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Hmm, my mistake, maybe it had not loaded when I looked.
I guess it would be ok for teaching trig in class but there are easier formulas as well as just using the DRO in your photos.
Are you going to teach a class with it?
During my career as a machinist I never saw any one using trig to solve a bolt circle. Everyone used the machinery handbook or a slide rule chart from Everede or the program in the DRO.
During my career as a machinist I never saw any one using trig to solve a bolt circle. Everyone used the machinery handbook or a slide rule chart from Everede or the program in the DRO.
Are you serious ????
No offense, but Where did you work ?
Trig'n a bolt circle is easy and quick.
Sine x angle x radius = one leg
cosine x angle x radius = opposite leg.
repeat x,y coordinates as needed around the circle.
I note that you are or seem to be using all +ve values for linear and angular values.
Using a DRO has its inherent problems.
If you are going to use the +ve and -ve quadrants (and angles) and you are referenced on the center of the circle/flange/pitch circle (X = 0.000, Y = 0.000) then you need to use both +ve and -ve angles and sides of triangles.
Further, you need to show +ve and -ve values of X and Y.
The math can get a bit "sticky" unless all values are all +ve or all -ve.
Its too easy to get "lost" in the +ve (top right and bottom left) and -ve (top left and bottom right) "quadrants".
There is a fair bit of geometry in amongst that trigonometry.
Most of the standard numbers of holes on pitch and other circles are equally divisible into 360 ie. 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24 - which is all nice and tidy.
In all of those cases it is quite easy.
It is when you come to 7, 11, 14, 16, 17, 19, 21, 22, 23 that problems arise if decimal parts of a whole are provided and where conversion of decimal degrees to degrees:minutes:seconds (d:m:s) is required for rotary tables, dividing heads, protractors etc. and any other non-decimal angular settings are required. Of course if an angle between two or more holes is in d:m:s it needs to be converted to decimal degrees for use in trigonometry (if digital calculation is used and not for use on a slide rule or a book of "Log tables") and for use on a DRO.
KiddZ, I worked in job shops and we didn't have time to sit around and do a lot of math. We had to get the job done and out the door. Since the Machinery Handbook has a easy way to solve we used it mostly unless we had a DRO with a bolt circle program. At one shop I worked I was shown the slide rule type chart by Everede that did the layout easier and I bought several of them and passed them out. It saved everyone a lot of time and trouble and errors. Why would I want to sit down with paper, pencil and calculator and use trig when it has already been done for me?
It's nice to know trig when your learning math and sometimes you will use it. In the real world not many machinists will use trig or have the time to use it unless needed for a certain job and bolt circles is not one of those special jobs, there are easier ways to do a bolt circle.
Never mind the "knockers" and "naysayers" Doozer. You are the right track and doing OK.
This is Shop Math 101 and needs to be taught, understood and used.
Only one other point I'd make is that it is quite OK to work in the first (top right) quadrant (where everything is +ve) and then to "mirror" (as in CAD) the result/s about the X and/or Y axis as required.
Its just a "recognition" or "identity" thing.
In that case no angle will be greater than 90 and all values will be +ve.
Working between 90 and 180 degrees (whether +ve or -ve) is prone to error and best avoided if possible.
I solved a similar problem in the woodshop the other day using geometry. 3 points (A, B, and C) on a circle. But I don't know where the center is. Draw line from A to B. Find midpoint. Draw normal line through midpoint. Repeat for B and C. Where the normal lines cross is the center of the circle.
Good thinking Tony. Making good use of what is available with lateral thinking to get the job done.
I'd suggest getting a good - even "Chinese" - Combination Square set. Here is mine:
The 12" ruler fits all three units: centre square, protractor and square (90 and 45 degrees).
Use the centre-square (left one). The rule will bisect (halve) the 90 degree angle.
Put the 90 degree square on the "round" you are measuring and scribe/pencil/mark a line on the top edge of the ruler on the "round". Do at least two lines this way. Where they cross is the centre of the circle/"round".
It's nice to know trig when your learning math and sometimes you will use it. In the real world not many machinists will use trig or have the time to use it unless needed for a certain job and bolt circles is not one of those special jobs, there are easier ways to do a bolt circle.
Its almost impossible to run a rotary head mill without Trig. Building molds and figuring draft angles and to ways to check the electrodes you just ground and such. Trig was used everyday from the minute I walked into the shop. I still use trig daily building and repairing molds.
Good thinking Tony. Making good use of what is available with lateral thinking to get the job done.
I'd suggest getting a good - even "Chinese" - Combination Square set. Here is mine:
The 12" ruler fits all three units: centre square, protractor and square (90 and 45 degrees).
Use the centre-square (left one). The rule will bisect (halve) the 90 degree angle.
Put the 90 degree square on the "round" you are measuring and scribe/pencil/mark a line on the top edge of the ruler on the "round". Do at least two lines this way. Where they cross is the centre of the circle/"round".
That was photographed some time ago - just after I bought it.
I keep my tools clean - and sharp - and "ready for use". I have most of them in boxes or drawers or on or under shelves. It only takes a minute to clean them and put them away. That particular box - as it the case (sorry) for many others was just too good to toss away.
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