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why are they called dividers?

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Jacob

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I was wondering about this when Brian was talking about how to mark up a virgin saw blade with say 14 tpi.
It came to me in the night, under the influence of Martson's Pedigree :shock: :
If you had thin batten alongside the blade marked in 14ths of an inch it'd be easy to line up and start the cut with a file.
But how would you divide the batten into 14ths?
Dividers?
But setting them at 1/14" and pricking out each mark looks incredibly fiddly. Even more so if you were aiming at 20tpi
SO
what about first setting them at say 1" and pricking out 1" marks. Or just doing 1" marks from a ruler.
THEN
set them at 15/14" and then marking from each of the first marks, then repeating this from the second ones, adding 1/14" each time?
It works I've just tried it on a piece of paper.
So is that why are they called dividers? For this, and similar tricks?
Maybe everybody knew this already except me, wouldn't be the first time.
 

Jacob

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If you compare a laser printer side by side with a pair of dividers, you will find that the dividers are simpler in many ways, not least in the number of components.
What is more you could make up a pair from any old scrap, which would not be at all easy for a laser printer.
 

Cheshirechappie

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bugbear":1op6qggo said:
NB: Laser printed template much more practical.

BugBear
A pair of dividers, however, does not require a 240V power supply or batteries. They don't need a computer to drive them, either; and they last longer - I have two pairs inherited from my grandfather, and they still work very effectively.

I stand to be corrected, but I have a vague suspicion that the invention of dividers preceded the invention of the laser printer by several hundred years. Indeed, dividers may have been one of the tools used by those inventing the laser printer.

Joking aside - perhaps we've come to rely too much on steel rules and tapes. A study of older books on geometry indicates many ways in which lengths can be divided up without any measuring. It's possible that many 17th and 18th century craftsmen did not have the numercy to do the mental arithmetic required to divide up by using a ruler to mark out dovetails and such jobs, but could use dividers perfectly adequately. (They could probably reckon up their wages well enough, though....)
 

AndyT

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Jacob - if you don't follow it already, I recommend you have a look at Peter Follansbee's blog - you could start with this entry: http://pfollansbee.wordpress.com/2010/12/06/a-paire-of-compasses/

He works on 17th century joiner's furniture as a historical re-enactor and is keen on discovering past methods through practical work. I think you would also enjoy his very practical approach to work which is quick and suitable for its purpose, and his close examination of old furniture. (That said, in this particular post, he is also looking back at written evidence.)
 

Jacob

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AndyT":2khnadh4 said:
Jacob - if you don't follow it already, I recommend you have a look at Peter Follansbee's blog - you could start with this entry: http://pfollansbee.wordpress.com/2010/12/06/a-paire-of-compasses/

He works on 17th century joiner's furniture as a historical re-enactor and is keen on discovering past methods through practical work. I think you would also enjoy his very practical approach to work which is quick and suitable for its purpose, and his close examination of old furniture. (That said, in this particular post, he is also looking back at written evidence.)
Thanks, very interesting.
He doesn't mention dividers or the dividing process though. Schwarzy does on p146 of ATC, which I admit to not entirely understanding on first reading, but I do now.
I think I've been missing out on dividers. Over the years I've divided hundreds of windows into equal sized panes, but basically by maths (on the rod)
 

Cheshirechappie

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Here's another way of using them.

Suppose you've got a workpiece you want to divide up equally, perhaps for setting out dovetails, but it's an awkward width. Take a ruler, and set it across the board, but not at right angles, at an angle that brings an easily-divided dimesion at one side. At this point, you'll have a triangle - the length you're trying to divide, an easily-divided length on the ruler making the hypotenuse, and the short side (length immaterial) making the third side of the right-angled triangle. Mark with a pencil from the ruler, and project with a try-square perpendicular to the side you want divided. Set your dividers to this length, and you can step off the divisions on all four sides of a carcase or box.
 

Jacob

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Cheshirechappie":4fiielie said:
Here's another way of using them.

Suppose you've got a workpiece you want to divide up equally, perhaps for setting out dovetails, but it's an awkward width. Take a ruler, and set it across the board, but not at right angles, at an angle that brings an easily-divided dimesion at one side. At this point, you'll have a triangle - the length you're trying to divide, an easily-divided length on the ruler making the hypotenuse, and the short side (length immaterial) making the third side of the right-angled triangle. Mark with a pencil from the ruler, and project with a try-square perpendicular to the side you want divided. Set your dividers to this length, and you can step off the divisions on all four sides of a carcase or box.
I like it!
There must be lots of ways of using dividers. I'm a bit irked with myself - I've been going on for years about the rod being a non numeric graphic calculator etc. etc. but I haven't got any dividers! Ebay here I come!

PS Ed is describing same process over here http://woodworkuk.com/
 

matthewwh

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Outstanding!

The one tool that I would have considered more Jacobish than any other in existance!

Try taking the radius of a circle and then walking that dimension around the circumferance - perfectly divided by six. Now use the dividers to describe an arc from each point between the lines both inside and outside the original circle and join them with a line eminating from the centre. By repeating this process you can theoretically divide a circle into individual degrees.

I have a feeling this may transpire into a thread of cool recipes for divider magic and I hope it will.
 

Vann

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Cheshirechappie":119uea0b said:
Suppose you've got a workpiece you want to divide up equally, perhaps for setting out dovetails, but it's an awkward width. Take a ruler, and set it across the board, but not at right angles, at an angle that brings an easily-divided dimesion at one side. At this point, you'll have a triangle - the length you're trying to divide, an easily-divided length on the ruler making the hypotenuse, and the short side (length immaterial) making the third side of the right-angled triangle. Mark with a pencil from the ruler, and project with a try-square perpendicular to the side you want divided. Set your dividers to this length, and you can step off the divisions on all four sides of a carcase or box.
That's how I was taught during my apprenticeship (many moons ago ! ) - that's assuming what you're trying to say, and what I think you're saying, are the same :mrgreen:

Cheers, Vann.
 

GazPal

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Vann":2prflv82 said:
Cheshirechappie":2prflv82 said:
Suppose you've got a workpiece you want to divide up equally, perhaps for setting out dovetails, but it's an awkward width. Take a ruler, and set it across the board, but not at right angles, at an angle that brings an easily-divided dimesion at one side. At this point, you'll have a triangle - the length you're trying to divide, an easily-divided length on the ruler making the hypotenuse, and the short side (length immaterial) making the third side of the right-angled triangle. Mark with a pencil from the ruler, and project with a try-square perpendicular to the side you want divided. Set your dividers to this length, and you can step off the divisions on all four sides of a carcase or box.
That's how I was taught during my apprenticeship (many moons ago ! ) - that's assuming what you're trying to say, and what I think you're saying, are the same :mrgreen:

Cheers, Vann.
But then we're moving into territory involving the use of squares, tangents and sliding bevel :D

Incidentally, dividers/compass are ideal tools for pattern making when producing bull-nose/lancet/flat arches, elipse, etc., as well as comparatively straight forward divisions of spans and proportional work.
 

Harbo

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They were always standard issue in Drawing Instrument sets.

Funnily Wiki calls them Caliper Dividers?

Rod
 

Alf

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Jacob":2v4ja7mt said:
I'm a bit irked with myself - I've been going on for years about the rod being a non numeric graphic calculator etc. etc. but I haven't got any dividers!
You might like the Sector too, Jacob. Pop Wood did an article on using one not long ago; should think a Google will drag some info.
 

Jacob

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Alf":3itqdr8q said:
Jacob":3itqdr8q said:
I'm a bit irked with myself - I've been going on for years about the rod being a non numeric graphic calculator etc. etc. but I haven't got any dividers!
You might like the Sector too, Jacob. Pop Wood did an article on using one not long ago; should think a Google will drag some info.
These things? Sort of angular slide rule. I use an ordinary slide rule occasionally.
The Gunther scale further down has parallel lines and angled lines crossing (diagonal scales) - which is where you'd set your dividers to the chosen measure plus fractions, depending on what the scale is designed to do. I bet a saw maker/doctor would have a similar purpose made scale for taking off tpi measurements.
 

Harbo

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I have a load of them somewhere that I inherited from my Grandfather - he was a Mechanical Engineer and worked at Kitsons & Co. Leeds who designed and made Locos in the early 1900's.

Never fathomed them out though?

Rod
 

Alf

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The PWW article simplified the use somewhat, for us poor woodworkers. Hang on, there was a video if I recall correctly... Here 'tis. Wouldn't say it was the be-all and end-all of knowledge on the matter, but it gives the gist.
 

DrPhill

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Can you use a triangle and straight edge to create parallel lines? If so, then this is how we were taught to divide a line A-B into n equal parts.

Draw a line starting A at an angle to AB, say 45 degrees, but it does not matter really. The mark of n equal units (any size, but approximately the right size is best. the last mark is point C Now draw line BC. Set up your triangle and rule to draw parallels to BC. Draw a parallel through each of the marks on AC so that the line intersects AB. You have just divided AB into n parts with no measuring.

This is almost the same as the method suggested above by CheshireChappie, except that you do not need to choose the length of AC. It can be completely arbitrary.

I find that sort of technique much more pleasing.....
 
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