Building An Automatic Faceting Machine CNC

[Nena]

Need some help!

I have found a simple diamond diagram on facetdiagrams and i want to draw the diagram in my software but if i calculate the hight of the pavilion with the angles, the messurements arent correct. How can this be?! What is the solution?! I have used the 42.10 and the 41.00 degrees. If i draw the angles with the heigth in my CAD software then the pavilion heigth is ore to long or to short?! What am i doing wrong!

Diagram: http://www.facetdiagrams.org/database/files/pc01006.html

Drawing is in inches as at the diagram

Or do i need to calculate from the bottom. I feel stupid it has been some years i calculated these angles...

3d results (these messurements ar not correct yet) three positions

 

[Nena]

Me again,

if i take the angle of 42.10 and the width of 1" than should my hight of the pavilion be 0,335..."

Calculation:

1 / 2 = 0.5 * sin(42.10) = 0,33521330947939955949703742947078

Why is the document saying: P/W = 0.435??? thats a diff from 0.1"

Thanks,

Christian

 

[Mr Magoo]

That's one of those brain annihilating questions but I think you are on the wrong plane. The vertical angle is 0* the horizontal is 90*. So 90 - 41 = 49*

Using this calculator http://www.cleavebooks.co.uk/scol/calrtri.htm

Width: a = 0.5 Angle A = 49*. Hit calculate and it chucks out the answer length b = 0.435 Which, if I have this right matches the ratio P/W 0.435 in Gem CAD

Could be wrong - its late.

 

[Nena]

Thanks Mr Magoo!

Did not thought about that! Thanks!!! hehehe, made the change and it works correct now! Hopefully i can draw the complete gem now, but first i need to solve some stupid errors. My build is shifted a few degrees and i need to get it under the horizontal row. Then i should make it totaly variable to draw also the other planes.

The new calculation would be then: X = Diameter / 2 * sin((90 - Degrees) * PI / 180)

Your message: 03:17 pm!!! there is a 9 hour time diff with here lol

Thanks again!!!

 

[Nena]

Got it!

Calculation: 0.5 / tan(49) = 0,43464336890811333110004781935197 = 0.435 it has taken some time but there is my awnser lol

Dont have the pavilion good yet but im coming close, first time working with 3d in my programming language i like it but its painstaking work.. my programming language is official not for 3d drawing

 

[Mr Magoo]

Got it!

Calculation: 0.5 / tan(49) = 0,43464336890811333110004781935197 = 0.435 it has taken some time but there is my awnser lol

Dont have the pavilion good yet but im coming close, first time working with 3d in my programming language i like it but its painstaking work.. my programming language is official not for 3d drawing

That will be it. But that's why I cheated and use the calculator. No real urge to relearn trigonometry this decade.

 

[Nena]

But it is not the correct measurement...

If i take the 41* gemcad has P/W = 0.435 (0.5 / tan(90 - 41) = 0,4346)

But... If i remove all settings for the 41* my new settings wil be 42.1* if i export it in gemcad then... P/W = 0.443 Lets recalculate again

P/W = 0.435 Calc: (0.5 / tan(90 - 41.0) = 0,4346)
P/W = 0.443 Calc: (0.5 / tan(90 - 42.1) = 0,4517) <-- Is NOT correct!!!

Im almost thinking that my first calculation was correct and that gemcad is using the 0.1" for its Girdle?! But it aint! Hehehe why am i doing this lol But i need to calculate all angles for and positions and... for my machine.

 

[Mr Magoo]

No. Your Gem CAD is having a bad day.

P/W =0.452 as per calculations. Just checked.

 

[Nena]

Hehehe its... dunno what to say verry strange! I see that my calculation is correct but why GemCad say's 0.443 is verry verry strange! Did you checked in GemCad?! The next thing is calculating meetpoints... Having fun... NOT lol hehehe!

 

[Mr Magoo]

Did you checked in GemCad?!

Yep! P/W=0.452

 

[Nena]

Thanks! GemCad BUG lol When i can calculate the meetpoints i could build up the stone easily, but this takes some time i think. using all the angles and calculate the meetpoints. An head breaker! And not shure how to but ill give i try! Or do you know the calculation?

 

[Nena]

If i am correct. This should be the meetpoint from the angles that i have. The last angle 41* gives the total height off the pavilion. The second 42.1* is larger that the height of the pavilion so that will be de widest facet of them all but it wil be cutted first. Than should the picture as drawed be correct.

The red lines are marking the meetpoint. Pavilion width is still 1". The drawing is half of the pavilion thats why you see 0.5".

If this is correct i can go on!

These calculations are not every day's work. On the lapidary machine you can set your angle just at the marked point, not mutch calculations have to be done, but if you want to draw a gemstone it is doing math...

I hope i did it correct

 

[Nena]

i think i got my meetpoint!

0.5 / tan(90 - 42.1) = 0,4517
0.5 / tan(90 - 41.0) = 0,4346

My new triangle wil be at 42.10*

Meetpoint Width: tan(47.9) * 0,4346 = 0,4809
Meetpoint Height: 0,4517 - 0,4346 = 0,0171

Meetpoint width coordinate is from center of the pavilion. The meetpoint height is from pavilion bottom.

I thought i calculated these correct! (Almost, i should measure from top to bottom) Ill try again...

 

[Mr Magoo]

Don't understand this meetpoint width as I thought it was being kept 0.5. Where's this width if not that?

But I am having trouble with your diagram.

 

[Nena]

Me to , the above diagram isnt correct! I think i know how i need to get the meetpoint, its a complexer calculation then i thought... I need to calculate a width from the removed triangle. And when the width is even/crossing the width of 2 of the 42.1 facets. It shoult be possible!

I Need somthing to do with the cutted angle. If the cut is larger then the stone it shoult give the meetpoint, but how i going to solve this one??? Dont know

The 0.102" did i took from Gemcad. I Need to calculate that specific point for completing my drawing.

 

[Nena]

I did found a drawing solution but its not rock solid (i think) i cant use the information to draw a another gem. But it does give a perfect reflexion when i look at the given degrees.

With these lines i drawed i could build up a diamond cut but it wont work for a other drawing i think. I need a calculation of the degrees positioning a meetpoint. At this way i didnt use the cutting degrees to get my meetpoint. This example uses only the symmetric of the drawing.

If you got a idea, please tell me! :8

 

[Mr Magoo]

I'm thinking. Not long seen diagram and it's near midnight. 8)

Actually now after.

Been looking at Gem CAD. It's got me confused - why the culet at 0.0, 0.0, -0.8 (-0.4). It's confusing me and now I doubt that 0.102. I'm done.

 

[Nena]

Working a few day's with this problem gives also a headache but if im thinking about the upper drawing it could be well perfect. Becouse it is a symmetric shape that is being done on a index. So one of the lines need to be exact from one side to the other side, also by the given degrees. But if i think about that, a drawing that does not have exact symmetric, the light ist breaking at the good spot. Mmmzz it logic but...

If you measure in gemcad, you need to measure at the meetpoint and the tip of the pavilion. It says: 0,20372558 but you need to divide it by 2! Then you get 0,10186279 thats 0.102

Greets

 

[Mr Magoo]

If you measure in gemcad, you need to measure at the meetpoint and the tip of the pavilion. It says: 0,20372558 but you need to divide it by 2! Then you get 0,10186279 thats 0.102 wink

I get that. But 0.102 from where? ..................Seconds later. Got it!!!!!

It's not -0.102. It's -0.137. Wrong.

The culet tip should be at -0.870 but it's not, it's at -0.800. The girdle (lower edge) should be at 0.000 but it's at +0.070. So you have to add (or subtract in this case) 0.070 from your figures to put it in the correct place.

0.000 is actually part way down the stone.

Edit: Got totally thrown by that -0.8. Now I know where you are at.

 

[Nena]

It's not -0.102. It's -0.137. Wrong.

You had it all right! the 0.137 is ok!

I drawed a solid in Autodesk Inventor 2016. What is that a problem to do by the way! Its not realy a program to make high res objects! But here is the awnser Took me a two hour to get it!

Dont know what it is but i cant get it from the buggy gemcad. Had some more troubles with it.

Here are the results of the drawing and finally i can look for the calculation to get the meetpoint! But i think i need to use 3 axis to get my awnser?!