Using Trigonometry for manual programming

# Thread: Using Trigonometry for manual programming

1. Plastic
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## Using Trigonometry for manual programming

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

2. Plastic
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Here's a pic of the print

3. Originally Posted by Dhoverson
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.
Excuse the curvy lines, I'm not right handed and can't draw with a mouse.
On the Vertical line where the red and green meet are your 90 deg angles for each triangle.

4. Diamond
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Originally Posted by Mtndew
Excuse the curvy lines, I'm not right handed and can't draw with a mouse.
On the Vertical line where the red and green meet are your 90 deg angles for each triangle.
Hello Mtndew,
Maybe I'm not seeing it, but I don't believe there is enough information to be able to use the triangles you propose. The only known side of those two triangles is the hypotenuse of the lower triangle.If you knew the chord from P1 to P2, then Heron's Form could be used with your two triangles.

There are more elegant solutions to this problem, but for the OP to use Trig, I think he would need to get the angle of the line from Y0.5 and tangent to the arc.

To do this, the acute angle of the Green Triangle (two sides known), shown in the following picture, will allow the acute angle of the Blue Triangle (two sides known after the Green Triangle is resolved)to be calculated. The combination of these two acute angels will allow P2 to be calculated using the Magenta Triangle.

Regards,

Bill

Last edited by angelw; 02-24-2021 at 04:07 PM.

5. Plastic
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First post, thought I'd better try and input something before I ask Bill about Fanuc servo drives!
Excuse the grease.
No one will ever give you a drawing like that. They are normally dimensioned to the intersection

6. Plastic
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Welcome to the trade. You'll regret it later. lol
Here's a fun one for you.

7. Diamond
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Originally Posted by Mtndew
Excuse the curvy lines, I'm not right handed and can't draw with a mouse.
trackball....................without CAD I think you are short a dimension for a solution, either and angle somewhere or a length or something. Where are the Y locations of those triangles ? In CAD you just draw the circle and make a tangent line and pick the point.
 just figured out Franks scrawl, damn what a pain, CAD is faster, I suppose they make you use trig tables too....

8. Stainless
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In industry, the correct answer is to spend three minutes to draw it up in Solidworks. Too much time and chance of error when you do it longhand. That said, it's good to be able to do that sort of thing longhand; I once had to prove longhand that the output of a rolldie post processor was correct before the customer would have their machine checked. Turns out they needed servo tuning.

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Originally Posted by mhajicek
In industry, the correct answer is to spend three minutes to draw it up in Solidworks. Too much time and chance of error when you do it longhand.
Absolutely, but the point of a school is to teach you how and why something works. When you know the whys you can take shortcuts, but if you don't even know why, you're lost. As we can see in many posts here asking very elementary questions.

I also think that particular drawing is evil, but obviously it was intended to be

10. Originally Posted by angelw
Hello Mtndew,
Maybe I'm not seeing it, but I don't believe there is enough information to be able to use the triangles you propose.
I know, he was asking how to draw initial triangles to solve problems like this.
I didn't want to do his homework but I gave him an example of how it's done (if all of the dimensions were there).

11. Diamond
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Originally Posted by EmanuelGoldstein
.....
I also think that particular drawing is evil, but obviously it was intended to be
This seems very evil for students just entering the world of trig. Is it meant to teach one that cad is much easier?
There is a button for line tangent to circle through a point. There are of course two but only one makes sense and the cad figures out which from the picks.

Wonder what project 53-06 was?
Bob

12. Everyone knows math is racist and 2+2=5

13. Plastic
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Originally Posted by thedude31
Welcome to the trade. You'll regret it later. lol
Here's a fun one for you.
Haha! That one looks like a headache. I really appreciate the responses everyone. I’ll take a look at your examples and see if I can make sense of them. I work in the Aerospace industry in WA. Been in if for 10 years now building commercial airline interiors. Everything from working on moving lines building luggage stowage bins to running larger infrared ovens for a vacuum form process for applying decorative laminate to parts, to now for about the last year I’ve been a 3 axis router table operator. Running the 3 axis routers isn’t a terrible gig. They give you your work package for the day and you just keep the machine running.

However, I really wanted to get a transferable skill under my belt. Something that could be applied to any industry in just about any place my family and I would ever live. I started looking into all things machining a while back and felt really drawn to it. It’s definitely the most technical, and vast subject matter I’ve ever looked into. And I thought going through automotive tech school back in 2005-2007 was technical. Haha!

We have tooling machinists at work that work on press dies and such. I’m aiming to get into that shop and go from there or get into the apprenticeship program if I can get accepted. It’s very competitive and not opened up very regularly. I’ve been bitten by the machining bug so bad I’ve even considered selling an extra vehicle we have to buy a mill for the home shop. Haha.

I hope to continue learning and as such hopefully I can contribute to this board some day. I’ll be sure to post some pics of the finished parts from school when I’m done.

Thanks again for your replies everyone.

Drew

14. Aluminum
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Originally Posted by Dhoverson

I hope to continue learning and as such hopefully I can contribute to this board some day. I’ll be sure to post some pics of the finished parts from school when I’m done.

Thanks again for your replies everyone.

Drew
You'll do fine. I also used community college to break into machining. And then I used it again to break into NC programming. Onwards and upward!

15. Plastic
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Originally Posted by davehud
You'll do fine. I also used community college to break into machining. And then I used it again to break into NC programming. Onwards and upward!
Right on. Glad to hear I'm not the only one. The machinists at work tell me to never stop learning. They take a Mastercam class every year to stay current among other things. Feels good to turn the brain back on after a decade of doing repetitive manufacturing.

16. Diamond
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Originally Posted by thedude31
Welcome to the trade. You'll regret it later. lol
Here's a fun one for you.
Hello thedude31,

You've got to make it a bit harder than that for him.

The hypotenuse = 8.6023

Therefore
A = 7 x 5 x 0.5
A = 17.5
Where:
A = Area

HP = (7 + 5 + 8.6023) / 2
HP = 10.30115
Where:
HP = Half Perimeter

R = A/HP = 17.5 / 10.30115
R = 1.6988

Regards,

Bill

17. Originally Posted by angelw
Hello thedude31,

You've got to make it a bit harder than that for him.

The hypotenuse = 8.6023

Therefore
A = 7 x 5 x 0.5
A = 17.5
Where:
A = Area

HP = (7 + 5 + 8.6023) / 2
HP = 10.30115
Where:
HP = Half Perimeter

R = A/HP = 17.5 / 10.30115
R = 1.6988

Regards,

Bill
I've had lots of higher maths and I've never been taught this shit. Wtf

Semiperimeter - Wikipedia

Learned something today. A=rs. huh.

18. Aluminum
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Originally Posted by Dhoverson
Right on. Glad to hear I'm not the only one. The machinists at work tell me to never stop learning. They take a Mastercam class every year to stay current among other things. Feels good to turn the brain back on after a decade of doing repetitive manufacturing.
I had a 40 year career in aerospace. Loved it. From running engine pylons on manual DeVliegs to programming landing gear parts on a 5-axis rotary head gantry.

19. Plastic
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Originally Posted by angelw
Hello thedude31,

You've got to make it a bit harder than that for him.

The hypotenuse = 8.6023

Therefore
A = 7 x 5 x 0.5
A = 17.5
Where:
A = Area

HP = (7 + 5 + 8.6023) / 2
HP = 10.30115
Where:
HP = Half Perimeter

R = A/HP = 17.5 / 10.30115
R = 1.6988

Regards,

Bill
Dear mother of god... lol

20. Titanium
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I had something like that to program a wire EDM to make a die. It had a tab hanging off part of it, not fully dimensioned. I struggled and struggled with it, and after many steps had a solution the machine would accept. I figured I just sucked at Trig.

Some time later a rep for the machine dealer stopped by and saw it. He'd been through some CAM classes, 'that looks pretty tough, how did you program it?'. By hand. 'Umm, how would you like to teach a programming class?' No thanks.

I've seen a lot more since. And as already noted, I generally draw it up in CAD and pull numbers off of it. Unless I'm feeling like I need a challenge for some stupid reason.