[DIY] Split-Ring Joined-Cycloids gear train - 3D Print

 

A ~1500:1 reduction ratio with only 4 main parts and in an extremely compact format ? Yes, this gear train can do that, at least in a prototype form: Hypocycloid Hyperdrive by the late great Robert Murray-Smith

Another advantage of a joined-cycloids gear is that for the same reduction ratio, in the same volume, it uses a much higher eccentricity value than a regular cycloidal disc drive. This means improved compatibility with materials like plastic that have much higher ductility than metal, and much larger contact surfaces that can stand higher loads and increase longevity.

 

So, of course, I had to quickly model an educational toy version to get familiar with it.

This one uses a high 6mm (1/4") of eccentricity and huge 20mm (0.8") ring pins, for a 120mm (4.7")  outside diameter and a 49:1 ratio. None of these parameters are optimized, of course, they just make the mechanical principles stand out, and helped match the size and ratio of the previous gearsets I've been playing with so far.

 

The compactness and the simplicity of this gear train are mind-boggling. Here it is next to other high-reduction ratio drives. They were all designed with a 40-ish:1 total ratio, 120mm outer diameter, and ~10mm wide (0.4") tooth contact areas:

 

However, one drawback with this design is the centrifugal imbalance, and one-sided force on the stator and output rings, like in a traditional single-disc cycloidal gear train. But this can be addressed with a Dual Joined-Cycloids design, which I have now also prototyped: Split-Ring Dual Joined-Cycloids gear train

 

The Fusion360 CAD model (very messy), STEP and 3MF files are on Github and MakerWorld

Feel free to copy, remix, whatever (non-commercially) 

Happy printing to all !

 

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Sections:

• Diagram
• CAD
• Printing
• Assembly
• Principle
• Resources 

Diagram

 

Single planet eccentric shaft compound gear train  (variant of 2K-H ?)

Note: showing a smaller output ring diameter, but can be = stator's
if the nb of pins is ≠ between the stator and output rings (like in this model)

 

 

CAD

The cycloidal profiles were generated via a Fusion360 script from woodenCaliper on Github and with the help of this video from Howey 

 

Shoutout to the extremely useful ME Virtuoso website where one can parametrically simulate their own planetary / wolfrom / cycloidal / harmonic / wave drives, and then download the STEP / DXF files. Some of which he also CNC'd or 3D printed, and tested on the ProMakina Youtube channel

 

 Printing

 

 Settings

• 0.4mm nozzle, 0.24 layer height
• 2 walls, 3 top, 2 bottom
• 25% Support Cubic infill

 

Note that the cycloidal profiles show the usual Fusion360 STEP export bug on such surfaces. But the deviations are small enough not to cause gear binding during rotation, so I didn't have to export a separate STL file this time.

 

Assembly

 

Assy is straightforward, first just glue the shafts together:

Then glue the output ring and wheel together:

Finally, make sure to align the 3 dots before gluing the stator:

Principle

 

The 1st stage comprises the cycloidal disc at the back that has 7 'teeth', so it results in a reduction ratio of 7:1. The 2nd has 6, but is used in reverse mode (inner disc driving the outer ring that has 7 pins), so its ratio is 6+1 = 7:1. Hence a total ratio of 7x7 = 49:1.

Turning this model's input shaft ClockWise (CW) makes the output also turn CW. But if the 2 stages were swapped, ie 6 teeth in the back and 7 in the front, the output rotation would reverse and be Counter-CW. Also, the ratio would now be 48:1, ie 6x(7+1), if I am not mistaken. To verify this, simply hold the model's output wheel and observe the direction of the casing's rotation, and also count the number of input shaft turns it takes to rotate the casing 360°.

 

Detailed explanation:

Formulas:

• Ns / No: nb of pins on stator / output wheel. Example: in this model Ns = 8, No = 7
• 1st stage ratio (stator):   R1 = Ns - 1
• 2nd stage ratio (output): R2 = No / (Ns - No)  >>> to be confirmed by mechanical engineers <<<
• Output rotation direction: same as input shaft if Ns > No, counter rotating if Ns < No

With that the reduction ratio can be plotted against the number of output pins. Assuming again that Ns = 8:

 

Now, let's play with high reduction values: for maximum reduction with close pressure angle values between the 1st and 2nd stage and likely-matchable eccentricities, the output stage should probably stay close to Ns + 1 teeth (right side of the graph above). So, assuming No = Ns + 1 and the formulas above, we can plot the total ratio against Ns (ie: (Ns - 1) x No):

Wow, reduction ratios get stratospheric real fast ! And that's using only 4 main parts (shaft, stator, joined cycloids, output wheel). J'en suis tout esbaubitouflé.

 

Digression: incidentally, at Ns = 39 the ratio is 1520:1, which doesn't match Robert Murray-Smith's claim of 1482:1 in his Hyperdrive video below. He used cycloidal discs with 38 and 39 teeth (ie Ns = 39 & No = 40) and calculated the ratio as 38 x 39. However, the 39-tooth disc is used in reverse mode (ie inside cycloid driving the outside 40-pin wheel) so, if I'm not mistaken, its ratio should be 40:1, not 39:1, resulting in 38 x 40 = 1520:1

 

Now, I'm not a mechanical engineer. So there is a good chance that all the above is a crock load of saké-induced bollocks. Case in point: I had to fix the formulas and graphs above several times already... Hopefully, someone knowledgeable will be able to confirm or debunk in the comments ?

 

Resources 

 

Not sure how this drive type should be called ? Dug up some history and papers going back to the 80s but there isn't much material and each source calls it differently, even misnaming it sometimes.

So why not me too ? Hopefully, Split-Ring Joined-Cycloids is more descriptive than most, although Joined-Cycloids Compound could be another candidate.

 

Called a Dojen Orbital drive in this Martin Marietta paper from 1987

Hypocycloidal reducer from Zincland - Hypocycloid Gear Reduction, circa 2010

 

The simplified spur gear single planet version is called 2K-H NN in this 2016 paper: Power analysis and efficiency calculation of the complex and closed planetary gears transmission

 

Similarly it is called Dojen / 2K-H NN in this 2022 review: Prototype Design and Efficiency Analysis of a Novel Robot Drive Based on 3K-H-V Topology

 

Interestingly, it is refered to as Wolfrom in this one from 2023: Impact of Cycloid’s and Roller’s Dimensional Errors on the Performance of a Cycloidal Drive for Power Transmission 

And the very much missed Robert Murray-Smith called it a Hypocycloid Hyperdrive in this 2025 demo video

Finally, the spur gear version is said to be the 2A-C variant of the 2K-H gear train type (aka sunless compound Wolfrom) in this 2015 study: A study on tooth profile design and loaded tooth contact analysis for 2S-C type planetary gear drives

So, I couldn't find clarity on the name of this joined-cycloids drive. Although it seems to be a cycloidal disc-based version of the 2K-H NN/2A-C type, with just 1 giant 2-tracks planet that is 1 tooth off on both the stator and output sides.

Also, unfortunately, none of that material is an actual deep dive into the design and performance of such a gear train. Graisse de trombone à coulisse, quelle pagaille !

Anybody else has more data or history on it ?