Nystrom Replica Build Diary

January 2020 - Initial builds

After I programmed the scales, I first did a couple of quick builds to verify that the scales are drawn correctly (by doing some trial calculations). For my first build I used heavy foamboard. I built the next one using card stock with MDF backing. I found I couldn't really do math with these builds.

Problems I identified with the versions were:

The scales were two small. In my first PostScript version, my guess as to the dimensions of the scales on the disk turned out to be bit too narrow. That meant that the ticks on the cursor arms were too close to be legible without magnification. Incidentally, the patent model at the Smithsonian features magnifiers on the cursors.
The locking mechanisms are required. My test models rely on 'normal' friction to keep the cursors together, and that proved insufficient. That's probably because there's too little surface area between the 2 cursors at the centre. I haven't found this problem before with modern circulars like the Gilson models.
The original Nystrom has 3 types of locking mechanisms: It had thumbscrews on each arm to lock a cursor at a desired location on the scales; it had something like spring clips at the origin of the scales, so that a cursor could held at 1.000 while the other cursor is set to one of the values in a computation; the third lock was in the knob, and it locked the two cursors together, when you needed to keep the angle between them while rotating them.
Parallax was a problem. When I was working with the foam board version, the upper B cursor wouldn't lay flat because it's separated from the disk by the thickness of the lower A cursor. Moreover, the foam was so thick that it was hard to make accurate readings. As is common with metal instruments, Nystrom's upper cursor is bent so that it meets the surface of the disk. The actual scales on the cursors are on inclined planes that slant to the face of the disk, obviating parallax. The card stock version actually had no problem with parallax. However, it was not rigid enough to be useful. Also, it was impossible to get the two cursors to lock together

August 2020 3D printer to the rescue?

I finally broke down and bought a 3D printer. I am using it to prototype cursors and the various locks used on the original instrument. The photo on the left shows the working prototype. It has been scaled to 10 inches diameter, up a bit from the 9.5 inch of the original instrument. This allows me to use wooden disks available from Amazon.

I've adjusted the relative dimensions of the scales on the disk, so that the cursors are now a lot more readable.

I am now experimenting with different cursor designs.

My new 3D printer makes it easier for me to attempt to replicate the shapes of the cursors, and rapidly prototype different designs. I'm a novice at 3D printing, so that means a steep learning curve head.

With this prototype, I have implemented the knob locking mechanism. This was sufficient to allow me to confirm to my own satisfaction that the scales are rendered accurately.

Nonetheless, I was trouble getting correct answers from the prototype. Part of this has to do with slight dimensional accuracies, but for the most part it is a problem with remaining parallax in the cursor design.

You can see why parallax might be a problem using the photo above. The scales' curves are almost radials. That is, they are often very close to being parallel with the cursor edge. For this instrument, the last 2 digits of a computation come from accurately spotting the precise intersection of the cursor with one of those lines; any amount of parallax significantly impairs that reading.

The original Nystrom used inclined planes on the cursors to produce a sharp edge where the cursors met the plane of the disk. Consequently, they would have had no parallax.

September 2020

I finally gave up on attempting to replicate the inclined plane. I suspect I could get much closer than I did to a reasonable facsimile, with more experience and probably a smaller extruder nozzle, but the issue was that the layering of the 3D printing material along with the paper scale layered on them led to parallax.

I switched to placing the paper scales on the bottom of the cursor, and added a cut-out on the cursors for them. After some fussing with alignment - the scales must meet and align with each other when the pointers touch - I was able to reproduce the first dozen calculations in the manual that Nystrom wrote, and obtain the correct answers. Mind you, Nystrom had a mistake in one of them...had me scratching my head until I realised that!

This was a long project, and I'll close it for now.

I really should do another pass at the knobs and cursors because they aren't quite right, but I'm pleased with the results I have obtained. I can see that the 3D printer will be very helpful in future projects.

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