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diameter calculation

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paul rayner10/10/2019 21:09:38
130 forum posts
40 photos

Hi all

I'm wanting to drill 3 holes in a triangular fashion on my mill with the PCD function I've already set up the work piece with the quill in the centre, The centre of the holes are 65mm equally distant apart from each other. Question is how do I calculate the diameter of the circle needed? I could do it on paper with a compass etc but I want it more accurate than that. I've had a look at the machinery's manual but cannot seem to find anything.

thanks in advance for any help

regards

Paul

Nicholas Farr10/10/2019 21:21:12
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1992 forum posts
950 photos

Hi Paul, a little bit of Trigonometry will give you the answer, just substitute the 100 shown on the diagram below with 65.

trig solution0001.jpg

Regards Nick.

Edited By Nicholas Farr on 10/10/2019 21:21:47

vintage engineer10/10/2019 21:21:44
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189 forum posts
1 photos

I will work it out in cad  for you. I make it 75.12mm diameter.

 

Edited By vintage engineer on 10/10/2019 21:37:15

paul rayner10/10/2019 21:37:08
130 forum posts
40 photos

Thanks Guys just the job, I will plot it out First job in the morning.

regards

Paul

not done it yet10/10/2019 22:26:15
3478 forum posts
15 photos

I make it only 75.06mm, not that it is likely to make any difference at all.

DMB10/10/2019 22:46:33
928 forum posts

I prefer Nick's answer. Why 3 diff?

Michael Gilligan10/10/2019 23:07:38
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14135 forum posts
615 photos

ndiy seems to be closer

MichaelG.

Mike Poole10/10/2019 23:15:21
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2147 forum posts
52 photos

75.0555349947 for rough worksmiley

Mike

Nicholas Farr10/10/2019 23:41:40
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1992 forum posts
950 photos

Hi Mike, have you been using my calculator?

Regards Nick.

not done it yet11/10/2019 08:01:03
3478 forum posts
15 photos

To be honest, as a mathematician one would only quote the result as 75mm - as one cannot provide an answer to more significant figures than the data supplied with any confidence.

That 65 value could be anywhere between 64.50 and 65.49 (extra significant figures shown to demonstrate the validity of the result after rounding to 3 sig. figs.). Had it been measured to greater precision, like 65.00mm, a more precise result could be provided with confidence.

In practice the result for 65mm could be anywhere between 74.5mm and 75.6mm. Hence 75mm, to 2 significant figures, is really the best one can offer.

Remember, the average of 1 and 2 is 2, but the average between 1.0 and 2.0 is 1.5. We often provide answers to greater precision than the real world measurements deserve!smiley

Edited By not done it yet on 11/10/2019 08:02:52

Mike Poole11/10/2019 08:08:00
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2147 forum posts
52 photos

Obviously as a Myford user working to ten decimal places is normal practicewink

Mike

Edited By Mike Poole on 11/10/2019 08:08:17

Nicholas Farr11/10/2019 08:31:12
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1992 forum posts
950 photos

Hi NDIY, the OP asked the diameter for 65mm without stating a tolerance of any kind. The mathematical answer is exacting within the practicalities of calculation and from that the OP can fashion his own tolerance and I'm sure he should be able to get it very close to his needs.

Regards Nick

paul rayner11/10/2019 08:31:22
130 forum posts
40 photos

75.06 will do for my needs

thank you for all your help, It was a head scratcher for me!

regards

Paul

Michael Gilligan11/10/2019 08:46:10
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14135 forum posts
615 photos
Posted by not done it yet on 11/10/2019 08:01:03:
[…]
We often provide answers to greater precision than the real world measurements deserve!smiley

.

yes ... I was tempted to show the full ‘resolution’ of the available calculator; but thought that might be excessive in these circles, so simply chose to endorse your answer.

That said; it does no harm to declare a theoretical target value, provided that you understand that reaching it may be impractical.

angel MichaelG.

.

Best I could get last night was:

(( 32.5 ÷ 0.866025403784 ) x 2 ) = 75.05553499468936

SillyOldDuffer11/10/2019 09:06:46
4785 forum posts
1011 photos

Nick's excellent solution is for the simple case ie a circle defined by three points of an equilateral triangle. What's the solution when the circle is defined by 3 randomly placed points?

3point.jpg

A mathematical solution must be possible: I drew the example above with QCAD, but most other CAD packages can draw circles specified by three points.

Please be gentle - maths doesn't come naturally to me...

Dave

Michael Gilligan11/10/2019 09:20:30
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14135 forum posts
615 photos

I’ve got that tucked-away somewhere, Dave ... it’s quite elegant.

I will post it later, if no-one beats me to it.

MichaelG.

.

idea Saved myself some effort

Just search for ‘perpendicular bisector’

Edited By Michael Gilligan on 11/10/2019 09:24:10

Andrew Johnston11/10/2019 09:28:46
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4893 forum posts
552 photos
Posted by SillyOldDuffer on 11/10/2019 09:06:46:

A mathematical solution must be possible

Simples!

The Equation of a circle has three unknowns. Three unique points give you three indpendent equations. Three equations and three unknowns allows a unique solution for the centre and radius, with a bit of algebraic manipulation.

Andrew

Nicholas Farr11/10/2019 10:05:06
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1992 forum posts
950 photos

Hi S.O.D., I've found this in one of my books, but it does give a couple of dimensions and an angle, but you've asking about random placed points and I suspected it would involve Algebra as Andrew has said. However I could never get to grips with Algebra, which seems that MichealG's search is full of.

example26001.jpg

Regards Nick.

Kiwi Bloke11/10/2019 10:06:06
261 forum posts
1 photos

I'd do it using co-ordinate geometry. Not sure if this is what Andrew is suggesting. I'm a lousy mathematician, and I bet there's a far easier way (no, not CAD).

The perpendicular bisectors of two chords intersect at the circle's centre. You can easily find the co-ordinates of the mid-point of a chord and its slope. The equation of the bisector of the chord follows, straightforwardly. It's then a few small steps to solve the two equations of the two chord bisectors, to get the co-ordinates of the centre. The diameter is the distance from the centre to any of the three points. The equation for the circle follows.

Incidentally, the radius of the circumcircle of a triangle, R = a / 2 * sin A, where a is the length of the chord opposite the angle (vertex) A. Sometimes useful...

Oh, Nick just beat me to it...

Edited By Kiwi Bloke on 11/10/2019 10:07:27

Michael Gilligan11/10/2019 10:44:28
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14135 forum posts
615 photos
Posted by Nicholas Farr on 11/10/2019 10:05:06:

[…]

Algebra, which seems that MichealG's search is full of.

.

Oh dear ... maybe this will help: **LINK**

http://mathworld.wolfram.com/PerpendicularBisector.html

MichaelG.

.

Edit: or this : http://tgbasics.weebly.com/construct-a-circle-given-3-points.html

Edited By Michael Gilligan on 11/10/2019 10:48:42

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