Ancient Tools - Divider & Compass

[Jim Koepke]

Well I bought the last display pair of big dividers from my not so local LV. Made in France! Perhaps they use them for wine barrels!
The points are somewhat square so will need careful honing unless they are designed to ream out the mark as you spin the compass.
Derek will know!

Maybe it is actually a mult-tool with built in bird cage awls for points?

jtk

[Patrick Chase]

Well I bought the last display pair of big dividers from my not so local LV. Made in France! Perhaps they use them for wine barrels!
The points are somewhat square so will need careful honing unless they are designed to ream out the mark as you spin the compass.
Derek will know!

FWIW I don't think there's any particular reason to buy dividers from a woodworking outlet. You can find plenty of very serviceable ones (with sharp points) anywhere that sells drafting tools. Mine are mostly Alvin (German made) FWIW.

[Ryan Mooney]

Mostly related is the clickspring video on laying out gears and making a dividing plate as part of his antikythera reconstruction process.

https://www.youtube.com/watch?v=BIUAdINXZmQ

Also Jim, the jeweling on that second set of drafting tools you have there is simply divine.

[William Fretwell]

This is Canada, we don't have a lot of shopping choices outside of the really major cities. You get used to it. These were a foot long. Postage rates here are also one of the highest in the world, add in crossing a border and it stops you buying much by mail.
The Alvin's I see on ebay are school size.

[Mel Fulks]

Ryan,that's a terrific video ,thank you. Always interested in the antithekera.

[James Pallas]

Ryan, Thank you for posting that video. Some very interesting info. Much of his set up could apply to woodworking as well as metal working. The part about expanding the fixture to make marking out easier is a good thing to remember.
Jim

[James Pallas]

This is Canada, we don't have a lot of shopping choices outside of the really major cities. You get used to it. These were a foot long. Postage rates here are also one of the highest in the world, add in crossing a border and it stops you buying much by mail.
The Alvin's I see on ebay are school size.

William, I have a large compass, about 12" I believe. I replace the pencil with an awl and use that if I have the need for a large divider. Works very well for me. As I recall it wasn't terribly expensive and does double duty.
Jim

[Patrick Chase]

This is Canada, we don't have a lot of shopping choices outside of the really major cities. You get used to it. These were a foot long. Postage rates here are also one of the highest in the world, add in crossing a border and it stops you buying much by mail.
The Alvin's I see on ebay are school size.

Yeah, with the Alvins you have to use an extension arm up to ~12" and then trammel points (or a "beam divider" as they call it) beyond that.

[Normand Leblanc]

A few years back while I was building this
IMG_4474.jpg

I wanted the drawers to be gradually thicker and the frame was already done. After some googling I found this site
https://www.popularwoodworking.com/t...working_design
where dividers where used (no measuring).

It worked great.

[Chris Parks]

Ryan,that's a terrific video ,thank you. Always interested in the antithekera.

Any Clickspring video is worth watching, his layout skills are very good. Many hours have been spent watching in amazement at his skills and the clocks he makes.

[Stanley Covington]

Here is a very ancient and reliable technique to accurately make perpendicular (right angle) lines using just divider/trammel and straightedge or dryline/chalkline/inkline, but without using graduated linear measuring tools like a ruler or tape measure. This simple technique has been used since ancient times as a very accurate way to determine if an angle is 90 degrees, and for drafting and laying-out everything from furniture to the Great pyramid.

Assume you have a line (reference line) and want to make another line perpendicular to it.

1. The first step is to use your divider to divide the reference line into 5 equal-length segments. Let's call the starting point of these segments, the point where you want the perpendicular line to intersect the reference line, Point A. Make a mark at each of the 5 segments. Let's call the end point of the 4th (not 5th) segment Point B.

2. Set your divider to the distance of three of these segments.

3. Place one of the divider's points at Point A, and draw/scratch an arc.

4. Change the divider's setting to equal 5 segments, place one leg at Point B, and draw an arc intersecting the previous arc. Let's call the intersection of these two arcs Point C.

5. Draw a line with a ruler, snap a line with a chalkline or inkline, or pull a dryline from point A and either to, or through, Point C. The angle between A-B and A-C is 90 degrees.

This is called a "3-4-5 triangle" and was used as a real-world graphical method to layout/check right-angles long before Pythagoras figured out that Asquared+Bsquared=Csquared. There are many applications for this triangle beyond this single example, as you can easily imagine.

The larger the segments, the more precise your layout will be.

On a modern construction jobsite, chains and transits/theodolites/stations are the preferred method, but you may not always have such pricey equipment on-hand.

6" dividers are useless for laying out excavations on a jobsite of course. The divider can be replaced with a stout dryline trammel using 2 nails as points, but the line tends to stretch and accuracy may suffer. A more accurate but cumbersome method is make a trammel from a 2x4 with a spikes as heads/points. Drill/insert one spike through the far end of the 2x4's narrow edge, and use a C clamp to secure the other spike to the 2x4's side. This trammel is used to scribe the soil. It takes at least 2 guys and maybe 3 to operate this ancient tool, but I have used them up to 12' long with good accuracy. Make sure the ground is clear and will allow enough clearance to swing the trammel.

Of course, the 3-4-5 triangle works with a tape measure or surveying chain too, but it is hard to beat the precision of a good pair of dividers or a trammel.

Stan




3-4-5 Triangle.jpg

[James Pallas]

Interesting example of trusting the tool instead of a measurement. Years back I had a young man come to work for the summer. Put him to work with the framers. After a few weeks I asked him how he was doing. He told me that he had gained a lot of respect for the people he was working with. He said he had no idea how complicated the job was to do. What he found interesting was that the crew used higher math all of the time but had no idea what to call it. It was things like Stanley's example that caught his attention. The young man was a college math major.
Jim

[Todd Stock]

Excellent! The 3-4-5 is such a useful construction. Great tool for laying out deck and porch joists when the ledger board is a little less than perfectly straight!

Another construction for a perpendicular that does not require a walk-off and minimizes divider resets is:

- Mark the point of the perpendicular on the baseline (we will call it P)
- Use a dividers to swing a circle of arbitrary radius around the point, creating two additional points along the baseline on either side of P - we'll call these P' and P''
- Reset the dividers to a larger, still arbitrary radius (the larger, the better) and swing arcs off P' and P''
- The perpendicular of the baseline passing through P is the line between the intersections of those arcs (although with less accuracy, just one of the intersections and P may be used)

Once the perpendicular is constructed, two additional arcs can be swung off the baseline and perpendicular to find the 45 degree from P, and the same form of construction will bisect any angle.

Perpendicular.gif

[Stanley Covington]

Excellent! The 3-4-5 is such a useful construction. Great tool for laying out deck and porch joists when the ledger board is a little less than perfectly straight!

Another construction for a perpendicular that does not require a walk-off and minimizes divider resets is:

- Mark the point of the perpendicular on the baseline (we will call it P)
- Use a dividers to swing a circle of arbitrary radius around the point, creating two additional points along the baseline on either side of P - we'll call these P' and P''
- Reset the dividers to a larger, still arbitrary radius (the larger, the better) and swing arcs off P' and P''
- The perpendicular of the baseline passing through P is the line between the intersections of those arcs (although with less accuracy, just one of the intersections and P may be used)

Once the perpendicular is constructed, two additional arcs can be swung off the baseline and perpendicular to find the 45 degree from P, and the same form of construction will bisect any angle.

Perpendicular.gif

Another classic technique! Thanks, Todd.

[David Eisenhauer]

Thanks for the link Normand. I see the article was written by George Walker - one of the authors of "By Hand and Eye" that I have been going through lately. This is a good practical application of the design ideas presented in the book.