Profile Shift - Educational Model

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]

The present model

This model demonstrates the profile shift of the involute gears.

Brief Description

This model demonstrates profile shift in involute gears.

The gears are built from three stacked layers. Notice that, although the three layers have different outer diameters, they all have the same number of teeth and can mesh with the same rack pitch. This is achieved by applying different amounts of profile shift to the involute tooth profile.

The middle layer is a standard, unshifted involute gear. Involute gears are commonly generated by rolling a gear blank against a rack-shaped cutting tool (such as a hob). A profile shift is introduced by offsetting the gear blank relative to the tool’s pitch line—equivalently, by changing the radial setting between the hob and the gear center during generation.
 

In this model, the larger and smaller layers use profile shifts of +0.5 module and −0.5 module, respectively. Correspondingly, they mesh correctly with racks whose pitch lines are offset by ±0.5 module from the nominal position. More generally, if one gear has a shift of +s and its mate has −s, they mesh at the same center distance as an unshifted pair. That is why two identical three-layer gears will mesh correctly in every layer when one gear is flipped up-side-down. When the total shift is not zero, the correct working center distance must be calculating by rather complex formula taking the pressure angle into account.
 

Profile shift modifies the tooth shape: a positive shift tends to make the tooth thicker at the root, while a negative shift tends to make it thinner. For small-tooth-count gears, unshifted designs are prone to undercut at the tooth root to avoid interference with the mating tooth tip. Applying a positive shift can reduce undercut and increase tooth-root strength.

Profile shift can also be used to match the effective meshing radii of gears with different tooth counts. Using this idea, it is possible to build compact mechanisms with very high gear ratios, such as the “Planetary Differential Gear” introduced earlier.

In summary, profile shift is a practical tool for strengthening involute gear teeth and for adjusting meshing geometry.

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.Printing

Sanding and Filing

Note that, in this model, the rotation of the bases for bearings is intentionally made not too smooth.

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

Just secure the gears by the retaining rings.

Other examples

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

Happy printing!

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)