My Educational Mechanical Examples Series

This model is one of my educational mechanical mechanism examples on 80mm x 80mm base plates.
You can find all models of the series in this collection => [Mechanical Mechanism Examples]

This set

This present set includes:

• Cycloid gear
• Magnified cycloid gear
• Magnified involute gear
• Internal bevel gear with straight teeth
• Internal bevel gear with spiral teeth

Brief description

The cycloid gear shown here is another type of spur gear. While the most common spur gear is the involute gear—whose working tooth profile is generated from the involute curve—the cycloid gear is typically used in precision machinery such as watches, where loads are relatively light and efficiency is critical.

The tooth profile of a cycloid gear consists of two cycloid curves. Here, a cycloid is traced by a point on a rolling circle that rotates without slipping on the pitch circle, not on a straight line.

• The external portion of the tooth profile is an epicycloid, generated by a circle rolling on the outside of the pitch circle.
• The internal portion is a hypocycloid, generated by a circle rolling on the inside of the pitch circle.

The two rolling circles do not need to have the same radius. However, for a pair of cycloid gears to mesh correctly, the radius of the rolling circle used for the internal hypocycloid of one gear must match the radius of the rolling circle used for the external epicycloid of the mating gear. In practice, the rolling circle for the internal hypocycloid is often chosen to be about one third of the pitch-circle radius.

Compared with involute gears, cycloid gears have fewer contact points and less sliding motion, resulting in very low friction. On the other hand, they are more difficult to manufacture, have lower tooth strength, and require precise center-to-center alignment. For these reasons, cycloid gears are used mainly in high-precision, low-load, and high-value applications such as mechanical watches, where minimizing loss is essential.

To compare the tooth profiles of involute gears and cycloid gears, magnified models are provided. The lines and curves engraved on the base plate show the paths traced by the contact points between the meshing teeth. You can observe that, in involute gears, the contact points move along straight lines, whereas in cycloid gears, they move along circular arcs. You can find non-magnified model of involute gears in my first set of gear examples.

As described before, the two axes of mating bevel gears can have an arbitrary angle. Here, I provided the models of internal bevel gears, where the angle between the two axes is close to 180deg. They are still meshing perfectly as you can feel by rotating them.

Case

This model is compatible with the case included in my first set.

Printing

• Use the models named ???-printable.stl for printing.
  The models named ???-assembled.stl are provided just to show how they should be assembled.
   
• Use well-dried PETG to have better dimensional accuracy.
• Use 0.1 mm or 0.08 mm layer height to have smoother surfaces.
• Use slow printing speed for overhangs.
• Select “Random” seam position to have smoother rotation.
  Randomly distributed seam should be easily worn out after some wearing.

Sanding and Filing

Sometimes, the gears suffer from the stringing effect and/or elephant foot effect, resulting in a too tight fit to the shafts (they are designed with a 0.15 mm radial clearance). 

If you see rough surface on the shafts due to stringing, sand off the roughness with a small piece of sand paper.

If you feel the gears do not rotate smoothly due to an elephant effect, widen the hole slightly by using a thin round bar file.

Without those issues, the parts should rotate very smoothly with minimal friction.

Assembly

No glue is needed, in theory. 

Just snap assemble the parts.

Other educational models

You may also be interested in the models in my educational mechanical mechanism examples.

Find them in this collection:
https://makerworld.com/collections/15048577-my-educational-mechanism-models

Acknowledgement

I got into gears thanks to K.$uzuki's amazing articles and YouTube videos. Many of the mechanisms shown in this series came from the introductions on his website. He also makes excellent gear models himself. This series wouldn’t have existed without his inspiration.

I learned a lot about technical detail of designing gear tooth profiles from Haguruma-No-Hanashi website. I’m truly grateful for that.

License (2026-03-13 updated)

• The 3D model(s) are licensed under Creative Commons Attribution 4.0 International. (unchanged)
• However, the text and images on this page are copyright reserved. (added on 2026-03-13)