2020-04-16 (Th) 2/9 Measurement Standard COMPLETED

Years ago, I tried to replicate a musical bell instrument my mother owned. My maker-eye said it was nothing more than aluminum bar stock and golf bag tubes, so I bought the pieces I spec'd and glued them together. Naturally, when I tapped it, I got a dull thud instead of a resonating tone. I chalked up the failure to my lack of musical knowledge and moved on to something else.
My mom's bell instrument

Years later, I found that if you want a bar to sound musical, you have to attach it at the right spot, whereas I just stuck tape at the ends and hoped for the best. The silver lining is that I learned the solution, but I didn't spend excessive time back then, because I didn't even know what question to ask. The place to attach a bar is approximately 2/9 (two-ninths) of the way from each end where the lateral vibration is the smallest due to nearby nodes.
Steel strap vibrating mid-air

I liked the idea of being able to cut an arbitrary length of steel or aluminum and find the sweet spot immediately. In practice, this is a thought experiment more than a productive project. The path I took exemplifies the natural procedure of starting with a sophisticated device and working it down to a simple and functional one.

The first idea was never fleshed out but should have been possible. In my mind, it would look like a compass/divider with four legs. The outer limbs would reach the ends of the bar in question, and through a series of linkages, the inner ones would always point at the 2/9ths point and the 7/9ths node.
Specialized compass

My next idea was like the compass/divider, but it would use gears instead of levers. Rotation is more challenging to calculate, whereas gear proportions are straight-forward. The posts would attach at right angles to a rack-type cog, and those would ride on a two-tier gear with a ratio of 5:9.
Gear ratio with extending legs

At this point, I started experimenting with less mechanical means, and I realized that a piece of paper with projection lines at appropriate angles would allow me to place a segment of metal across the tracks. When the ends lined up with the outer borders, the inner markings would rest at the 2/9 point.
Paper scale sketch

I developed this idea since it was simple to draft and print. As I thought about it more, I added a central line, like a spine, and perpendicular lines, like ribs. This solution was pretty simple, and I could quickly replicate it with a piece of paper, a ruler, and a pen.
Drafted 2/9 lines

My final solution was so simple that it made the first ideas seem laughable. I stretched a rubber band across a ruler and made black marks at 0" and 9" and then blue lines at the 2" and 7" points. So long as the rubber stretched uniformly, those marks would always be proportionally the same, and I had a way to test this with my printed line paper.
 Marked rubberband
Lines compared to paper
Stretched and still accurate

Here is yet another story about developing an idea until it cannot get any simpler. That's how you know it's done.

First time here?

Completed projects from year 1
Completed projects from year 2
Completed projects from year 3
Completed projects from year 4
Completed projects from year 5
Completed projects from year 6

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