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3 hole pcd

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mark mc15/04/2013 08:03:50
92 forum posts
16 photos

I know this sounds stupid but how do i work out the diameter  of 3 holes to get the pcd that have already been bored into something? We never done anything like this in school so any help would be great. I'm making a mount for a small grinder to make a poor mans tool and cutter grinder.

Edited By mark mc on 15/04/2013 08:06:20

Michael Gilligan15/04/2013 08:11:30
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16408 forum posts
715 photos

Mark,

Not stupid at all.

Try this

or this

MichaelG.

Edited By Michael Gilligan on 15/04/2013 08:14:38

Lambton15/04/2013 08:12:20
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694 forum posts
2 photos

Mark, Can you please explain in a little more detail exacttly what you want to know as I am confused by your post.

John Haine15/04/2013 08:16:50
3347 forum posts
178 photos

Measure the centre to centre distance of any 2 of the holes. Multiply by 1.1547.

mark mc15/04/2013 08:31:43
92 forum posts
16 photos

OK thanks all, just to enlighten my post i have a small bench grinder that I'm trying to make a mount for which has three holes at either end for mounting of the to disk guards, I'm going to use them to make a mount to hold the grinder to a shaft so i can raise and lower the wheel/ grinder on a vertical shaft. I'll get some pictures up when I'm finished. Trying to use as many of the shelf bits as possible to keep things easy.

Paul Lousick15/04/2013 08:32:57
1547 forum posts
580 photos

CAD drawing software can draw a circle thru 3 points and then can be dimensioned to find the centre and diameter.

Joseph Ramon15/04/2013 09:07:12
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107 forum posts

Hi Mark,

Put a bit of paper over the end of the grider (with a hole for the spindle). Push a pencil through each of the mounting holes and spin it round. It will be much easier to measure the spacing of the holes from the paper copy, or you can use it as a template..

Also, it is easier to meaure between the edges of the holes than their centres, just make sure you use the same point (e.g. far right edge) of the two holes!

Joey

Gary Wooding15/04/2013 10:24:04
763 forum posts
196 photos

It's difficult to accurately measure the centre-to-centre distance of holes. A simple way is to use a digital or vernier callliper to measure the "outside" and "inside" distances, add them together, and divide by 2.

hole centre.jpg

Gary

Robert Dodds15/04/2013 10:47:29
275 forum posts
39 photos

Mark,

If, as I suspect, you can only measure the centre distance of the three holes you may find the following trig formulae helpful.

Diameter is obviously 2 x r

Bob D

belgrave011.jpg

mark mc15/04/2013 10:51:19
92 forum posts
16 photos

Some useful tips thanks, should be able to get this sorted now.

John Haine15/04/2013 11:17:46
3347 forum posts
178 photos

And if you substitute a = b = c in Bob's first formula (assuming the holes are equally spaced around the circle), the PCD diameter is 2a/sqrt(3) = 1.1547a

Robert Dodds15/04/2013 12:30:14
275 forum posts
39 photos

Ok,

So maybe we've got Mark going but how far do you have to go up the present day education tree before they teach you that sort of stuff?

I know it is all there on the internet as Michael Gilligan has shown but its so much better if you can work it out from 1st principles like wot was taught in Trigonometry and Geometry.

Bob D.

 

Edited By Robert Dodds on 15/04/2013 12:32:11

mark mc15/04/2013 14:48:30
92 forum posts
16 photos

Not sure but in my day (20 odd years ago) when I did my gcse's, we covered none of this type of math.

Edited By mark mc on 15/04/2013 14:48:52

Michael Gilligan15/04/2013 15:15:07
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16408 forum posts
715 photos
Posted by Robert Dodds on 15/04/2013 12:30:14:

Ok,

So maybe we've got Mark going but how far do you have to go up the present day education tree before they teach you that sort of stuff?

I know it is all there on the internet as Michael Gilligan has shown but its so much better if you can work it out from 1st principles like wot was taught in Trigonometry and Geometry.

Bob D.

Edited By Robert Dodds on 15/04/2013 12:32:11

.

Quite so, Bob

That's why I pointed Mark to a page which showed the "working-out"

MichaelG.

Robert Dodds15/04/2013 17:53:02
275 forum posts
39 photos

Michael G,

Begging the earlier question has caused me to think a little deeper about my interpretation of the Geometry.

I saw Mark with a piece of metal with three holes in it. and he wants to find a centre point and figure out a unique diameter passing through the three holes.

Unless he has some form of cordinate measuring machine to generate a datum point and x,y, coordinates for each hole he cannot readily derive the position of the three holes or work out the diameter using the coordinate formulae.

Without really thinking about it previously I now realise that I was brought up on Euclidian Geometry that has much less dependency on cordinates being defined and leans to solving problems based on the old Geometry theorums.

This method may have limitations in solving advanced mathmatics problems that are more readily handled with coordinate geometry principles. However, at the workshop level it is more likely that the simpler methods will suffice

I hope Mark can get his Tool Grinder problem sorted with the aid of just a pair of dividers, a steel rule, paper and pencil.

My schooling was at a Grammar School but more like 62 years ago and yes, I loved that form of Maths but I also was lucky enough to be involved in coordinate geometry through my working life so hopefully I see both sides

I still think its a pity that there is so little emphasis on the Mathmatics in current education programmes

Bob D

Michael Gilligan15/04/2013 18:14:00
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16408 forum posts
715 photos

Bob,

Fair comments! and I'm with you 100% regarding the state of modern "Education"

There was a reason for my pointing Mark in the direction of the co-ordinate geometry method ... Because it is the way that the CAD programs [as mentioned by Paul Lousick] do it.

Many people are fascinated by CAD's ability to draw a circle through any three points, and I thought it worth showing how it's done.

MichaelG.

.

P.S.  Here is a very handy little chart 

Edited By Michael Gilligan on 15/04/2013 18:20:11

Gary Wooding15/04/2013 18:51:25
763 forum posts
196 photos

If you can mark the hole centre positions on a piece of paper held against the metal, the PCD centre is simply the intersection of the perpendicular bisectors of the lines connecting the centres.

The lines connecting the hole centres are chords of the PCD circle. The bisectors of these lines must pass through the PCD centre. This is trivial geometry.

The diagram shows that it works even for non-equilateral triangles.

pcd.jpg

Gary

Robert Dodds15/04/2013 19:10:22
275 forum posts
39 photos

Gary,

Thats an odd word to use. "trivial"

What is its origin inn the current context?

Bob D

michael m15/04/2013 19:15:17
60 forum posts
3 photos

A rather bizarre aspect of poor maths ability is that so many celebrities and TV presenters seem to be proud and somewhat amused by their lack of mathematical comprehension. Lack of numeracy (and also literacy) is an ongoing complaint by prospective employers due to so many students being failed by the teaching profession. (?)

...............................................................................................

 


1. Teaching Maths In 1970
A logger sells a lorry load of timber for £1000.
His cost of production is 4/5 of the selling price.
What is his profit?


2. Teaching Maths In 1980
A logger sells a lorry load of timber for £1000.
His cost of production is 4/5 of the selling price, or £800.
What is his profit?


3. Teaching Maths In 1990
A logger sells a lorry load of timber for £1000.
His cost of production is £800.
Did he make a profit?


4. Teaching Maths In 2000
A logger sells a lorry load of timber for £1000.
His cost of production is £800 and his profit is £200.
Your assignment: Underline the number 200.


5. Teaching Maths In 2008
A logger cuts down a beautiful forest because he is totally selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands.
He does this so he can make a profit of £200. What do you think of this way of making a living?
Topic for class participation after answering the question: How did the birds and sheep feel as the logger cut down their homes? (There are no wrong answers.
If you are upset about the plight of the animals in question counselling will be available)

6. Teaching Maths 2018
Ø£ المسجل تبيع حموله شاحنة من الخشب من دولار. صاحب تكلÙ?Ø© الانتاج من> الثمن. ما هو الربح له؟

 

Michael

 

...............................................................................................

Edited By michael m on 15/04/2013 19:15:47

Edited By JasonB on 15/04/2013 20:52:02

Stub Mandrel15/04/2013 20:17:32
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4311 forum posts
291 photos
1 articles

Well done Gary!

Rob - that use of trivial is the mathematical meaning of the word as in "of no difficulty or interest", in other words in no need of further explanation.

Michael

In all years the answer is £0 - if he has a half decent accountant, what about the running costs of that lorry for a start? He needs to go on a small business training course.

I take it that in 2018 the logger is swearing because either he can't find any trees or buy any petrol.

Neil

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