# Origin of precision



## Koi (Sep 27, 2019)

Yeah so I have been questioning myself frequently how did all of this came from.obviously a true flat surface can be made with the three plates me to but how about true squarness or roundness I don't see them mentioned on the internet like when you ask for the invention precision,it's all gonna sound like you get a very flat surface and something something calibrating.Is there any method to it.


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## RJSakowski (Sep 27, 2019)

Koi said:


> Yeah so I have been questioning myself frequently how did all of this came from.obviously a true flat surface can be made with the three plates me to but how about true squarness or roundness I don't see them mentioned on the internet like when you ask for the invention precision,it's all gonna sound like you get a very flat surface and something something calibrating.Is there any method to it.



A flat surface can be used to verify a straight edge.  A square with two straight edges can be verified square with a surface with one straight edge.   If you scribe two lines atop each other on the surface, one with the off leg to the left and the other with the leg to the right and the lines coincide, the square is square.  Refinements on the procedures can yield whatever accuracy you desire.  
A parallel can be verified parallel by placing on a flat surface and sweeping with an indicator.  Roundness can be checked by rotating the surface in a vee block and checking for variation in height with an indicator.  Note that the indicator doesn't have to be calibrated to function.


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## RJSakowski (Sep 27, 2019)

There was an interesting tv program on about twenty years ago where teams of contestants were placed on a deserted island and given various tasks like accurately mapping the island using only objects that they found on the island.  They essentially had to recreate technology from scratch to make the tools required to complete the tasks.


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## Koi (Sep 27, 2019)

RJSakowski said:


> There was an interesting tv program on about twenty years ago where teams of contestants were placed on a deserted island and given various tasks like accurately mapping the island using only objects that they found on the island.  They essentially had to recreate technology from scratch to make the tools required to complete the tasks.


But how you make something square when you have no square though you can draw a square with a compass.


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## Bob Korves (Sep 27, 2019)

Koi said:


> But how you make something square when you have no square though you can draw a square with a compass.


You make (or buy) a reference square to work off of:




Keep in mind that there is no such thing as perfection, only working closer as required with more carefully built tooling.  As shown in the video, you can pretty easily test what you have, to see if it is within your needs for what you are working on.


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## Mitch Alsup (Sep 27, 2019)

The above talk in geometrical terms: flatness, squareness, roundness.

In order to make his steam engines work, James Watt had to invent the micrometer.


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## RJSakowski (Sep 27, 2019)

Koi said:


> But how you make something square when you have no square though you can draw a square with a compass.



With two squares back to back the other two sides will be a straight line.  A third square will tell you which one is out, much like the three surface plates.  This is essentially what I outlined above.  

In checking my try squares for accuracy, I will draw a perpendicular line from a straight edge, flip the aquare and draw a second line.  The two lines should be parallel.  For a more exacting measurement, , I would use a parallel.  Bring the parallel into contact with the perpendicular edge of the square and fix it in place.  Flip the square and check for any gap with the opposite edge of the parallel.  With a feeler gage, you should be able to check to within a thousandth over 6".   There are other methods which can be used based on other geometric principles.  Four squares back to back will touch, a good way to check 1-2-3 blocks.  

I machined a  7", 45º reference square from some 1/2"aluminum plate.  I used my rotary table to make the cuts as it was the best tool that I had at the time to make accurate 90º cuts. The square turned out to have be 90.006º to 90.021º with 45.003º to 45.007º for one 45 and 44.976º to 44.987º for the other 45. by direct measurement of the three sides and some trigonometry.

 Not having access to a mill to cut a square, I could fabricate one from three pieces of sheet metal fastened to make a triangle.


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## Koi (Sep 27, 2019)

Bob Korves said:


> You make (or buy) a reference square to work off of:
> 
> 
> 
> ...


So that means that there's no perfect square in the world only how close you can get.but how do they make right angle object back in the days with no measurement tool and do they even know it's existence.


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## Koi (Sep 27, 2019)

RJSakowski said:


> With two squares back to back the other two sides will be a straight line.  A third square will tell you which one is out, much like the three surface plates.  This is essentially what I outlined above.
> 
> In checking my try squares for accuracy, I will draw a perpendicular line from a straight edge, flip the aquare and draw a second line.  The two lines should be parallel.  For a more exacting measurement, , I would use a parallel.  Bring the parallel into contact with the perpendicular edge of the square and fix it in place.  Flip the square and check for any gap with the opposite edge of the parallel.  With a feeler gage, you should be able to check to within a thousandth over 6".   There are other methods which can be used based on other geometric principles.  Four squares back to back will touch, a good way to check 1-2-3 blocks.
> 
> ...


Sorry I'm having a hard time to understand how does the technique work is there any pictures of it so I can understand .


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## RJSakowski (Sep 27, 2019)

Koi said:


> Sorry I'm having a hard time to understand how does the technique work is there any pictures of it so I can understand .







Here is a diagram I did up some time ago.  It shows the actual out of square  conditions of  three imperfect squares, A, B, & C.  For any pair of squares, you can measure the out of squareness of that pair but you can't determine what the contribution is by each square.  However, if you pair each of them in turn with the others, you now will have three measurements, one for pair AB, one for AC, and one for BC.  These measurements are shown in green in the upper left.    With some algebraic manipulation, you can calculate the contribution of each square, shown as the red numbers.

I know you thought that you left algebra behind you when you left school.  Sorry for that.  Here is the original post: https://www.hobby-machinist.com/threads/are-these-squares-worth-it.57978/page-2#post-477082 post #34


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## Bob Korves (Sep 27, 2019)

Koi said:


> So that means that there's no perfect square in the world only how close you can get.but how do they make right angle object back in the days with no measurement tool and do they even know it's existence.


Ask Pythagoras.  A triangle with sides of 3, 4, and 5 units of length on the sides will make a perfect square at one corner.  The 3, 4, and 5 can be repeated lengths of anything you want to use to lay it out, could be a piece of bone.  You do not need an existing angle or a scaled rule to make a 90 degree corner.


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## Bob Korves (Sep 27, 2019)

RJSakowski said:


> I know you thought that you left algebra behind you when you left school.


I really learned geometry and trigonometry in high school, and now at 68 years old, I am really glad I did.  I can work those problems just about as well now as I did then, and I got straight "A" grades then (in those classes, anyway) and that would have been 52 and 53 years ago.  It is a matter of using the memory often enough to keep them at places in the brain that store commonly used inputs and outputs.  I am now sadly learning what happens to stuff you do not revisit often enough...


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## Koi (Sep 27, 2019)

RJSakowski said:


> View attachment 302843
> 
> 
> Here is a diagram I did up some time ago.  It shows the actual out of square  conditions of  three imperfect squares, A, B, & C.  For any pair of squares, you can measure the out of squareness of that pair but you can't determine what the contribution is by each square.  However, if you pair each of them in turn with the others, you now will have three measurements, one for pair AB, one for AC, and one for BC.  These measurements are shown in green in the upper left.    With some algebraic manipulation, you can calculate the contribution of each square, shown as the red numbers.
> ...


Algebra I like simple algebra but not the complicated one.


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## whitmore (Sep 28, 2019)

RJSakowski said:


> There was an interesting tv program on about twenty years ago where teams of contestants were placed on a deserted island and given various tasks...


Yes, Rough Science was ... wonderful.   The BBC issued a 3-DVD set, maybe your library has it...
<https://www.imdb.com/title/tt0363367/?ref_=fn_al_tt_1>


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## whitmore (Sep 28, 2019)

Koi said:


> So that means that there's no perfect square in the world only how close you can get.but how do they make right angle object back in the days...


Using trickery, of course.   To check an angle block, park it on a straight edge, and sight down the straight edge; the reflection
you see won't 'kink' the image of the edge.  Similarly, a corner-cube reflects an erect image of (for instance) your face.
Get the angles wrong, it is rather obvious.

Also our ancestors used great reservoirs of ... tolerance.


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## Downunder Bob (Sep 28, 2019)

Google basic geometry and you will find numerous courses, some are free. They will explain a lot of the basic principles, from which you can create all kinds of shapes. Going back to the ancient Egyptians they had a very good understanding of geometry, which enabled them to build the pyramids.


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## Koi (Sep 28, 2019)

Downunder Bob said:


> Google basic geometry and you will find numerous courses, some are free. They will explain a lot of the basic principles, from which you can create all kinds of shapes. Going back to the ancient Egyptians they had a very good understanding of geometry, which enabled them to build the pyramids.


Ok


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## Koi (Sep 28, 2019)

whitmore said:


> Using trickery, of course.   To check an angle block, park it on a straight edge, and sight down the straight edge; the reflection
> you see won't 'kink' the image of the edge.  Similarly, a corner-cube reflects an erect image of (for instance) your face.
> Get the angles wrong, it is rather obvious.
> 
> Also our ancestors used great reservoirs of ... tolerance.


What do you mean by reservoirs of tolerance?


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## mcdanlj (Sep 28, 2019)

There was a recent general interest book introducing the history of precision. It was generally well-written and I enjoyed reading it.





__





						The Perfectionists: How Precision Engineers Created the Modern World: Winchester, Simon: 9780062652553: Amazon.com: Books
					

The Perfectionists: How Precision Engineers Created the Modern World [Winchester, Simon] on Amazon.com. *FREE* shipping on qualifying offers. The Perfectionists: How Precision Engineers Created the Modern World



					www.amazon.com
				




It opens with the author's experience as a child learning about wringing jo blocks, and as a coincidence I read it the day after I had just been explaining exactly this concept to my son of about the same age the author was when he learned... ☺


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## Bob Korves (Sep 28, 2019)

Koi said:


> Algebra I like simple algebra but not the complicated one.


What we are discussing here is pretty much all trigonometry.


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## RJSakowski (Sep 28, 2019)

whitmore said:


> Yes, Rough Science was ... wonderful.   The BBC issued a 3-DVD set, maybe your library has it...
> <https://www.imdb.com/title/tt0363367/?ref_=fn_al_tt_1>


That's the one!  Thanks for the link!


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## Downunder Bob (Sep 28, 2019)

Bob Korves said:


> What we are discussing here is pretty much all trigonometry.



Well yes it is, however its' quite amazing what geometric shapes and angles you can generate without using any numbers, trig,or calculations, just basic geometric principles that I learned in primary school. All you need is teh ability to draw a circle and a straight line. From there you can generate a perfect right angle (90) deg triangle, So we have a true 90 deg, we can then define 45 deg, and 22.5, and etc. We can also generate 30,and 60 degree angles, also 15 and 12.5 deg plus many others without ever measuring or calculating anything

This is how the ancient Egyptians did it using Pythagoras theorem and other geometric theorems and rules etc.


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## whitmore (Sep 28, 2019)

Koi said:


> What do you mean by reservoirs of tolerance?


I had in mind the inverse of precision.   Apply a stone or file if it doesn't fit, or keep the
part A in a box until you make a part B that accidentally mates to it...  

All the Morse tapers were intended to be 0.625 inch per foot, I hear, but vary from 0.59858 (MT1) to 
0.63151 (MT5) .   A normal  tolerance is 0.002 inch per foot nowadays.

As long as you always copy the master sample, it works (but the 'nominal' taper is a plan that
got implemented VERY loosely.


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## dart70ca (Sep 29, 2019)

Koi said:


> Yeah so I have been questioning myself frequently how did all of this came from.obviously a true flat surface can be made with the three plates me to but how about true squarness or roundness I don't see them mentioned on the internet like when you ask for the invention precision,it's all gonna sound like you get a very flat surface and something something calibrating.Is there any method to it.


There is a book called 'Fundamentals of Mechanical Accuracy' by Wayne R. Moore. Supposed to be the bible on this subject. Very expensive book though.


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## RJSakowski (Sep 29, 2019)

The task here is creating and then verifying a master square using a minimum of tools for evaluation.  Several means of creating right angle are available.  The 3-4-5 triangle is one.  Bisecting the 180º contained angle of a straight line is another. a quadrilateral with equal sides and equal adjacent angles is a third.

Accurately verifying a 90º angle is a little more complicated.  Particularly if you want to resolve angles to a minute of arc or better.  A 3-4-5 triangle works great for landscaping or architectural work but an error of 1/16" over a 10 ft span of a 6-8-10 triangle will result in result in an angular error of 30 minutes.

If I were trying to verify a reference square with 10" sides using a minimum of metrology tools, the three square method will do it in much the same manner that surface plates are made flat.  If two candidate squares, A and B, are brought together and to a straight edge, there will most likely be a small gap at either the base or the apex of the joint.  The gap can be removed by milling, grinding, filing, scraping, or lapping half from each square to make a perfect joint. The fit can be checked by bluing.  The sum of the two angles will then = 180º.

The process is repeated for squares B & C, and then for squares C & A.  Each iteration will bring the squares closer to a true 90º.  Starting with errors greater than 1º, nine iterations will yield a true 90º to within 1 second of arc.

A straight edge can be made by milling, grinding, filing, scraping, or lapping a metal bar  or piece of stone and checking against a surface plate.   And  of course three limps of rock can be used to make a surface plate to whatever flatness you desire.

So there you have it.  A prexcision square made usng no sophisticated metrology tools and no mathematics.


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## StevSmar (Sep 29, 2019)

RJSakowski said:


> ... So there you have it.  A prexcision square made usng no sophisticated metrology tools and no mathematics.


This sounds like it would be very tedious if granite squares were used instead of metal.

I’m intrigued by the process of how you get from a flat plate to being able to check a machines ways for flatness and trueness!


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## nnam (Oct 1, 2019)

I wonder if they use pour glass to have flat precision surface.  I am sure it's not normal pour, but has to have certain way like control cooling to not have a dent in the middle, but who knows.  It just seems an easy method compared to others.  Glass is weak, but it's a bootstrap to stronger material.


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## RJSakowski (Oct 1, 2019)

nnam said:


> I wonder if they use pour glass to have flat precision surface.  I am sure it's not normal pour, but has to have certain way like control cooling to not have a dent in the middle, but who knows.  It just seems an easy method compared to others.  Glass is weak, but it's a bootstrap to stronger material.


Float glass is used for optical devices.  Molten glass is floated on a lake of molten tin and allowed to solidify to create a flate plate.  I had thought about using some plate glass as a flat surface but my measurements showed that it wasn't nearly flat enough. 

There are precision optical flats which are very flat but they are quite expensive and usually not that large.  An 8",  .03 micron optical flat from Edmund Optical will set you back more than $4K.  Optical flats are useful for evaluation other flat surfaces.  Tom Lipton, OxTools, did a good video on using them.


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## Koi (Oct 1, 2019)

nnam said:


> I wonder if they use pour glass to have flat precision surface.  I am sure it's not normal pour, but has to have certain way like control cooling to not have a dent in the middle, but who knows.  It just seems an easy method compared to others.  Glass is weak, but it's a bootstrap to stronger material.


Heard it before


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## matthewsx (Oct 1, 2019)

Read this book:



			http://frank.villaro-dixon.eu/public_upload/Foundations%20of%20Mechanical%20Accuracy%20by%20Wayne%20R%20Moore%20-%201970.pdf
		


More to learn about flat than you ever imagined.

John

Edit, I see someone has already mentioned it, you can download it for free though.


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## RJSakowski (Oct 1, 2019)

matthewsx said:


> Read this book:
> 
> 
> 
> ...


It will make for some great reading on those cold winter nights.  Thanks for the link!


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## DAT510 (Oct 1, 2019)

Here’s a great video asking the same question. 






The channel has a number of other videos looking at the history of machine technology.


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## Koi (Mar 1, 2020)

RJSakowski said:


> The task here is creating and then verifying a master square using a minimum of tools for evaluation.  Several means of creating right angle are available.  The 3-4-5 triangle is one.  Bisecting the 180º contained angle of a straight line is another. a quadrilateral with equal sides and equal adjacent angles is a third.
> 
> Accurately verifying a 90º angle is a little more complicated.  Particularly if you want to resolve angles to a minute of arc or better.  A 3-4-5 triangle works great for landscaping or architectural work but an error of 1/16" over a 10 ft span of a 6-8-10 triangle will result in result in an angular error of 30 minutes.
> 
> ...


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## stupoty (Mar 1, 2020)

dart70ca said:


> There is a book called 'Fundamentals of Mechanical Accuracy' by Wayne R. Moore. Supposed to be the bible on this subject. Very expensive book though.












						Foundations of Mechanical Accuracy by Wayne R Moore   1970 : Free Download, Borrow, and Streaming : Internet Archive
					

Foundations of Mechanical Accuracy by Wayne R Moore 1970



					archive.org


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