# [Drawing circular and non-circular gears for FDM 3d-printing](https://blog.hirnschall.net/gears-for-3d-printing/)

author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/)

meta description: Design circular and non-circular gears for FDM using a circular tooth profile — simpler than involute, uniform teeth on any gear outline. Includes PDF.

meta title: Gears for 3D Printing — Circular & Non-Circular Design

date published: 30.05.2021 (DD.MM.YYYY format)
date last modified: 03.04.2026 (DD.MM.YYYY format)

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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](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/gear-profile.png)


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](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/drawing-a-gear.png)


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](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex1.png)


Figure 3: Circular gears with given gear ratio and centerdistance

### Internal ring gear

![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex2.png)


Figure 3: Internal ring gear

### Planetary gearbox (epicyclic gear train)

![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex3.png)


Figure 3: Planetary gearbox (epicyclic gear train)

### Rectangular/square gear with given side length

![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex4-1.png)


(a) Corners are not teeth


![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex4-2.png)


(b) Corners are teeth



Figure 4: Rectangular/square gear with given side length \(r=22/12\)



![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex4-3.png)


(a) Corners are not teeth


![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex4-4.png)


(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](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex5.png)


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](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex6-1.png)


(a)


![Two circular gears with given center distance](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex6-2.png)


(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](https://blog.hirnschall.net/gears-for-3d-printing/resources/img/ex7.png)


Figure 8: Elliptical gear and square gear that fit together