Gears

Microphone holders, especially American ones, tend to have a 5/8″ 27tpi (turns per inch) thread. I have no idea where to buy a tap or die to cut that. Threadcutting on the lathe, though, looked like a good exercise. I reckoned I could do the M12 threads I wanted, too. In fact, I may never have to buy another tap or die! I read up on how to do it, went to the lathe to practice, and hit a slight snag…

To quickly fill in for anyone who has neither done this before nor spent half the night reading up on it, cutting threads on a lathe is pretty simple in principle. All you have to do is contrive to get the saddle moving the tool along the workpiece at exactly the right rate relative to the spindle rotation. So if you want a 16tpi thread, for example, you just need the saddle to move an inch for every 16 turns of the workpiece. Then you skim along taking successively deeper cuts until you have your thread. There’s a bit more to it, the devil being in the detail as ever, but there’s loads on the web about that elsewhere. The saddle is driven along by the leadscrew. The leadscrew on my lathe has 16 threads per inch itself, so to cut a 16tpi thread, the leadscrew must turn at the same speed as the spindle. To cut a 32tpi thread, it must turn at half the speed. For normal power feed on this lathe, it runs at 1/16 the speed of the spindle – so the tool marks left by a sharp tool under power feed, then, are kind of a shallow thread of 256tpi.

To pick the speed of the leadscrew, you assemble a set of gears to get the required drive ratio. The gears needed for some common thread pitches are given in a table attached to the lathe, and it was here I hit my snag – no entry for 27tpi. I looked in the manual I’d downloaded. The table in there was the same. It also dawned on me that metric threads were going to be a problem, with an imperial leadscrew. Dave, who loaned me the lathe, had suggested that he has the optional metric leadscrew “somewhere”, but this has yet to surface.

So how to figure out what gears gave me 27tpi, and/or some “close enough” metric pitches? Here, I felt I was back on familiar turf, and quickly knocked up a little command-line program in C to generate all possible combinations of the set of change gears I had (ten, plus four others normally used just for power feed). Then I sorted and searched the results for the ratios I was after, and quickly found a plausible few combinations which got (surprisingly) close to 1.75mm pitch, and also exacty 27tpi – I have no idea why this handy pitch is left out of the official table (unless it’s ‘cos no-one outside of the US microphone stand industry uses it for anything?)

To try out my “metric” 1.75mm pitch gearing, I was very restrained – rather than diving in and carving up a 12mm bar, I chucked a length of standard M12 bolt, set the lathe up for thread-cutting (with the top slide at around 29 degrees) and edged the tool up close to the official M12 thread. Then I ran the lathe at low speed and watched the tool tip – it seemed to track the thread peak accurately. I returned the carriage to the start of the bolt, engaged the halfnuts again and edged the lathe forwards to take out the backlash, then moved the tool carefully into the V of the thread with a hair’s-breadth of light showing around the edges. Crossing my fingers, I ran the lathe slowly forwards. The tool tracked along in the thread trough without touching, for the entire length of the bolt (around 3 inches) – I was surprised it was that close, until I sat down with a calculator and worked out that it was only going to be a shade over a thousandth of an inch out after the length of bolt I compared against. The gears (from the standard set) I used for M12(x1.75) on an imperial leadscrew are:

1.75mm (12.51 tpi): A 40T, B 35T, C 55T, D 57T

I tried a similar exercise with my 27tpi gearing which was, as expected, bang on. The gears I used for that were:

27tpi: A 40T, B 45T, C 40T, D 60T

There are other combinations which will give the same results.

Emboldened by these minor triumphs, I decided to actually cut a thread, leading to my first Thing.

Fiddling around with my little gears program, I noticed that, while many metric threads can be closely approximated with the supplied gears and the imperial leadscrew, there are a number of integer imperial threads which can’t be done – fortunately, none of them are ones I have a use for right now.

Reading around, it’s clear that programs to work out gear combinations, being the obvious way to go, aren’t exactly uncommon. Various people have made them available in different forms. Some can be accessed simply via a browser, some need to be downloaded (and only run on windows). The browser ones seem to use CGI for the most part, running on the web server – the author of at least one of them implores the user not to re-calculate new sets of gears too often. I use either Macs or Linux machines, so the Windows/DOS programs didn’t appeal much, but I did want something a bit more user-friendly than grepping the output of a command line program, so I decided to turn my rather simple bit of combination-generating code into a Javascript version. I reasoned that the UI is taken care of by the browser, and everyone has prodigious amounts of spare CPU these days so the inefficiency of an interpreted language wouldn’t matter. Also, I prefer the idea of people running it on their spare CPU rather than my webserver via CGI.

The only snag with this brilliant idea was that I’m an embedded software engineer, not a web designer – I do C and C++ and assembly code on “bare metal” embedded systems, I don’t HTML and CSS much, and I’ve never used Javascript. Still, software in general is my thang, and it’s just another language… so here’s my initial effort for your delectation and amusement, written over a day or so as I taught myself some Javascript. Obviously I twigged as I went along that Javascript could be used in much more elegant ways, but a less hacky re-write can wait for a while. This ‘un works, more or less – usual disclaimers apply, naturally. I haven’t tested it on IE, and I wouldn’t expect it to work on any browser more than a couple of years out of date. Also, I’m sure it’s pretty easy to make it foul up by being unkind to it in some way – this isn’t mission-critical software designed for solidity, it’s a quick hack to get some handy info. (I couldn’t resist trying to draw little pictures of gears, mind 🙂 )