# Using three pin gauges to extend measurement range



## Larry42

By using two pins the check a hole you can nearly double the range.


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## RJSakowski

Larry42 said:


> By using two pins the check a hole you can nearly double the range.


You can extend the range slightly more by using three pins.  The math gets more complicated but if you have CAD capability, the CAD math engine will solve it easily.  If you use three pins differing by +/- .0001, the diameter is 2.1547 x the middle pin diameter.


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## woodchucker

RJSakowski said:


> You can extend the range slightly more by using three pins.  The math gets more complicated but if you have CAD capability, the CAD math engine will solve it easily.  If you use three pins differing by +/- .0001, the diameter is 2.1547 x the middle pin diameter.


yes, but holding 3 pins in line becomes a little more difficult. You can do it, but you need to use 2 bars, sticks whatever to keep them in line... if they triangle out on you, you lose your measurement.


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## RJSakowski

woodchucker said:


> yes, but holding 3 pins in line becomes a little more difficult. You can do it, but you need to use 2 bars, sticks whatever to keep them in line... if they triangle out on you, you lose your measurement.


It isn't three pins in line. They form a triangle.  It is actually more stable than two pins as two pins have to be exactly parallel to each other to get an accurate measurement.  

An added bonus  is that three  pins can extend the precision of the measurement.  My pin sets all measure out at +.0002 or -.0002 from nominal, depending on whether a plus or minus set but the pins increase in .001" increments so the best I can do is to measure to within .001"  However if I use three pins, two of which are slightly under the radius of the hole, a third pin will actually resolve to about a tenth.  It requires some math to do this but my CAD program comes to the rescue for that.


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## Winegrower

RJSakowski said:


> If you use three pins differing by +/- .0001, the diameter is 2.1547 x the middle pin diameter.



RJ, this is really interesting, but not sure what you mean?   Do you really mean 0.0001?


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## RJSakowski

Winegrower said:


> RJ, this is really interesting, but not sure what you mean?   Do you really mean 0.0001?


Here is an illustration.


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## Winegrower

Really interesting.   I could make a table showing the hole size formed by the three adjacent pins all the way through the set.   Anybody ever do that?   Oh man, I wish it would rain around here so I can spreadsheet this out!


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## Doug Gray

RJ beat me to it!


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## Winegrower

Excellent, thank you guys!  So now I want to figure out the math without the cad package and work out tables for the three pins (X-0.001, X, and X+0.001), let X run from 0.062 to 0.249.    Now THAT would really expand the range.   If it's too sparse a set, then we need the arbitrary solution for three diameters and the superscribed circle.

Fun!


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## Winegrower

Oh man, you have to love the internet.   Found it:  http://www.ambrsoft.com/TrigoCalc/Circles3/Tangency/Tangent.htm

I guess Descartes figured this out for himself a long long time ago.


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## RJSakowski

One more comment.  I collect wrist pins from ICE pistons as they are hardened and very tight toleranced for roundness, cylindricity, and diameter. A 3.4" pin along with my .250 to .500 pin gage set extends my measurement capability to 1.250".  A 1.000"  and 1.250" pin extend the measurement capability to 1.750" holes.


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## Larry$

I have gage pins up to .500 by 0.001 steps minus up to .0002. I had to run the #s on the site given by Wingrower. Running for the greatest variability of my pins (from full size to  full undersize for all 3 pins) I get .00088" diameter max. variation.  So the maximum size hole I could measure by the 3 pin method is 1.07306 with a possible 1.07218 result.  Using the two pin method I can only get to 0.999 ( +.0000 to - 0.0004 max variation)
Hope I ran the #s correctly.
This exercise assumes a lot about my ability to handle and feel the fit of the pins.


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## Winegrower

Well, this has been fun.   Looks like as RJ said, you can fine tune the target diameter to tenths by careful selection of the three pins.   And Larry$ can indeed use his half inch gauge pins for up to an inch range.  You can roughly double the size range available.


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## Larry$

Winegrower, thanks for that link, I book marked it. Will come in handy


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## Winegrower

When I posted in the "What did you buy today" thread about getting a pin gauge set, there were comments from Larry42, RJSakowski and Doug Grey that using multiple pins could extend the range of the set to larger diameter holes.   This seemed interesting, because the basic set I got included pins from 0.061" up to a maximum of 0.250"

Here's the set:






But RJSakowski and Doug Grey added drawings showing how three tangent pins can be circumscribed by a larger circle tangent to each of the three pins:




This was apparently first observed by Descartes long ago, who showed that...get this...the sum of the reciprocals of the 4 radii is equal to twice the sum of the squared reciprocals of the radii.    Who knew?  http://www.ambrsoft.com/TrigoCalc/Circles3/Tangency/Tangent.htm

So in the machining context, given three gauge pins, you can solve for the diameter of the larger hole they fit.  

The attached spreadsheet shows calculations for given any three arbitrary pins finding the larger surrounding hole.

But how to know the right three pins to try?   The spreadsheet also calculates the larger hole assuming three adjacent pins, 0.001" apart, are chosen.   The range of the measurements is at least doubled.

Additionally if you add a much larger known diameter pin, you can extend the range to significantly beyond the basic set, and improve the resolution as well.   The spreadsheet shows the incremental resolution achieved with the given pin set.  

Overall, with a 0.061" to 0.250" pin gauge set, which cost me about $55, and four additional pins, which I had, or you could make, 0.375, 0.500. 0.625 and 0.750, you can measure up to over an inch with 0.001" resolution.   

That seems pretty cool to me.   Thank you Descartes and HM posters.


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## Ken226

Winegrower said:


> I could not resist getting a gauge pin set…0.061 to 0.250 covers a good range that snap gauges can’t.
> 
> Edit:  these are minus sets, no bigger than the stated diameter, no smaller than two tenths under.
> 
> View attachment 387075



I can remember dozens of times I needed a bigger pin and didn't have one.  I could have used this trick every time, and never thought of it.  Thanks for sharing this.

I suppose the small pin could be any size.  Even if it never touches the hole,  it'll keep the other two aligned with each other and and side by side.  A minus .251" pin and a minus .249 pin would be perfect to gauge a half inch hole!


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