Gearing Ratio Calculator

Check out the Beta version my Lego Technic Gearing Ratio Calculator Tool:

This tool allows you to upload your Lego Technic project .ldr file and analyse the gearing ratios between any two connected gears or axles. Currently supports most gears, axles, worm gears, some differentials, cv joints and universal joints. See the video tutorial on how to use it. It is a work in progress and I would love to hear your feedback on it. Click here to try it out.

Note: As of 25 Septemeber 2021 the tool supports CV joints, linear speed via the radius of the component and improves on the frame rate for higher numbers of parts in a model).

Technic Elbow Art

This is a tool to create "Lego Technic Elbow Art" - a series of intertwined elbow pieces as a single sequence. Choose your dimensions and search parameters and search for new dense solutions and set a record! 

Download your Elbow Art as an .ldr file and build it yourself. Click here to try it out!

How do you make a 1:N gearing ratio?

31 Oct 2021

So you need to make a 1:N gearing ratio for your project where N is some whole number like 21, 40, or even 100?  In general this can be easy or difficult depending on your number N. One general solution is to create a gear chain using n gearing ratios of 1:M0, 1:M1, 1:M2,... ,1:Mn. such that M0 x M1 x ... x Mn = N then the overall gear chain ratio will be 1:N. So that means you need to break down your number N into a number of factors that can be created by a pair of Lego gears. For example if N is 36 then you can write

36 = 3 x 3 x 2 x 2

So then you create a 1:36 gear ratio by creating a gear chain of simpler gears using 1:3, 1:3, 1:2 and 1:2. Now of course since the order of multiplication doesn't matter you can put these in any order, e.g. you could also use 1:2, 1:3, 1:3 and 1:2. So below is an example solution for a 1:36 gearing ratio using the first order shown.

Here the gearing ratio between the brown input axle and yellow output axle is 1:36.

Now due to the limited number of gears available in Lego Technic, it is only possible to create the gearings ratios of 1:2, 1:3, 1:5 and 1:7 directly using just two gears (i.e. without differentials) so that means your number N must be a product of one or more of the numbers 2, 3, 5 and 7 for this method shown here to work. For example below are the possible 1:N gearing ratios up to N <= 50 using this method:

Possible 1:N ratios using the factors 2,3,5 and 7
N Factors
2 2
3 3
4 2 x 2
5 5
6 2 x 3
7 7
8 2 x 2 x 2 x 2
9 3 x 3
10 2 x 5
12 2 x 3 x 3
14 2 x 7
15 3 x 5
16 2 x 2 x 2 x 2
18 2 x 3 x 3
20 2 x 2 x 5
21 3 x 7
24 2 x 2 x 2 x 3
25 5 x 5
27 3 x 3 x 3
28 2 x 2 x 7
30 2 x 3 x 5
32 2 x 2 x 2 x 2 x 2
35 5 x 7
36 2 x 2 x 3 x 3
40 2 x 2 x 2 x 5
42 2 x 3 x 7
45 3 x 3 x 5
48 2 x 2 x 2 x 2 x 3
49 7 x 7
50 2 x 5 x 5


Now of course you are not limited to just 1:M gearing ratios in the product, especially since 1:7 can only be made with an 8 tooth gear driving a 56 tooth turntable and so it is more convenient to use a 20 to 28 which gives 4:7 and you then need to cancel out the 4 by placing it in the denominator.

In summary, to create your 1:N gearing ratio, just look up your number in the table above and use the required factors (you will have to work them out for yourself for N > 50) in a gear chain.

Now what if you need to create a gearing ratio of 1:N where N cannot be created as a product of 2, 3 ,5 and 7 (e.g. 13, 17, 71 or other  primes)? The answer is to use a differential! (see the section of differentials for more details when that becomes available...).

More to explore

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Lego Technic Gearing Ratio Calculator Tool

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