The Steffens method
My home-brewing interest is principally in making replicas of long-scale slide rules. I've put most of my attention on circular and especially spiral scales, as they give the most precision from the smallest printable area. These usually fit on paper that fits in the average home printer. Lately, I've come across a couple of models that require larger format paper, as well.
Calculators using spiral scales require 2 cursors, with the cursors acting as a pair of dividers. Some scholars consider these instruments to be circular Gunter scales, rather than true slide rules. A circular slide rule would have 2 disks and one cursor, which corresponds to the frame slide and cursor of a standard linear slide rule.
With these 'Circular Gunter' calculators, you use the angle that is set by these dividers in order to add (subtract) logarithms and consequently multiply (divide). Accurate computation depends on the dividers remaining locked together under rotation.
When I have made Gunter-style calculators I have almost always had problems with keeping the dividers locked. Modern examples like the Gilson Atlas rely on friction between cursors to keep them together, the lower cursor is the lever arm used to rotate the dividers. Many earlier models used a lock nut in the center of the dividers. This can be replicated in a homemade calculator, but keeping the dividers locked remains difficult.
I recently purchased a fine slide rule made by Oliver Steffens. Oliver designs his own calculators and sells a series of models via eBay. I have added mine to my Unusual Slide Rules page, and if you haven't seen his work, I encourage you to check out his eBay items. I'm pretty sure I'll be back soon, myself.
After I received my slide rule, I was immediately drawn to the elegant way Oliver solved the locked cursor problem. I asked Oliver if he would mind my using it. Oliver replied this technique was used by the Fowler company and makers of circular pocket watch style calculators.
I have been making homebrewed scales for about twenty years now. Embarrassingly, I never once thought of this technique, nor even noticed it on the one watch style calculator I own.
For the homebrewer, the method is this:
Print the scales and glue them upon a disk of the same size...nothing new for homebrew scales.
Print cursors that extend beyond the disk. Likewise, this is also always used in the calculators for which I have made replica scales.
Lay the scales disk over a second plate, which can be a larger circular disk or even a rectangular sheet. You need the lower plate to be larger than the scales disk, no smaller in diameter than the cursors.
The calculator is assembled using a pin through the center of the scales and the hairline of the cursors.
The lower cursor is glued to the lower plate (so that the disk spins freely under the cursor). The convention I see most often is the left cursor is the lower cursor.
When you use the calculator, you rotate the disk on the plate rather than rotating the dividers over the disk. As one end of the dividers is fixed, you can hold the other (top) cursor in place with a finger against the plate. That eliminates the locking problem and is very easy to do with a home build.
Other benefits from this approach:
You can use a pin through the centre of the disk and the cursors because you won't need a bolt with a locking nut to secure the dividers. For a homemade calculator, this is the easiest way to get the best accuracy from the scales. Sticking a pin through a bullseye is easier (at least for me) than accurately cutting a hole for a much larger diameter bolt.
The cursors can be made very thin because you don't need a big surface area for friction lock. Essentially, you just need the hairline, and enough transparent material to hold the line. That also means you can make them from any available transparent material. You need only punch a hole through the hairlines to obtain accurate dividers.
I'll be using this technique in the future and for the purpose of this site and it'll be called the Steffens method.
My thanks to Oliver.