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Branching this off from the what's happening in your shop thread so it will be easier to find later...

I am attempting to design and fabricate guitar tuners using a fancy mechanism called strain wave gearing which can be lightweight since many teeth are engaged at any given time, and has no backlash thanks to the involvement of a flexible component.

Here is a recap of my posts from the other thread:

Post 1:
Experimental strain wave #1 is not quite right, but does show promise.

Here's how I write the programs for milling the teeth.


The highlighted circles are tool positions. The big one is a 1/16" mill, used to cut a circle around the outside and then clear some material between teeth. The non-highlighted circles represent the radius for arc commands. After copy/pasting the positions of those circles, the C++ code looks like this:

And the resulting G-code looks about the same, just a lot of repetitions with the positions changed according to that rotation setting and backlash compensation.

Here's a shot of the machine in action. This is the 0.5mm end mill, using vertical motion to nibble away material between teeth before cutting the curvy profile. This approach never puts a heavy side load on the delicate little bit. This piece of aluminum has 3 holes in it and a failed gear from a previous project. But just enough material left in the middle for the 3 components of this project.


And here are the finished pieces. The ring gear's outside diameter is 1/2".


Note: The 4mm hole with keyway is just for testing, because I happen to have a corresponding shaft on hand from a previous project. For actual tuners I'll probably use a 5/32" shaft with 1/8" flats, for compatibility with standard closed gear tuner buttons.

The flexspline does not want to go into the ring gear, so I need to re-make it with a bit more clearance. And remake the wave generator because I accidentally doubled the x/y radius offsets, so it's much more eccentric than it should be. I was able to get it into the flexspline, but it deformed permanently. I also need to reduce the flexspline wall thickness even further (this one is 0.25mm). Even if the eccentricity was correct, it still feels too stiff. I think I'll try 0.2mm next time, but even that may not be thin enough, especially for steel.

Post 2:
Here are some exploded views of the current Blender model (I would include the .blend file too, but this forum only allows uploading image files. PM me if you want it). Hopefully this is enough to make the idea un-patentable for the future. The ring gear will either be press fit or glued into the housing, permanently closing it. Weight should be around 14 grams with a wood button, including the mounting screw and headstock bushing.




Post 3:

Direction just depends on which of the 3 components is input, output, and fixed. Page 32 in this document (a little over half way through, labeled page 10 in the engineering data section) shows all the combinations for strain wave, and cycloidal is more or less the same https://www.harmonicdrive.net/_hd/content/documents1/CSG-CSF_Component.pdf

The photo you posted looks like ring-out, so it would be same direction. Nothing novel about that. My design is reverse rotation, which I consider a worthy sacrifice for lighter weight. But you could design a strain wave where the flexspline is fixed and ring is the output, in which case it will rotate the same direction as the input.

And yes, the teeth are very small About 0.3mm tall, 0.9mm wide, and 2mm face width (limited by the length of the end mill). But since a lot of them are engaged at any given time, I think they will be strong enough. 120N string tension (about 27lbs) wrapped on a 3mm radius post gives 0.36Nm torque. The gear pitch radius is about 4.4mm, so that's 82N tangential force on the teeth. Assume contact angle is about 45 degrees, giving equal radial force, and it works out to 115N total force on the teeth. If 12 of the 30 teeth are engaged, that's right about 1kg/2.2lbs on each tooth.

But it would be no problem to rework it for a larger diameter gear if necessary. My design is ultra-compact, with the housing for the non-toothed portion of the flexspline sized to fit up inside a standard 10mm headstock hole. But even if you put the entire housing outside so it can use 1/4" headstock holes, it would still only be 9mm tall, and have no restriction on gearbox diameter. That would allow higher reduction ratios too, since you could fit more teeth of the same size. But personally I prefer lower ratios anyway, and I think high ratio will be even less necessary when you don't have to fiddle with backlash.

And now the new update:
Attempt #2... better, but the flexspline still doesn't quite fit into the ring gear.

I went ahead and made the shaft with flats and screw hole for the tuner key. This should be usable for an actual tuner.

The new ring and flexspline were made using a different 0.5mm end mill which is slightly larger diameter. End mills are typically toleranced within 0 to -.002" diameter, so I test and categorize them as large (close to nominal diameter), medium (around .001" smaller) and small (close to .002" smaller). Normally I would adjust part tolerance in software, but since my gear tooth toolpaths are hardcoded it's easier in this case to use a slightly larger mill instead. The toolpath was written for a 0.45mm mill (.002" smaller than nominal) with this in mind.

I also fiddled the code a little bit to reverse the movement direction when milling the flexspline teeth. I accidentally had it climb cutting last time, but my machine produces more precise dimensions with conventional.

I increased the inside diameter by 0.1mm, so the wall thickness of the non-toothed portion should be reduced from 0.25mm to 0.2mm (about .002" thinner). Doesn't sound like much, but it's plainly visible in this shot

I think the flexibility is about right now. Steel will probably need to be a bit thinner. I think it's the tooth profile that I need to adjust. This is what the teeth at the center of the engagement should look like:

But I'm not sure how to precisely simulate the neighbors, so they may be clashing a bit. I tried taking some photos to see if I could see which teeth are the problem, but I can't tell for sure. I think I'll try making the flexspline teeth a little narrower and see how it goes. I may also make a new wave generator... it looks like I was a little generous with the tolerance on this one. Also the center hole is rather rough due to a mistake in the program making it undersized so I had to file it out by hand.

I got curious and whipped up a ring-out version of the model (so the post turns the same direction as the input shaft). Looks like the weight addition would be a gram or two. And can't do the thing where the housing is partially up inside the headstock, but that's probably better anyway since it allows 1/4" holes and eliminates the restriction on gearbox diameter.

A lathe would be even more necessary for this version unless I can make the ring and post separately and join them together somehow. That would reduce material waste too, since it would otherwise start from a 1/2" steel rod, with most of it becoming the 6mm post (the flexspline-out version would start with 3/8" rod). And it would open up the possibility of an aluminum post, which would cut 3.7 grams (about 25%) off the weight. And would make the whole thing feasible to do without a lathe. That tricky area on the flexspline between the teeth and flange can be done with a T slotting bit on the mill.

Well after spending some time studying, it seems I was trying to cheat physics with my reduced-eccentricity tooth design. Basically I've altered the gear pitch so it's like trying to force different sized gears to mesh with eachother. Even though an individual pair of teeth can mesh just fine, the neighboring teeth do not mesh because the tooth-to-tooth distance is wrong.

Unfortunately this makes low tooth count impossible since the flexspline always has 2 fewer teeth than the ring, so when the tooth count is low the flexspline is much smaller diameter than the ring and needs a lot of eccentricity to make the teeth reach eachother, and excessive bending will fatigue the metal.

So I have two options: use more teeth, or use a more flexible material (i.e. plastic).

The lowest ratio made by Harmonic Drive is 30:1, so that means twice the size I'm currently working at, and higher reduction than I'd like. The outside diameter would be close to an inch, and that's too much. 20mm would probably be the absolute limit if I go to 1/64" end mill (which would mean 3/64"=1.2mm tooth face width). Or I could try titanium with lower tooth count since it's more flexible than steel.

I think I'll try ring-out configuration with a delrin flexspline first, which will also allow making the ring gear out of aluminum. Could scale for 16.5mm OD, which would allow making the ring/post from 5/8" rod and flexspline from 1/2", or 18mm OD (similar to Gotoh midsize 510) for a bit more strength. Calculated shear stress on the teeth and flexspline wall is around 4-5MPa, and delrin's tensile strength is over 60, so in either case I should have plenty of headroom.

An interesting project and, although I have nothing to contribute, I am enjoying the updates

_________________
Steve Smith
"Music is what feelings sound like"

I haven't finished the model for the delrin flexspline version yet, due to distraction by a possibly even better idea: What if we turn the flexspline inside out? I've never seen a strain wave in this configuration before, but I see no reason it shouldn't work. It may even be a good solution for robot actuators, building the inverted wave generator into the rotor of an outrunner motor. Not sure... the inertia would be problematic for acceleration. But that's certainly not an issue for guitar tuners And it reduces stress on the flexspline since the bending metal is at the larger radius, so an all-metal design may be back on the table.

If it is a truly novel idea... well, good luck patenting it now!
EDIT: After reading the original 1955 Musser patent US2906143A, this variation has been known since the beginning. Just not used very often, I suppose.

For starters I have an all-plastic design, except for the string post.

This should actually work, and weigh all of 6 grams or so. Not very classy, but to reduce the neck weight on a harp guitar I'd do it. I could be really tacky and electroplate them It would look all shiny for a little while...

You could even injection mold them and crank them out for pennies. Although for mold separation the flexspline teeth would have to be extended to the floor of the housing and hope it's still flexible enough, or have it open on the back and make the floor as a separate piece and ultrasonic weld it in.

I 3D printed it and surprisingly even that works (on the first try, too).

Another option is to make only the flexspline out of plastic, with a metal housing concealing it.

Fabrication-wise, the post is much simpler now because you can just use a 6mm rod and glue the gear onto it. Although I have identified a minor issue in the current model, there's nothing preventing the post from pulling out of the housing... may need to machine a groove for a circlip, or step it down to a smaller diameter inside and glue the gear on after inserting the post into the housing.

An all-metal housing/flexspline would be fairly difficult to machine since it would have to be steel or titanium for fatigue resistance, and is a lot of material removal (at least for my little machine).

This configuration is back to having the output turn in the opposite direction from the input. I don't think it's possible to do same direction this time because the internal-tooth flexspline would have to be on the post and then how are you going to get the stationary inner gear to transmit its force to the headstock while also driving the flexspline from the outside?

One idea is to make the wave generator out of clear plastic so you can observe the gears inside and understand why it turns backward

An inspired piece of design, Dennis. Well done! I think the reversing/non-reversing motion is only an issue from the point of view that 3-a-side tuners will not all turn in the same direction, but a bit of neutral plasticity should sort that out.

_________________
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Burton, did you get my PM response the other day? There was a thread recently about the PM system not working properly...

I finished the model for the delrin flexspline, although it still needs something to lock the input shaft from pulling out, and I'm not sure if just press fitting the flexspline into the housing will have enough friction to keep it from spinning, or if it will need roughed up and epoxied in there.

It has occurred to me that I can machine the post just fine without a lathe, going at it from above. It looks tall in the model, but in reality it's little more than an inch So all that's holding me up is waiting on a tool for undercutting the flexspline teeth (which is also necessary for making the external flexspline version).

In the meantime I've been exploring the "pancake" style, which has two ring gears and a single flexspline that engages both of them. But it typically requires higher tooth count and has lower rated torque than the cup type, because one of the rings needs to have more teeth than the other, and that means having a different effective tooth pitch than the flexspline so you can't have a proper mesh on both halves at once. The more teeth you have, the less significant the discrepancy is.

Here's a rough model of it with inverted flexspline engaging two external tooth gears:

For machining the flexspline, I'd have to go at it from both sides of the material to get enough face width. And one interesting option with that is I could have different tooth profile or tooth count on each half to improve the mesh. Different count could have proper tooth pitch on both halves, but unfortunately results in excessively high reduction ratios. For example 42 flexspline and 40 gear teeth on one half, and 40 flexspline and 38 gear teeth on the other gives 1-(42/40)/(40/38)=0.0025, which is 400:1 reduction.

Another possible way to improve the mesh would be a not-quite-elliptical wave generator, where the half-engaged teeth are not forced together as far. Triangular tooth profile may work better for that than this S-curve I've been using (traced from a Harmonic Drive graphic)

But I'll probably abandon the pancake style because I think the total machining time would be the most of any of the designs so far. Although I'm not entirely sure, because while it would require four passes of tooth cutting instead of just two, the total material removal is the lowest of all the designs.

The one I'd most like to do is the external cup flexspline in titanium, for its greater durability than plastic, lower Young's modulus than steel, and so I can anodize it to pretty colors. But it may be too much to ask of a little wooden milling machine. Delrin and aluminum is probably the way to go.

The tool has arrived! I did a test cut with it, widening out the hole left from one of the earlier test pieces until a 16mm bearing fits just right. Now that I know the exact cutting diameter of the blade (12.3mm), I can make precise outside diameters with it too.

But upon further consideration, pancake style has some advantages that put it back in the running. It can have the output turn the same direction as the input, and the flexspline can be made from steel tube rather than flat stock, saving a lot of stress on my machine since there would be no full width slotting operations. However that would only allow working it from one side, limiting the face width to 2mm with the 0.5mm end mill, so each of the rigid gears would only have 1mm of face width engaged with it.

One possibility is to do flexspline with 1/32" mill and rigid gears with 1/64". The flexspline teeth would be skinny with large gaps between them, and rigid gear teeth would be wide with narrow gaps between them. Then I'd have 1/16" engagement on each. The teeth need extra clearance due to the imperfect mesh, so I can probably still get a decently high tooth count.

The body will still require a fair amount of full width slotting, but I can probably make it out of brass which is a bit more gentle than steel, and nice looking even without electroplating.

This is a very interesting post to follow. I'm wishing you all the best of luck.

I've been machining parts for the delrin version, with mixed results. Machining the post went well. Too slow for any significant production quantity, but fine for prototyping. Quite a pile of chips just for one little post...

Here are the tools used. 1/4" end mill for most of it, 6mm drill used as a 120 degree chamfer mill to give the top a nicer looking shape, and a 12mm spherical router bit to create the string wrapping scoop.

Then I flipped it over so that post was held in an ER11 chuck pointed upward, and milled another post into what was previously the workholding end. This would be a nice system to minimize scrap, but unsurprisingly this second one vibrated a lot due to being held by the skinny end. Hopefully a lathe chuck will be able to grip it so the post flange is butted firmly against the jaws to prevent that. The ER chuck always opens up a little gap as it's tightened down the last bit, so the flange is not touching the face of the chuck.

Then to drill the string holes, I used a little jig I made for milling keyways in shafts. Just a piece of wood with a V groove in it, and a piece of 1/16" aluminum that's flexible enough to get a good grip on round things.

#1 center drill to get started and create the chamfer, then drill through with 2mm, then turn it over and center drill again to chamfer the other side. This is pretty quick already, but even better would be to use a #2 center drill (2mm pilot), which I think would be long enough to get half way through from each side and connect without having to change tools. Then run through by hand with a reamer or slightly oversize drill to clean up any little step.

To saw the posts apart, I constructed one of my instant cam clamp jigs

Then used the ER11 chuck again to hold the post and mill the internal gear teeth.

The flexspline did not go so well. My dad gave me a block of plastic that he thought might be delrin, but after measuring the density I think it's nylon or UHMW. Both will creep over time, but should be fine for prototyping... or so I thought. Whatever it is, it's extremely stringy. Chips don't detatch, and are difficult even to cut free with a sharp knife. Here's the result fresh off the machine.

That's actually the second attempt, which was even worse than the first. Both were plagued with programming errors and imprecise dimensions due to the plastic compressing rather than cutting, and the inside of the cup is too rough to use even after cleaning it up as best I could (plus I punched a hole through the wall...). Maybe my end mills just aren't sharp enough. But that would get expensive if I have to buy new ones for every few tuners.

I also made the housing, which went reasonably smoothly.

I think I'll buy some actual delrin and use a new 1/8" mill and see how it goes. And a titanium tube to make the flexspline for the all-metal pancake style. But that will be a week for shipping, so I'll work on other projects in the meantime.

Hi Dennis,
How do you think Richlite would work? I have a piece of 2" thick scrap I could send you for the price of the postage. It is a phenolic type material which I have milled with saws, routers, and sanders.
I look forward to your success!

Thanks for the offer, but I doubt it would work for this. Similar to 3D printing, the repeated flexing under load will probably delaminate the layers eventually. And it's a fairly stiff/brittle type material, isn't it? Acrylic is another potential candidate, but also seems too brittle. Although it does have good creep resistance. PEEK would probably work, but is expensive. Hopefully the humble delrin will do the job

I decided to give acrylic a shot since I remembered there was a suitably thick sheet down in the basement. Luckily it still has the protective sticker paper on it, because I needed to glue it to a block of wood to hold it with the vise so the undercutting blade can get at the sides of it, and glue doesn't stick very well to bare plastic.

This stuff machines incredibly easily. Using the same end mills as before, it came out perfectly dimensioned with no strings at all. The surfaces done with the 0.5mm mill and undercutting tool have a frosted look, but the bottom rim done with the 1/8" mill is almost completely transparent, and the top surface was too when I shaved 1mm off the thickness with a 1/4" mill at the start.

It's also impressively stiff. The 0.3mm wall thickness felt too stiff, but I decided to go ahead and make a wave generator for it and see how it held up. Here's a shot after turning it a few times, with grease squeezed out from between the teeth. It's also neat that you can see the wall thickness through the perfectly clear bottom surface.

It never did turn very easily, and after playing with it for a while I heard a couple of little crack noises. It looks like one of them was due to the wave generator migrating down to the floor of the flexspline and putting pressure near the base of the wall and cracking it. The other was the teeth breaking off.


So yes, it was too stiff. And it needs a spacer to make sure the wave generator stays where it should be. And acrylic may be too brittle to use. But I'll make another tomorrow with 0.2mm wall and see how that feels.

Success!

The 0.2mm wall flexspline was sadly destroyed in a cam clamp accident when trying to separate it from the wood block. But fortunately I had gotten a feel of its stiffness first, and playing with the fragments of that one and the broken 0.3mm wall, it's really just the toothed part that's too stiff, not the cup wall. I decided to go with 0.25mm, although 0.3mm would probably be fine if I increase both the OD and ID so the cup wall stays the same as the first one and just the backing behind the teeth is thinned.

I'll probably also increase the clearance on the teeth just a touch on the next one, because they were very tight at first. But after forcing them to turn for a while they've loosened up some.

Weight is just over 7 grams, excluding the heavy key that I've temporarily borrowed from another tuner. I'll make wood keys in the future, so including the mounting screws and headstock bushing, they should be around 10 grams each. 130g for a full harp guitar set

I forgot to take a picture of everything before putting it together, but the only thing not shown in previous pictures is the input shaft+wave generator and a little 3D printed spacer between the wave generator and flexspline floor. The shaft has flats along the full length of it, and wave generator is epoxied on, with 2mm of shaft protruding past it to be supported by the hole in the center of the ring gear. The wave generator is aluminum, but I'll probably use brass in the future since it's quickly colored the grease gray. Brass will need to be highly polished to ensure that it doesn't abrade the plastic. The aluminum is probably self-polishing so the wear rate will decrease with time.

I'll need to find a source for the little washers that go between the key and the tuner body, as well as the headstock bushings. I suppose I could make all those myself too, but it seems like a waste of time...

Now to get it mounted on a guitar and see if it survives under string tension for a week. Then I'll try spinning it a lot with a drill to simulate a few years of wear.



EDIT: It works! Although it did struggle on the initial tune-up. Hit a point where turning the key no longer increased pitch. I'm not sure if it was teeth skipping or the press fit into the housing slipping, but after going back and forth a few times it made it up to pitch. I've added a mark to see if the press fit slips in the future.

EDIT2: Yep, flexspline slipping in the housing. Next time I'll try scratching the aluminum surface with a knife to give it some bite into the plastic.

Unfortunately after tuning up and down repeatedly to test backlash (which it appears there is some), the flexspline cracked. I'll try to get it apart and see exactly how it failed. But I think the verdict on acrylic is that it's just too stiff and brittle. Hopefully delrin will work better.

EDIT3: The flexspline broke entirely in half. I found one tooth in the ring gear, and placing the pieces together it looks like that's where the fracture started. I did feel the resistance to turning increase just before it cracked, so that tooth must have jammed for some reason. The rest of the teeth still look perfectly smooth. I wonder if it was due to the overly tight mesh, or just friction from the whole thing being so small.

Flexibility of the fragment feels just about right. If anything it should be slightly stiffer.

EDIT4: Giving it some more thought, I think it was jamming the whole time and the press fit slipping was acting as a failsafe. After confirming that it was slipping I wicked some thin CA around it, and it broke shortly afterward.


Also, here's a picture of the input shaft with wave generator and spacer I described before.

Wonderful! If you are going to ever make sets for sale let us know. I've been using the Rickard banjo tuners on my vintage OM's and they are quite nice but I'd love to try something else too and love the homegrown sort of thing of these.

Really enjoying the whole thread Dennis!

Very exciting how quickly you're progressing with your testing and development.

I do intend to, but not until longevity is reasonably verified. Once I have a design I'm confident with, I'll make a few sets and give them out to anyone willing to be beta testers. If they all survive their first year, then on to production

The delrin should at last be arriving any minute now, but in the meantime I've been fiddling with more acrylic, this time in the external flexspline style.

The knob/wave generator is 3D printed, with a step to wrap carbon fiber onto it to increase the stiffness. Tack one or two strips to it with CA glue, and then wet with epoxy as you wrap them around. Then use some stretch wrap or scotch tape around the outside to keep it from coming undone until it sets up. It was supposed to have a little flange at the bottom to keep the carbon from slipping off the edge, but it broke off and I decided to just deal with it instead of printing another.

Then machine out the support material and refine the wave generator ellipse and the center shaft hole. One nice thing about 3D printing is that you can also print out negative shapes to make perfectly fitted cauls

Assembly of this style is pretty tricky because you have to apply grease and epoxy at the same time, and getting either of them where the other goes is not good. Much like playing that old kids' game "Operation" First the shaft goes through the hole in the housing, with grease applied from the outside before fully seating it. Then some grease carefully applied to the floor of the housing without getting it on the shaft. Then epoxy in the spacer and slide it carefully onto the shaft without getting epoxy on the threads (actually I should just put masking tape on that). Then grease on the flexspline teeth without touching the spacer. Then epoxy and grease on the post gear, and stick it on. Finally clean off the epoxy from the bit of shaft sticking up, and it's done. After the epoxy sets up, more grease can be added.

The knob is held on by a nylock nut. Stick it into the hole and grip with pliers, using a couple of 1/4" aluminum discs to reach into the hole. Grip the post with a drill chuck, and screw it on.

This first attempt was 0.3mm wall, and during the initial tune-up the whole flexspline sheared off at the base. Mostly because the knob was too tight and I forced it to turn anyway (acrylic and PLA both seem to have surprisingly high friction), so that added a lot of force on top of the string tension.

It was a little more flexible than necessary, so I made another with 0.35mm wall, plus a fillet at the base to reduce the stress riser. Took me all day yesterday due to incompetence. Wrecked two of them before I finally got it right. And this one somehow got a chipped tooth. Not enough to matter, as long as it doesn't serve as the starting point for a crack.

I also had to make a new knob for it due to the slightly larger outside diameter (and old knob being slightly too small anyway), and took the opportunity to increase the inside radius by 0.2mm so I could fit a strip of teflon between the flexspline outside and knob inside, which has successfully reduced the friction to a nice level. This one almost made it up to pitch, but it seems the wave generator isn't quite stiff enough and flexes rather than forcing the teeth to advance. I wanted to keep the diameter small enough that I could get the mounting screws in without removing the knob, but I guess the roughly 1mm thick carbon band just ain't gonna cut it. Flexspline OD is 16mm and knob OD is 19mm, so 1.5mm wall thickness is pretty skimpy to begin with. But about 0.5mm is lost to the teflon and the remaining plastic after machining.

I may try making one out of metal and wood so the full 1.5mm contributes to useful stiffness. Plus that would keep alive the dream of a plastic-free design I tried calculating the flexspline wall thickness for titanium in this style. Young's modulus is 116GPa, versus 3.2GPa for acrylic. So to get the same stiffness as 0.35mm, multiply by cube root of 3.2/116 and it would be about 0.1mm thick. Probably doable. Steel would be 0.9mm, so I could try that too.

Delrin machines much better than the white mystery plastic I tried before. It is more stringy than acrylic, but dimensions come out accurate.


Stiffness seems a little low at 0.25mm wall thickness. I tried scoring vertical lines around the flange with a knife to help stop it from rotating in the housing, but this stuff is super slippery and wouldn't even stay fully seated, so it needs criss-cross cuts and epoxy to lock it in.

It seemed hopeful at first. Tuned up to pitch no problem. But apparently it was just barely strong enough, and instead of fracturing like the acrylic it stretched to where the wave generator doesn't make it turn anymore. Running calculations again, it looks like I'm cutting it a lot closer on the strength than I thought. Maybe time to give up on this internal flexspline style.

Next task is to make a stiffer wave generator for the one from the previous update. If that survives, I can make one like it out of delrin too (this 3/4" rod is large enough to cut into a rectangular blank for that style). And perhaps steel as well. Ideally I'd like a 7mm thick blank (2mm teeth, 4mm smooth cup, 1mm flange), but I can reduce it all a bit to fit in 1/4". I have a piece of 1" x 1/4" stainless, but it's cupped so badly the usable thickness is more like 5.5mm. But still might work if I reduce the tooth face width to 1.5mm or less and flange to 0.75mm or less.

Pancake style is also still on the table.

Ok, here is what I had originally envisioned when I designed this knob. Metal for the wave generator, and wood for the part you grip. It's not shaped quite like I intended, due to forgetting the importance of climb cutting when milling wood and splitting a chunk off of it and then carving it a bit by hand. And brass might be better for lower friction and a bit higher stiffness. This acrylic/aluminum combo is rather grabby. Although delrin is so slippery, aluminum will probably be fine with it, and brass would add over a gram to the weight (come to think of it I forgot to weigh it before putting it on the guitar, but I think it's about 8 grams).

Scratch it up with x-acto knife and wash with soap and water.

Glue it together with JB Weld (great stuff, even held directly in a flame it was difficult to separate the post and gear after I broke the first flexspline last week). To reduce glue starvation, I coated the wood, let it absorb for a few minutes, scraped it off, and reapplied. The high viscosity reduces the ability of the wood to absorb it, but it does still try. It would be interesting to try pre-coating with hide glue to clog the endgrain. But it does seem to be "strong enough" in any case.

And here it is fully assembled.

Once again it seems hopeful at first tune-up, although it's far from the zero backlash I had hoped for. About 60 degrees of knob rotation difference depending on whether you tune up to pitch or down to pitch.

Hard to believe I've been at this for an entire month... seems like just a couple of weeks. Probably time to set it aside and get back to more important projects. Although I may make one more of this style with delrin body first. And I still want to try that all-metal pancake version eventually.

That's how you know you're having great fun!

Thanks again for all your posts Dennis. Very enjoyable and inspiring!

Sorry guys, I'm just not smart enough to be a machinist

Turns out I've been using half the eccentricity I was supposed to, for everything except those test pieces in the first post (where I had effectively mismatched tooth pitch so that didn't work either). So the teeth were never being fully engaged or disengaged, and thus couldn't skip past eachother without clashing the tips, and were being forced to bear the full load of the string with minimal engagement. It's amazing that the last acrylic external flexspline survived. Looking closely at the failed delrin internal flexspline, I can see where the teeth got crushed against the ring gear teeth due to not having enough clearance to skip past. Seeing how extreme the ellipse is now, I'm reminded why I thought it had to be plastic and not metal But the external flexspline style should still be possible in metal.

So now both styles work fine. Still not the instant response to direction change that I'd hoped for, but lower effective backlash than before (about 15-20 degrees difference in knob position to get the same pitch by tuning up or tuning down). Delrin is definitely better than acrylic for friction. Even with the proper ellipse, the acrylic has strong static friction with its aluminum wave generator. Grease doesn't seem to help.

So delrin external flexspline should be great (aside from the minor annoyance of backward rotation), and delrin internal flexspline works for now but remains to be seen whether it will hold up over time under such high stress.

Dennis, there's clearly a huge amount of effort that you've put into this and thanks for making it available.

Behind your initial wiki link is this one with a bunch of Matlab code. The reason I mention this is that I wondered what happens if the height of the gear teeth is reduced, which would mean that the eccentricity of the wave generator could be reduced and maybe even the stress on the teeth also.

The reason I mention this is that I know there are some Matlab experts on the forum, though I won't mention them by name, (and I'm not one of them) who may be able to do some modeling of a lower tooth profile before you try to make it, if it seems like a reasonable idea to you. Of course, there may be some very obvious reasons why the tooth height can't be reduced that I'm failing to see!

Thanks again!

_________________
Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

Yep, that's what I tried in those first experiments, which resulted in inability to mesh due to mismatched tooth pitch. Eccentricity is linked to tooth count, not tooth profile. And with my equipment, tooth count is limited by the available size of end mills.

Although now that I think about it, it may be possible to do the internal flexspline style with one tooth difference between flexspline and circular spline instead of two, reducing the eccentricity by half (and doubling the reduction ratio) for the same tooth size. It will produce unbalanced force on the input shaft, but because the shaft is supported at both ends that should be ok. It's usually not done because high speed rotation it would cause vibration from the unbalanced mass, but that's irrelevant in this case.

So much for taking a break from this project. It's just too much fun

EDIT: Interesting. I do have to use a much shorter/wider tooth profile for 1 tooth difference. It's almost the same thing as a cycloidal at this point, just using flexibility rather than the rigid pins to transmit torque and prevent the disc/flexspline from rotating. I think the ideal tooth profile will be the same as a cycloidal disc.

EDIT2: Actually, I don't think it will work at all. The toothy part remains circular and only gets dragged around in a circle, but the cylindrical cup will not flex that way easily. Gotta be 2 teeth difference.

Pancake style is different, though. In that case with one tooth difference, the flexspline wouldn't flex at all. It could be a rigid ring. This would be more like a compound planetary gear set. Or with internal non-flexing flexspline, it would be the same thing as a compound cycloidal, which is the first mechanism I wanted to design a tuner for and never was able to come up with a good one. Maybe I should try that again.

Here's a quick design for compound planetary with external eccentric, 16:1 reduction (1 - (3/4) / (4/5) = 0.0625). The compound ring would have to be machined from flat stock so you can do one side, flip it over, and do the other. Everything can be done with a 1/8" end mill, which is nice. Not sure if I'll actually go to the trouble to make one.

You could also do it in ring-out style of course (fixed ring on body, moving ring on post, and compound disc driven by eccentric shaft), but that necessitates making the post from large diameter stock which I don't like.

And here is what I do want to make. A new version of the pancake strain wave. Hopefully the teeth will work. It's impossible to have properly matched tooth pitch with this style, so I took a guess.

It has a new feature that will be applied to the external cup flexspline style as well. Instead of gluing the post gear, I'll mill the post to 4mm square (with rounded corners) and mill a matching hole in the gear. This eliminates the tricky epoxy-and-grease step, and makes it possible to fully disassemble. The nylock nut holds it all together.

The square post means that the wave generator has less side bearing area against the post, since it only contacts the 3mm diameter step now instead of the 5mm step. But that does mean I can eliminate the little stump from the wave generator, so it can be machined all from one side (and use 1/8" stock instead of 3/16" for the cup flexspline). Although that reduces the glue area for the epoxy a little bit. Neither of these details should matter in normal use, but make it more vulnerable to damage from impacts. The nylock nut also seats deeper down in the hole now, so hopefully the flats will still be sticking up enough to grip with my pliers. I could add a little spacer under it, but at that point I might as well just keep the stump.

This model is for banjo peg style mount rather than flange with screws. I can't actually make it at the moment since I don't have the proper thread tap for standard grommets (I think it's M8x0.75mm, though I'm not 100% sure), or any 3/4" round aluminum, so I'll do one with flange mount instead. It's frustrating that I could do it from 5/8" round stock except for that tiny lip below the fixed gear, which is necessary to reach the 17mm inside diameter of the wave generator and seal the whole thing against dirt. I suppose could add a separate sealer ring to fill the gap between 15.3mm and 17mm.