose to look like this roughly like this:

Thats a antique diamond lead pattern in the glass. I dont want any of the diamond leads going over these cyan lines.

I hope that helps you understand what I am after.

Re: Diamond lead pattern, how to draw this

leeminardi — Fri, 23 Sep 2022 10:40:42 GMT

This is an interesting problem in that you have many interrelated dimensions and constraints. I first tried to determine the dimensions of the diamond and corresponding offsets with AutoCAD's parametric solver but that got a bit messy so I went to an algebraic solution aided by Excel/s Goal Seek solver.

If we assume basic dimension for the diamond as follows:

and since we know that the overall dimensions are 403 x 1195 the following expression can be stated from the width:

3 * a - 2 * c =403 [1]

and from the height

6 * b - 5 * d = 1195 [2]

Re-arranging [1] and [2] we have

a = (403 + 2 * c)/3 [3]

b= (1195 + 5 * d)/6 [4]

Since a/b = c/d, and using equation [3] and [4] we can write that:

c/d = ((403 + 2*c)/3)/ ((1195 + 5*d)/6) [5]

rearranging we have:

6*d*(403/3 - c/6) - 1195 * c = 0 [6]

The challenge here is to determine values for c and d (other than 0) that will yield 0 for the left side.

We also know that the offset line for c and d is related to the thickness t of the lead strips and that t = 12.

From similar triangles we have:

t / c = b / (a^2 + b^2)^0.5 [7]

solving for t yields:

t = (b * c) /((a^2 + b^2)^0.5) [8]

I set up an Excel spreadsheet as seen below. Cells E1, E2, E3 contain equations [3], [4], [8] repsectively.

Cell B5 contains equation [6]. I make an initial guess of c= 10, d = 20 and note that b5 = 3970. It should equal zero. Using Goal Seek as follows:

yields the following:

Note that B5 is 0 but t = 11.05599. We want this to be 12.

By changing guesses for d and computing the corresponding value for c with Goal Seek we find that d = 21.8 and c = 14.44 yields a value of t = 12.038 which may be close enough to 12. If not we can tweak the value for c and recalculate.

We now have all the dimensions we need to draw that pattern.

Edited a couple of typos 9/23/2022.

Re: Diamond lead pattern, how to draw this

Kent1Cooper — Thu, 22 Sep 2022 18:20:01 GMT

So which is it, really?

Outside of diamond leading/muntin touching inside of perimeter frame [red], or outside of diamond touching outside perimeter [yellow], or inside of diamond touching inside of perimeter [blue]?

As a stained-glass hobbyist, and an architect who knows something about windows, I know that in a real leaded-glass or muntined-glass panel, the red-circled relationship [used in @leeminardi's suggestion] would never be the situation -- whatever is between the panes must engage the frame, not just touch it at a point. This is what it would look like if the intersections of the leading center-lines touch the inside of the perimeter:

Is the cyan perimeter also leading/muntin material, or an outer frame that a leaded-glass panel [which would also have perimeter leading] is set into, so that there should be some green leading showing around the perimeter inboard of the cyan parts?

Re: Diamond lead pattern, how to draw this

leeminardi — Thu, 22 Sep 2022 19:37:32 GMT

@Kent1Cooper my goal was to solve the geometry problem as stated by the OP. I did not consider fabrication issues. I think my process can still be used to meet the requirements you highligt. The overall width and height values would need to be adjusted to meet your configuration requirements. Just substitue those width and height numbers for the 403 and 1195 in my equations.

Re: Diamond lead pattern, how to draw this

tromekhimself — Fri, 23 Sep 2022 08:37:34 GMT

Thank you for your hard work and providing solution. You helped me alot.

Re: Diamond lead pattern, how to draw this

tromekhimself — Fri, 23 Sep 2022 08:39:31 GMT

According fabrication you are right. for the glass size you should consider the inner rectangle, the outer one is just a 11mm offset guide line for the unit. The picture I have provided was just an image of what I have achieved so far. Thank you anyway 🙂