1896 - J Michaelson's computing instrument
See this patent on the International Slide Rule Museum page.
I chose this patent because the inventor devised a mechanism to automatically determine the spiral turn where the results of computations will land.
The design shows a 20 turn spiral, a 10 turn 'square' scale, and a log mantissa scale. I estimate this to be about a 9-10 inch diameter model with the scales shown.
The right-hand cursor in the drawing has a vernier that rides on an annulus on the outer edge.
On the cursors are a series of small bars parallel with the scales. These are pointers, in lieu of a hairline. I am guessing that the author did not intend for them to touch the face of the disk because the one closest to the disk centre would catch at the intersection of the 2 cursors during computatoin.
Description
The calculator is a spiral model, shown here as a 20 turn (x) scale and a 10 turn (x squared) scale. The inventor's claims had provision for a second spiral calculator (e.g., sine x and cosine x) on the opposite face of the disk. The scale and cursors on the backside are reversed.
If the above cursor arrangement is added to both faces of the disk, and the cursors are locked together, values can be transferred from one face to another.
The inventor seemed to have a metal cursor in mind, as the edges of the cursors appear to be folded over the racks. I'll have to resort to 3d printing, which means my cursors will be much thicker than the inventor would have intended.
The linking and locking mechanism uses 3 gears along with racks built into the cursors. One of the three is directly beneath the gear labeled W in the picture above, so isn't visible. It's resting on the bottom (left) cursor and shares a common axis with W and is labeled K in the patent description. Gear T in the picture transfers the rotating motion from W to the right cursor rack.
The basic concept is that the pointers are attached to gear racks that turn the two gears K and T.
During multiplication, the operator initially sets the pointers on both cursors (the left cursor is at 1.00, the right cursor and its pointer are over the first number). The operator then locks the cursors together, rotates the sector over until the left cursor is over the second number, and then fixes the sector in place.
The operator next locks gears W and K together then moves the pointer on the left cursor until it is over the number. Because W is connected to T, the rotation of W causes the pointer on the right cursor to move in the same direction as the left cursor pointer and by the same distance.
At the end of the procedure, the pointer on the right cursor will show where the answer is.
The problem with the invention is that the locking mechanism provided does locks the cursors together, but also locks the gears to the cursors. This prevents the transfer of gear rotation along the axis of W and K.
Initial comments
I should point out that this is a patent that did not come with a working model, and the few problems that I'm about to describe probably related to that. The inventor seemingly had a metal cursor in mind, something like sheet metal as the edges are folded over to hold the racks in position.
I completed an initial cut of the gear mechanism, following the patent. The initial build helped me surface some issues that I found hard to spot reading the patent.
I found that the gear locking mechanism as described in the patent won't work. I made a small change to the locking mechanism, and it now appears to work.
First full version
This model has a set of scales having an outer diameter of about 9.7 inches (246 mm). I've made it as a cardboard-backed disk of scales, which rotates over a slightly larger disk, or plate.
Instead of a circular annulus for the vernier, I am using a transparent plastic extension.
Racks, gears, and cursors are 3D printed.
I added a transparent plastic hairline to both cursors and I'm using lines on the top of the racks in lieu of the bars shown in the patent drawing as my turn-keeping pointers.
I don't have the final indicators on the racks yet; these are pretty close.
Because I'm still testing, the cursors don't yet have a mechanism to prevent the racks from falling out. I'll use some transparent material for that after I get the device working better.
The long bar of numbers shown lying on the face of the disk will sit on the right edge of the right cursor.
Observations
First, I can say the slide rule would have worked had it been manufactured. There were a couple of errors that needed to be fixed but they are of the sort that the inventor would have spotted had he been able to make a working model. From the drawing, it's clear that he would have needed access to something like a machine shop to make one, so I suppose that may have been too expensive.
The patent described thumbscrews at the ends of the cursors that bear on the face of the disk. I thought those would not be able to provide a reasonable braking force, so initially, I tried thumbscrews at the end of the cursors that screw into the ends of the disk. Unfortunately, my 'improved' locking mechanism also failed. I found that the thumbscrew acted to torque the center post towards the end of the cursor. Because the center post was no longer perpendicular to the disk, that caused the gear brake to pop out of alignment, and the mechanism wouldn't work. So, instead, I am using a technique I call the Steffens method.
In the working model, I've replaced the cursor lock on the A cursor with a small amount of foam that holds the cursor snug to the lower disk. When doing a calculation, I hold the A cursor in place with a finger and rotate the scale disk to line it up to the B cursor. Additionally, the other cursor (the left "B" cursor), is glued to the lower disk, which means I only need to lock the other A cursor, in this case by hand.
With this configuration, I'm able to consistently get 4 significant figures from a calculation and repeatably find the right turn.
At first, I was finding the turn and getting a good answer. I initially attributed this to side-effects from homebuilding: loose gears and off-center scales. I finally realized from experimenting with different calculations that the racks are a bit too short.
In particular, the left rack wasn't properly seated and that was a bit hard to spot because it's hidden. By relocating it a bit further down the cursor, I was able to find the right turn consistently. I'm pretty sure the fact that I'm getting better results in computation is just practice with manually locking the cursors.
However, I have found situations where I ran the cursor A rack off-scale and couldn't complete the calculation. I need to make the racks longer so that I can put the indicators over any point on the entire scale.
Even though I have a very tall cursor (10 cm+), I feel I'm not having too much difficulty with reading the right turn when the indicator is so far from the face of the disk. Nonetheless, there is clearly parallax.
As I was able to use the indicators even on the right cursor, I decide not to attempt bars as shown in the patent.
I'm actually using TWO knurled knobs stacked on the top of the center post (a brass bolt) because I found that when I used a single knob, the action of the gears on the racks would loosen it.
About the Cursors, Racks, and Gears
I'm still new to 3D modeling and 3D printing. My very first attempt was for much thinner racks and gears (to minimize parallax in reading the turn counters). I found those to be dodgy - they weren't well-formed and also were unable to engage reliably. I ended up making the gears 5 mm thick. I may be able to reduce the thickness a little, but I think I'll not make that attempt.
The change I made to the principal locking design is visible in the gear to the right of the brass bolt. I added an annulus to the top of the gear and made the hole for the cursor wide enough to accommodate it.
The annulus on the top gear rests directly on the lower gear (not shown in this photo) and along with the nut, this proves the gear locking mechanism.
As mentioned above I simplified the locking mechanism. The scales rotate under the fixed left cursor, which is now held fast to the underlying disk. I replaced the screw lock on the right cursor, which now has a foam brake that keeps it from easily moving. When I am calculating I use a finger to lock the cursor and the rack.