Using Trigonometry for manual programming - Page 2

# Thread: Using Trigonometry for manual programming

1. Diamond
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Originally Posted by angelw
......R = A/HP ......
At the root of this formula is the geometric proposition that the center of an inscribed circle within a triangle is at the intersection of the lines bisecting the acute angles of the triangle.

2. Hot Rolled
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I used to be quite good at algebra and geometry back in the school (which wasn't THAT long ago), but the triangle incircle had completely slipped out of my mind...

Looked up the theorem and the proof and it was quite obvious why a lot of people are turned off by these things, I mean - the geometric relationship between the center of the circle and the bisected angles is very intuitive and obvious, but the mathematical relation just isn't, and the latter is how it is "explained" in the articles I could find quickly after seeing Bills solution

regarding the OP, that is pure sadism to give such tasks to students or machine operators/programmers, that print should have never left the drawing board like that, if it did - the engineer making it should be the one made to do the math to find the P2 "by hand" so he'd learn the lesson and not hand out a half finished drawing... total waste of time calculating it, not to mention possibility of errors, had it been a critical dimension - it MUST have been dimensioned by the draftsman, and if it isn't - use a ruler or calipers to find it on the drawing, adjust according to scale - since it doesn't matter anyway

3. Plastic
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Originally Posted by jz79
I used to be quite good at algebra and geometry back in the school (which wasn't THAT long ago), but the triangle incircle had completely slipped out of my mind...

Looked up the theorem and the proof and it was quite obvious why a lot of people are turned off by these things, I mean - the geometric relationship between the center of the circle and the bisected angles is very intuitive and obvious, but the mathematical relation just isn't, and the latter is how it is "explained" in the articles I could find quickly after seeing Bills solution

regarding the OP, that is pure sadism to give such tasks to students or machine operators/programmers, that print should have never left the drawing board like that, if it did - the engineer making it should be the one made to do the math to find the P2 "by hand" so he'd learn the lesson and not hand out a half finished drawing... total waste of time calculating it, not to mention possibility of errors, had it been a critical dimension - it MUST have been dimensioned by the draftsman, and if it isn't - use a ruler or calipers to find it on the drawing, adjust according to scale - since it doesn't matter anyway
I was going to ask my teacher under what scenario I’d ever see a drawing with missing dimensions like that. sounds like it doesn’t happen often. Haha. However, still probably a good skill to have in the toolbox. I solved some sides and angles of the triangles that have been posted here but I still haven’t figured out how to calculate point 2 in the print. I’m headed to class now though so I’d imagine I’ll have it figured out soon, or be more confused. Haha. I’ll post what I learn. Thanks everyone!

4. Originally Posted by Dhoverson
Hello all,

Extreme novice machinist in training here. I’m currently enrolled in a CNC course at the local community college. We’ve covered a number of basic skills so far such as setting work coordinates, tool length offsets, dialing in a vise, picking up an edge, picking up holes and bosses, etc. We’ve also got the chance to run a few programs to make some parts out of stock that we squared up on the manual mills during the last course that I took.

This last week, homework has been about using trigonometric functions and right triangles to find missing dimensions on prints. It’s been very challenging for me as before these classes I haven’t really done math since about 2005 in college. haha. And even then I never did take a trig class. So I’ve kind of given myself a YouTube crash course in trigonometry over the last week and learned Pythagorean Theorem and all that so I could maybe understand what we’re currently learning.

I’ll attach a pic to this post. What they’re looking for is for us to be able to calculate the two XY points of a blend arc. I’m not asking for anyone to do my homework but I feel if I could at least see the right triangles required to do the math I might have an ah ha moment and be able to figure out other similar problems with missing dimensions. So if anyone would care to draw the required triangles or point me in the direction of a good resource it would be much appreciated. I’m just trying to learn all I can and this stuff has me stumped. I have class again on Thursday and would like to come in with some knowledge.

Thanks for any help. Hopefully this was the correct forum to post in.

Drew

I only read the first 10 replies, but I doubt the answers changed after that.

I am actually quite surprised that the general consensus is that you don't have enough info.

Personally I would need the angle on the BRH corner to be able to figger it quickly, but I always ass_u_med that was just b/c I quit taking math my Sophomore year, and didn't actually take "trig", but only geometry.

However - I did learn sumpthing in Geometry that I can apply here to find the answer. It takes some time, but not longer than posting the Q to the forums and waiting for an answer.

It's called "The Guess Method", and has been used along with the "Because I said so" theorem.
I have always had name memorization issues, so the names would slip my mind, yet I could always git the answers.

For me to find your answer, I need to know the angle of that BRH corner, so in this case - I would simply look at the pic, and take a stab at the angle, and then run the numbers from both ends, and then play the "Higher or Lower" game, and adjust until all the numbers agree.

It's quick and easy if it's a whole and even number. (30*, 45*, 50*...)
But when it is just "whatever it comes out to" it can take time to hone in on a 44.26* answer...

I'm not the guy to show you the right way on many things, but I can back door most, and at the end of the day - all that matters is what was accomplished, not how you got there.

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Think Snow Eh!
Ox

5. Aluminum
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Don't know why you think the consensus is not enough information. The method at least was shown in posts 4 & 5
The consensus is it's a dumb drawing. Which is true. But it's purpose is to teach the student to think.

6. IDK why it's a dumb drawing?

It's what they want.
Maybe they don't know the angle or point of intersection either?

Maybe you've never gotten prints like that, but I sure have.

From Bill's post in #4, it seemed to me that he said that there wasn't enough info to doo it with trig and that you would need CAD to get the answer.

My guess was that the CAD would perform the Higher and Lower game to find the answer as well.
IDK how CAD werks. I didn't program it.

I would really have to study #5 for some time to follow it. (as I would if I tried to follow my own sketches that I have done many times as well)

Otherwise, the method that I posted above will get you there. Eventually ... But quite possibly quicker than the other way...

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Think Snow Eh!
Ox

7. Diamond
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Originally Posted by Dhoverson
I was going to ask my teacher under what scenario I’d ever see a drawing with missing dimensions like that. sounds like it doesn’t happen often. Haha. ....!
I would say it more common than one would expect.
If you have had to make cutter bodies or special inserts from the supplied customer prints out of Kenna, Carboloy, Valenite, or any of the big names a lot more than this is missing.
Often a lot of dimensions all over the print to make it look good but not quite enough to make the part.

To be fair I have to admit to doing this on customs when the customer will not pay for engineering, design or drawing time particularly if I think they will shop it out once the concept works.
Of course any made part and in hand can be copied by a local house who invested no work.

Sometimes a opps or miss. Sometimes just a quick draw, other times intentional and not solvable.
Bob

8. Diamond
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IME, features without full explicit dimensions were very common in the earlier years of my machining career. When one was setting up a turret lathe with a form tool to generate the angle and radius, one needn't know down to the gnat's ass where the angle to radius tangency was. Kind of like Ox mentioned, you made some assumptions and maybe scaled the drawing. Ground the tool and maybe even checked it with a comparator (though most likely a protractor and radius gage).

Only when NC started showing up and some poor schmuck had to generate code for such features did it really start to be helpful to get full explicit dimensions on the drawing.

9. Stainless
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I would expect it to have been common 50 years ago, when people were designing things by hand on a drafting board. Today there's no excuse for the dimension, at least that angle, not to be included, as all it takes is to snap a dimension on your sketch in whatever CAD you're using.

10. Diamond
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Originally Posted by Ox
...
From Bill's post in #4, it seemed to me that he said that there wasn't enough info to doo it with trig and that you would need CAD to get the answer.

My guess was that the CAD would perform the Higher and Lower game to find the answer as well.
IDK how CAD werks. I didn't program it.
Think Snow Eh!
Ox
CAD not needed but I think way easier.
Cad does not do the guess and check method inside the brains as it where.
Circle known and line tangent through a point in space. How hard can that be?
Turns out to be mess.
Salute to angelw and those who get deep into these things and like it.
I think these guys like brain teasers.
Bob

11. Diamond
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Originally Posted by Ox
......From Bill's post in #4, it seemed to me that he said that there wasn't enough info to doo it with trig and that you would need CAD to get the answer.
Bill's response in post 4 was saying the triangles depicted in an earlier post would not work because of insufficient information. Bill's image in post 4 shows a geometric/trigonometric solution with the dimensions supplied by the OP. It's actually a pretty easy problem and, from my early years of CNC programming, a common solution to have to find.

12. Back in '89 when I first started on a cnc lathe we didn't have cad. We had a calculator, pencil and paper.
I can't tell you how many programs I wrote for Poly-Vee pulleys that were all incremental with no cutter comp, and with sub programs.
I must have drawn a million tangent triangles like the OP needs.

It still haunts me to this day.

13. Titanium
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'83 here, but I had it easy. Sodick wire EDM that actually had 'cutter comp' (G41/2) and the ability to subroutine programs. Made multiple finish passes a lot less work.

I used to send drawings to a friend for laser cutting. I'd add every dimension to tangency points and arc centers. Saved him time and hassle of going thru the programming dept, and he could just punch it in at the machine whenever he had some down time between jobs.

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Originally Posted by Ox

From Bill's post in #4, it seemed to me that he said that there wasn't enough info to doo it with trig and that you would need CAD to get the answer.
Hello Ox,

My reference to not enough information was in relation to the two triangles proposed by Mtndew, where the dimension of only one side of one triangle is known. I made reference to there being more elegant methods of obtaining the answer, mathematically, along the lines of my solution to the fun problem in Post #16 by the dude31, but the OP's question was specifically about triangles required for Trig to calculate the coordinates of P2, so that's the answer I provided.

I've seen plenty of hard copy drawings like the OP's, where clearly they have been generated by CAD and not enough dimensions provided on the hard copy to be able to just plug the numbers into a calculator to get the answer more directly than my solution. If the angle had been supplied, the solution for P2 would be two steps in Trig, but overall, it's not a difficult problem using Trig.

Regards,

Bill

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Well, here’s what I came up with in class today working with my teacher. My head was spinning afterwords. Definitely need to practice this stuff. Repetition will be key for me here.

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Originally Posted by Dhoverson
Well, here’s what I came up with in class today working with my teacher. My head was spinning afterwords. Definitely need to practice this stuff. Repetition will be key for me here.
Hello Dhoverson,
So is what you came up with the same as your Post implies, that being nothing, zero?

Regards,

Bill

17. I just about posted that same thing, but I let it go.

LOL!

Not sure I've ever seen a humorous post from Bill before?

You're up kinda late aint'chew William?

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Ox

18. Plastic
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haha! whoops. tried to post a pic from my phone. I'll have to try it from the computer in a bit.

19. Plastic
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bad pic quality. see page three.
Last edited by Dhoverson; 02-25-2021 at 11:09 PM.

20. Plastic
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bad pic quality. see page three.
Last edited by Dhoverson; 02-25-2021 at 11:09 PM.