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Gear profile

Under normal circumstances, involute gears are the way to go as they offer many advantages when compared to other gear profiles. However, if non-circular gears are required drawing an involute gear profile can become complicated as not all teeth are the same size.

As FDM 3d printed parts are (in general) not as strong as metal parts and therefore torque and transmission efficiency is not as important, we can try to use a different gear profile. If we use circular teeth we ensure that all teeth have the same size regardless of the gear outline.

Circular gear profile
Figure 1: Circular gear profile

This gear profile is therefore very easy to construct, as you can see in fig. 2 below.

How to draw a circular gear
Figure 2: How to construct a circular gear

Calculating the correct tooth size

To calculate the required tooth size \(r\) we have to solve a simple system of equations using a computer algebra program like maple for example.

As the required system of equations is dependant on the gear shape, please take a look at the linked PDF paper for more details on how to assemble it.

Examples included in the PDF

The linked PDF paper contains several detailed examples of how to calculate both circular and non circular gears using the proposed gear profile. Listed below are the results of all included examples:

Circular gears with given gear ratio and centerdistance

Two circular gears with given center distance
Figure 3: Circular gears with given gear ratio and centerdistance

Internal ring gear

Two circular gears with given center distance
Figure 3: Internal ring gear

Planetary gearbox (epicyclic gear train)

Two circular gears with given center distance
Figure 3: Planetary gearbox (epicyclic gear train)

Rectangular/square gear with given side length

Two circular gears with given center distance
(a) Corners are not teeth
Two circular gears with given center distance
(b) Corners are teeth
Figure 4: Rectangular/square gear with given side length \(r=22/12\)
Two circular gears with given center distance
(a) Corners are not teeth
Two circular gears with given center distance
(b) Corners are teeth
Figure 5: Rectangular/square gear with given side length \(r=22/24\)

Rectangular and circular gears with given gear ratio and center-distance

Two circular gears with given center distance
Figure 6: Rectangular and circular gears with given gear ratio and center-distance

Elliptical gear with given size and number of teeth

Two circular gears with given center distance
(a)
Two circular gears with given center distance
(b)
Figure 7: Elliptical gear with given size and number of teeth

Elliptical gear and square gear that fit together

Two circular gears with given center distance
Figure 8: Elliptical gear and square gear that fit together

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Sebastian Hirnschall
Article by: Sebastian Hirnschall
Updated: 30.05.2021

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