Hesitation, repetition and deviation

A project log for Strain Wave Gear with Timing Belts

Strain wave or harmonic drive gears are cool. As a cheap analog for metal or flex filament splined cup, try using timing belts.

Simon MerrettSimon Merrett 01/23/2018 at 03:1211 Comments

Well, it's been a while...

...sorry about that. Definitely counts as hesitation (ps the title is tribute to the British comedy radio contest called Just a Minute).

This log may not be satisfying to everyone following the project. Just to update you, I returned my attention to this project in December when @Dan Royer asked about whether it could be used in his new design of robot arm. You may recall that only @Ken Kaiser had put a motor in his gear up to this point. What you didn't know was that shortly after my "getting stronger" log/video, I made a version of the strain wave gear with a large bearing (a 6011 ZZ 55mm X 90mm X 18mm ) and built it around a "standard" NEMA 17, 59 Ncm stepper motor frequently found in 3D printers. I'll show that in a future log as that's the repetition part (more strain wave gears and variations upon the design of the wave generator).

In this log, I want to share with you the deviation part - I made a hypocycloidal gear. With a motor. The very same model of motor I put in my motorised strain wave gear. The reason, you see, for heading off down the hypocycloidal gear route is because on the one hand you have people showing home-machined hypocycloidal gears on YouTube that appear to work very nicely and on the other hand you have #5+ Axis Robot Arm having to give up on $3k development because they couldn't get theirs to work. What was the difference? Well one aspect was load. The people on YouTube (like ZincBoy or RockyMountains2001) aren't putting their gears under load. Dan's robot arm needs to be able to apply forces both to lift its own weigh but also to have an effect on its environment.

So, the basic designs online have one cycloidal disc (see the diagram in Dan's project log for common terms). Dan also complained that as soon as load was applied to his developmental gear, there was binding between the cycloidal disc and the ring gear pins. I also happened to see AvE's teardown of a nice Sumitomo cyclo gearbox / torque multiplier where he explained that a second cycloidal disc was used 180° out of phase with the first one, to prevent vibrations at high speed. 

These two got me thinking and I decided to use a second cycloidal disc and bearings for the ring gear pins. Here's a single disc prototype:

You can see here how there are 10 ring pins/bearings. The cycloidal disc has 9 "teeth" or nodes, so that's a 9:1 ratio (I think). Now encouraged with this version, I designed another version with two discs and 11 nodes on each disc (12 ring bearings). I used four 6805 Thin Section Deep Groove Ball Bearing 25x37x7mm, which went in a stack of (from stepper body outwards) output disc backplate, cycloidal disc 1, cycloidal disc 2, output disc ( with output rollers x 3 mounted. You will notice that the diagrams and models rarely show the output disc/shaft because they tend to prevent you from seeing the mechanism of the cycloid discs following their hypnotic, eccentric path. However, if you're going to harness the torque, you need the output disc/shaft. The other foreign part name in that bearing stack was "output disc backplate". I put an almost identical disc to the output disc behind both cycloidal discs for the shafts of the output shaft rollers to screw into and add strength to the output. Here's a photo of assembly after the first cycloidal disc went on (of an interim prototype, so you can't see any output disc backplate):

The two holes either side of the shaft are locating and clamping holes for the stack of eccentric and centred discs that go on top. This is especially important because the shaft isn't long enough for four 6805 bearings stacked up! You need to take care with this stack arrangement that the holes are lined up either side of the shaft flat face, so that the clamping nut/grub screw can locate the flat later.


So now we want to see how much torque we can convert from our stepper motor. But what are we comparing this gear to? I decided to baseline test the motor on its own. The spec sheet says 59 Ncm holding torque, which is no use to us as we want dynamic torque. I used a grbl board with acceleration settings and reasonable steps / mm settings that I can't recall at this point. I added a DRV8825 in 1/16 microstep mode and set Vref to 2A/phase. I tested from 9V to 24V (finding 9V to be the best at these relatively low step speeds) and found that I could reach around 20 Ncm before the motor stalled. I have tried to do these tests with less microstepping in order to achieve more torque but in a dynamic situation they seem to stall just as easily as the microstepped tests. Maybe I'm doing something wrong, maybe there's a characteristic of this application which explains this observation. Certainly sounds quieter and feels smoother with 1/16 microstepping.

Loading up

Clamping the stepper (this time the one with the hypocycloidal gear attached) to the bench, I set about loading it up. The beam is an M6 steel threaded rod and the load is just steel brackets and neodymium magnets.

There are two M3 bolts protruding from the drive disc which are forming two points of contact for the beam to cantilever from. A slightly closer shot:

And here you can see the two, diametrically opposed cycloidal discs and the ring bearings:

I have printed a slight chamfered lip on the edges of the cycloidal discs to encourage them and the ring bearings to stay located!


I measured the output of this gear, lifting the threaded rod "beam" and steel/magnet "load" as 2.67 Nm. That's 13.6 times the dynamic torque achieved with the plain motor using the same current/voltage/microstepping/pulse/acceleration settings. How did a 9:1 ratio gear multiply torque by nearly 14 times? I think it's got to be in the way that the stepper motor needs to "jump" between poles for each step and the gearing just helps with the threshold where this becomes the mode by which the motor enters a stall. Someone please correct me if I'm wrong!


I'm  pretty pleased with this result. I don't know whether I'll carry on this kid of gear in preference to strain wave gears but I'll certainly show you where I got to with the strain wave gears before coming back to it. If you wanted to put this in #5+ Axis Robot Arm @Dan Royer thinks it'd need to produce 20Nm to achieve the full design target lift capability.  This could be perhaps achieved through a second stage of the hypocycloidal gear which takes the current output disc rotation as the input rotation for another set of eccentric cams that drive another pair of cycloidal discs (although speed is clearly a tradeoff). Two other points are worth mentioning about the hypocycloidal gear I made: firstly, it allows back driving, so there appears to be relatively low friction loss here; secondly, the 3D printed version I made hasn't had much in terms of a dimensional tolerance check but although it seems to be low backlash, there is some, which is a problem in some applications (just needs designing/manufacturing out!).  It would be great to see others try this out and share their results - robot arms need you!


Xing wrote 03/10/2018 at 00:56 point

Would be interesting to see a few more photos / drawings on the cycloidal disks , the black plate for the output disks and their interconnections.   I am designing my own, but am still puzzled about how the pins on the output disk interacting with the two cycloidal disks.  Would you be able to share some photos or drawings?  Many thanks!

  Are you sure? yes | no

Dan Royer wrote 01/23/2018 at 20:27 point

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Simon Merrett wrote 01/23/2018 at 23:12 point

And it spun freely with no load? Did you manage to notice where the friction contact was happening? Only thing which I got caught out on was my cam eccentricity being too great to start with but if you have been able to run the gear easily without load that wouldn't be an issue in your design.

I'm wondering where to go with this next. I.e. what should I try and improve next. Second stage? Make it smaller? Can't spend forever on it but it seems like progress.

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Florian Festi wrote 01/23/2018 at 18:47 point

Also AvE is wrong about the output shaft being in one piece. It is made out of three separate pieces that are kept together by the big, pressed in bolts. These bolts go through the cycloid disks. Guess the holes are big enough that the bolts don't touch and the shaft is driven by the slightly smaller bolts that can be removed easily (and replaced when worn out).

So to build the core you stack up the three output shaft parts with the cycloidal disks (including the cam or the whole input shaft) in between and then press in the bolts that keep the output shaft together. Then you add the bearings and drop it in the housing.

Oh, you can have a spacer between the parts of the output shaft and then just screw everything together...

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Simon Merrett wrote 01/23/2018 at 23:18 point

Yes, although that arrangement has quite a narrow shaft (a bit like Dan's last version) and I would think that we want a reasonable diameter if we're using weaker materials than steel.

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Dan Royer wrote 01/23/2018 at 16:27 point


Above 2.67 it stalls?

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Simon Merrett wrote 01/23/2018 at 16:57 point

Yes, the motor stalls - glad that's the failure mode at the moment as I wouldn't have enjoyed seeing the gear fail so soon! 

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Florian Festi wrote 01/23/2018 at 16:03 point

Interesting to see how thoroughly the cycloidial disks are sandwiched between the disks of the drive shaft in the Sumitomo gear. Obviously to prevent them from tilting and jamming which is what Dan attributes the failure of his attempts to.

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Simon Merrett wrote 01/23/2018 at 16:59 point

Other than the opposing discs, the most significant thing for me in the Sumitomo gear was the use of round pins dropped into slots to create the ring pins. That's a good way to keep costs down _and_ fit a higher gear ratio into a given diameter. 

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Dan Royer wrote 01/23/2018 at 17:46 point

we used round pins, too.

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Simon Merrett wrote 01/23/2018 at 20:18 point

@Dan Royer can you dig out any photos or drawings for us?

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