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Speaking of Precision

Speaking of Precision is a knowledge preservation and thought leadership blog covering the precision machining industry, its materials and services. With over 36 years of hands on experience in steelmaking, manufacturing, quality, and management, Miles Free (Milo) Director of Industry Research and Technology at PMPA helps answer "How?" "With what?" and occasionally "Really?"

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Math Use On The Job - Precision Machining

Posted May 03, 2013 12:00 AM by Milo
Pathfinder Tags: careers math precision machining

The Atlantic titles their article "Here's How Little Math Americans Use at Work."

Spoiler alert, in Precision Machining, we all use a lot of math through algebra, geometry trig and statistics.

"…the best blue-collar jobs do in fact require a level of mathematical literacy on par with what you'd expect a student to know if they were college bound. To me, that hints at an argument for more high level vocational programs: It might help if students actually knew that those boring equations really one day would earn them a paycheck."

If you can do the math, the precision machining industry has a great job and career for you.

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Editor's Note: CR4 would like to thank Milo for sharing this blog entry, which originally appeared here.

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#1

Re: Math Use On The Job - Precision Machining

05/03/2013 4:06 AM

Can't arge with the graphs.

The big problem is the people who make the laws and set the wages are virtually all in the 'upper white collar' brigade. Who you will see are well versed in statistics.. if you added the 'bull and self presevation' column they'd be up in that too (although to be fair, that's not a branch of maths )
Del

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#2

Re: Math Use On The Job - Precision Machining

05/04/2013 12:24 AM

I'd like to see some definitions of "Upper White collar" etc...

Personally, as a machine designer, I use Trig nearly every day. I believe I have actually used Calculus twice in the last 40 years, but to be honest, I would have used it much more frequently if I had really understood it, and didn't have to dig out the textbooks each time!

I do use statistics, but mostly at a subconscious level...

Fortunately, or unfortunately, depending on your point of view, much of the Trig is being incorporated in the machines (bolt circles on DROs, for example).

There is clearly a weakness, for those young enough to have never used a slide rule (which is the vast majority of the workforce today), in understanding significant figures...

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#3
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Re: Math Use On The Job - Precision Machining

05/05/2013 12:49 PM

Here is an interesting problem that might be solved from a couple different approaches.

.

A circle of radius 1 is tangent to a horizontal line. A second circle of radius 1/4 is beside (not inside) the first circle and tangent to both the line and the first circle.

.

Two additional circles can be made that will be tangent to both circles and the line. If you tell me the radii of the two circles, I'll trust the placement would be a snap.

.

I'm sure there will be multiple people who can quickly solve this.... it will be interesting to see who does so first. I'd also be interested to see if anyone has an unusual or clever method.

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Re: Math Use On The Job - Precision Machining

05/05/2013 1:23 PM

OK, so the vertical, horizontal, and sloped lines through the centers make a 3,4,5 right triangle.

The other two circles must be the ones already there: one of infinite radius (the line), and one of zero radius (the point of contact between the two circles.

If there are any others, you got me!

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#9
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Re: Math Use On The Job - Precision Machining

05/05/2013 6:29 PM

Ignore C1

C3 and C4 are not to scale with the original given dimensions for circle 1 and circle 2, but hopefully it helps to visualize where the other circles will be.

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#5
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Re: Math Use On The Job - Precision Machining

05/05/2013 1:28 PM

1/16th and 1.0.

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Re: Math Use On The Job - Precision Machining

05/05/2013 2:02 PM

Not quite, but you pointed me in the right direction.

Its 1/9 and 1.

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Re: Math Use On The Job - Precision Machining

05/05/2013 4:27 PM

Good, I imagined the picture, the 1 seemed obvious and the other was rough estimate.

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Re: Math Use On The Job - Precision Machining

05/05/2013 6:11 PM

This is correct...

My hack for doing it quickly is to

change radius to curvature k=1/r,

then take the square root of the curvatures of the two circles

then square the sum for one solution's curvature and square the difference for the other solution's curvature

and of course the radius is the inverse.

In this case:

Circle one has a radius of 1 and a curvature of 1. The square root of the curvature is also 1.

Circle two has a radius of 1/4 and a curvature of 4. The square root of the curvature is 2.

1/(2-1)^2 = radius 1 for one solution.

1/(2+1)^2 = radius 1/9 for the second solution.

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#11
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Re: Math Use On The Job - Precision Machining

05/05/2013 6:59 PM

Just on the chance anyone also geeks out and finds this interesting....

This problem is a simplification of Descartes theorem.

Descartes theorem is used to find the two additional mutually tangent circles to three mutually tangent adjacent circles.

This problem is a simplification in that one of the three mutually tangent circles is a degenerate circle in that it has a curvature of zero....i.e. infinite radius.

.

Descartes theorm states that for 4 mutually tangent circles (not more than two circles tangent at any one point),

The square of the sum of the curvatures will equal twice the sum of the squares of the individual curvatures.

.

(k1 + k2 + k3 + k4)2 = 2 (k12 + k22 + k32 + k42)

.

The curvature of the unknown circle will be equal to the sum of the curvature of the other three, plus or minus, two times the square root of the sums of the products of three possible pairs of known curvature.

.

k4 = k1 + k2 + k3 ± 2 √(k1k2 + k1k3+ k2k3)

.

Having one curvature of zero simplifies things greatly.

Assuming k3 = 0

k4 = k1 ± 2√(k1k2) + k2

....= (√k1 ±√k2)2

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#10
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Re: Math Use On The Job - Precision Machining

05/05/2013 6:33 PM

1/16 will actually be the the one that fits between and tangent to the straight line, 1, and 1/9.

.

then 1/25

1/36

1/49

1/64

1/81

.01

......

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#12

Re: Math Use On The Job - Precision Machining

05/05/2013 8:52 PM

How about Meth Use On The Job? Probably on the increase.

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#13
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Re: Math Use On The Job - Precision Machining

05/05/2013 9:35 PM

Clever, but unwelcome around powered equipment. Milo

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