What math subjects are used when Machining/Programming?

I'm trying to figure out what type of math is used when machining/programming. If it could be narrowed down to a specific subject, that would be good. So I can get a book and self-teach on that subject. Besides basic math, I've heard trigonometry. But them I'm reading that you may need to know other things before getting to trigonometry. I've really only got basic math down at this point. I'm trying to G-code a 2 axis lathe and can't do any radius/chamfer that isn't a 45. I also don't know how to single point thread, much less a NPT or BSP. (Just confused on what little I know about it, something about angle of the threading tool and how that works when threading)

I looked for a off topic sub-forum and didn't see one. Sorry for being blind, if there is.

I would say basic algebra, geometry, and trig. You can solve a huge number of problems by cobstructing triangles. The high school textbooks teach this material pretty effectively and can be purchased used on ebay for under $10. Theres also khan academy woth free video lessons and quizzes. I recommend Glencoe McGraw hill books geometry and alegebra(pre algrbra if really behind) to start. You need to know algebra to do trig, geometry you can get by with more basic algebra skills.

For determining angles, learn the trig functions sine cosine and tangent. Easy to implement on a calculator without much algebraic manipulation and can do 80% of basic machining angle calculations

Glorifire said:

I would say basic algebra, geometry, and trig. You can solve a huge number of problems by cobstructing triangles. The high school textbooks teach this material pretty effectively and can be purchased used on ebay for under $10. Theres also khan academy woth free video lessons and quizzes. I recommend Glencoe McGraw hill books geometry and alegebra(pre algrbra if really behind) to start. You need to know algebra to do trig, geometry you can get by with more basic algebra skills.

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Thank you! I didn't think about looking on ebay for used HS books.

Not to discourage you from learning more math (I'm a big fan of continuing education), but look into getting a simple CAD system for doing geometric layouts. You can generally construct most shapes by only knowing part of the features and then solving for the rest by adding radius blends or angled chamfers where needed.

Then pull the geometry coordinates from the file, and use them for programming. You can do offsets to account for tool nose radii, once you're handy with it you'll find it quite useful.

Perhaps a seat of Fusion 360 would help you out, or one of the other low cost CAD/CAM packages out there. Even with my poor math skills, being able to draw in CAD has removed most of the limitations in a machining environment.

Able to count above 21 without removing footwear...or underwear…..

I agree learn sin, consine, and tangent trig functions.
Also memorize A squared + B squared = C squared for any right triangle. C is always the longest side, known as the hypotonuse. This is known as the Pythagorean theorem.
Also memorize that a 3,4,5 triangle is a right triangle.
Learn circular function of relation of radius, diameter and circumference. Circumference equals Phi X Diameter
Bill D

Circumference = pi * Diameter

Er, ok, that could have come off as being a dick. But phi is used for a number of other specific things, most applicably angles or polar coordinates.

On further reflection, it was probably just a typo. Sorry.

I have a cheapy CAD program I use for layouts. One thing to be aware of is that the minimum unit used by some CAD programs can throw off results - you get a slightly different result on the calculator than what the CAD program tells you.
These CAD programs use a unit, and the world is a set number of X units by Y units. The unit can be feet, giving a big world,or thous, giving a tiny world - and better accuracy.
I now use the CAD program as a sanity check when doing trig on the calculator.

Milland said:

Not to discourage you from learning more math (I'm a big fan of continuing education), but look into getting a simple CAD system for doing geometric layouts. You can generally construct most shapes by only knowing part of the features and then solving for the rest by adding radius blends or angled chamfers where needed.

Then pull the geometry coordinates from the file, and use them for programming. You can do offsets to account for tool nose radii, once you're handy with it you'll find it quite useful.

Perhaps a seat of Fusion 360 would help you out, or one of the other low cost CAD/CAM packages out there. Even with my poor math skills, being able to draw in CAD has removed most of the limitations in a machining environment.

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I am all for using cad/cam for anyything more complicated than 2+2!

Seriously though, I *had* to learn trig in my tool and die apprenticeship classes, and promptly forgot most of it in the next year or two when I started using cad/cam software. What sucked, was we (as a class) had to go back to basic algebra (like pre-algebra I took in 7th or 8th grade) because so many in the class could not do it. Which meant our time with trig was shortened substantially.

I think really basic algebra is plenty. You can look up all the trig formulas in one of those pocket guides, no need to memorize them IMO. One thing that has helped me through the years is learning/memorizing alot of metric-inch conversions. It makes it easier IMO when looking at prints that are in metric instead of breaking out the calculator trying to figure if the feature is that big or this big and what is a tight tolerance and what is not.

I would say that Glorifire basically has it.

Yes, some basic algebra. You don't have to do the entire book, but get the basics. You can probably quit after solving two equations with two unknowns.

Geometry, again the basics would be needed. Again, you don't need to do the whole book, but keep it for future reference when you hit something you don't know.

And Trig! Trigonometry if probably the most important in the shop. You probably don't need the whole book, but probably more here than in algebra or geometry.

Start with the algebra as it will be useful with trig and possibly with geometry as well. And skim the parts of the book that you don't study in detail. Then the geometry because trig is built on top of geometry. Again skim the book and keep it for later reference. Do as much of the trig as you can. It will probably be the most useful in the shop. Skim the rest so your eyeballs will have at least seen it.

I love the idea of E-bay but you can also look at local thrift shops and second hand book shops if there are any in your area. The principles here do not change, so 50 or even a 75 year old books are almost equally useful as a year old one. Perhaps, even better due to "the new math".

Glorifire said:

I would say basic algebra, geometry, and trig. You can solve a huge number of problems by cobstructing triangles. The high school textbooks teach this material pretty effectively and can be purchased used on ebay for under $10. Theres also khan academy woth free video lessons and quizzes. I recommend Glencoe McGraw hill books geometry and alegebra(pre algrbra if really behind) to start. You need to know algebra to do trig, geometry you can get by with more basic algebra skills.

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It would help to have a good grasp of geometry and algebra. Trying to determine a solution is recognizing what is known and what is unknown. A good grasp of geometry and algebra helps to identify both. I'll draw on scratch paper pads for a visual image to get it in my head what I'm after sometimes. Doing layout using pencil on paper with a compass, protractor, and straight edge for practice can help develop your "feel" for bisecting angles, chords, and tangent. Trig is something I took in high school and thought it would be useless knowledge. I used trig on a daily basis on the job for over 25 years. It would be very helpful to learn the solutions of right triangles. Trig also deals with both acute and obtuse triangles (and other matters) but learning to work with triangles with ONE 90° angle will be easier to learn and solve the majority of things you'll encounter. These equations can be worked on a fairly basic calculator once you've worked out what is known and what is unknown, you don't have to memorize much (although it helps) beyond how to identify when you want sine, cosine, and tangent as others have already stated. A CAD program can be nice to quickly find an answer but it can also cause unit errors as posted above. There will also be many times the CAD program isn't available when you need it so it would be best to simply develop a working knowledge you carry in your head. Algebra, geometry, and trig are all tools so getting comfortable using them will serve you well. Used textbooks, videos, however you learn best is up to you. If the math is difficult for you then take heart, it wasn't easy for a lot of us either. Even Einstein had his difficulties with Mathematics. I hope this was of some help. Good luck.

microsoft excel (there are free versions of office type software too) can do math easily and formulas saved in worksheet is like a programmable calculator. change a factor and press enter and it can recalculate dozens of formulas in less than a second. made to do algebra and trig. quite popular with scientist and business accountants to do math
.
librecad which is free 2D cad software and youtube videos on it can be used to draw and the pick dimensions of what you want to do the math for you. when printed it is basically a hand held drawing with dimensions already figured out

Another good general purpose formula to know is the Law of Sines. Useful to solve any triangle, and a right triangle is a special case with simplified calculations.
I never encountered it until college level calculus and analytic geometry.

The basic math of add and subtract,
Then the ability to click and point with a mouse.
Once upon a time you needed to read a sundial to know what time it was, not so much now.
You do need to know X-Y-Z coordinates and maybe A-B-C in a relationship to the real (or part) world.
Rise over run is useful, and when to use sine but that is confusing.
Even on a manual machine a CAD program can help.

Old time machinists can still read sundials, that has been replaced by smartphones and computers.
Bob

digger doug said:

Able to count above 21 without removing footwear...or underwear…..

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So THAT'S where I went wrong

I think this is the book we had in high school.
Access to this page has been denied.

Higgins909 said:

I'm trying to figure out what type of math is used when machining/programming. If it could be narrowed down to a specific subject, that would be good. So I can get a book and self-teach on that subject. Besides basic math, I've heard trigonometry. But them I'm reading that you may need to know other things before getting to trigonometry. I've really only got basic math down at this point. I'm trying to G-code a 2 axis lathe and can't do any radius/chamfer that isn't a 45. I also don't know how to single point thread, much less a NPT or BSP. (Just confused on what little I know about it, something about angle of the threading tool and how that works when threading)

I looked for a off topic sub-forum and didn't see one. Sorry for being blind, if there is.

Click to expand...

Trig ,trig trig. I started(hand programing) 3 axis g code in 1975. Their were NO COMPUTERS IN AVERAGE TOOL AND DIE SHOPS.Many days I did 50 or 60 trig problems,figuring radii start and stop points copensateing for tool nose radius.Some machines were set up so that all xyz coordinates were at the center of the tool . Some lathe programs were set up from edge of tool radius. Lots of confusion. If you draw up 30 or forty right triangles with missing dimentions on diferent sides and angles ,and then solve them,it will help you a lot. Good luck.Edwin Dirnbeck

edwin dirnbeck said:

Trig ,trig trig. I started(hand programing) 3 axis g code in 1975. Their were NO COMPUTERS IN AVERAGE TOOL AND DIE SHOPS.Many days I did 50 or 60 trig problems,figuring radii start and stop points copensateing for tool nose radius.Some machines were set up so that all xyz coordinates were at the center of the tool . Some lathe programs were set up from edge of tool radius. Lots of confusion. If you draw up 30 or forty right triangles with missing dimentions on diferent sides and angles ,and then solve them,it will help you a lot. Good luck.Edwin Dirnbeck

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If you haven't noticed, times have changed!

Seriously, nothing wrong with knowing trig, but you (OP) are certainly not going to need it to this extent.

As an aside, how many shops don't have a pc with some type of cad and/or cam program loaded? It's like working in FL without AC, sure you could do it, but why???