Idiosyncratic gear ratios

[Peter Nolan]

A little while ago I became interested in some slightly unusual gear ratios (for a few reasons covered below). More recently though, I gained access to a laser cutter, and hence the ability to make custom lego gears. With this in mind, I decided to work out all the possible custom gear combinations that will fit on a standard technic beam (ie all the combinations where the centre-to-centre axle distance is a whole number of studs). I found the website https://www.cailliau.org/en/Alphabetical/L/Lego/Gears/Dimensions/ handy for figuring out the meshing.

I'm not sure if this is of interest to anyone else, but here is what I found:

One custom gear with one standard gear

(Standard gear, Custom gear, Ratio)

12    52    3/13
16    32    1/2
16    48    1/3
20    44    5/11
20    60    1/3
28    52    7/13
36    44    9/11
36    60    3/5

Two custom gears where both have a prime number of teeth

(Custom gear, Custom gear, Ratio)

11    53    11/53
11    37    11/37
17    47    17/47
17    31    17/31
23    41    23/41
37    59    37/59
19    29    19/29
13    19    13/19
43    53    43/53
37    43    37/43
53    59    53/59

There are also plenty of 'loose running' combinations where the centre-to-centre distance between axles is only 0.5 mm off an integral number of studs. I tried one of these, and it seemed to work fine.

Loose-running combos (standard gears in bold)

(Gear 1,  Gear 2, Ratio)

8    23    8/23
8    39    8/39
8    55    8/55
11    20    11/20
11    36    11/36
12    19    12/19
12    35    12/35
12    51    4/17
15    16    15/16
16    31    16/31
16    47    16/47
19    28    19/28
20    27    20/27
20    43    20/43
20    59    20/59
23    24    23/24
23    40    23/40
23    56    23/56
24    39    8/13
24    55    24/55
27    36    3/4
28    35    4/5
28    51    28/51
36    43    36/43
36    59    36/59
39    40    39/40
39    56    39/56
40    55    8/11
55    56    55/56

 

SO the big question is, why would I be interested in such things? The first is that a while back I built a 'phase revival' machine (video below). In this situation I wanted a ratio close to, but not exactly 1:1. In the video I used 20:24, which means that the first cog has to rotate 7776 times before all the parts line up again. If I used a custom ratio of 39:40, and had 11 modules instead of 5, it would take 10 billion years (rotating the left-most gear at 1 revolution/second) before all the pieces realigned! I'm not quite sure why, but the idea of a machine that takes the entire lifetime of our sun to reset is appealing! 

And now for the prime numbers... I've been interested in making lego spirographs recently, and the key to interesting patterns is the lowest common multiple of the two gears. If you have a gear with a prime number of teeth, you are pretty much guaranteed of getting lots of 'knots' in the design. In the second video below, I used a 43 tooth gear meshed with a 36 tooth gear.

To actually make the gear profile, I used https://www.festi.info/boxes.py/Gears?language=en with a modulus setting of Pi (3.14) to make lego compatible gears. You also need to tweak the burn correction depending on the cutter and material. I also set 'profile_shift' to zero. I suspect that a little more fine-tuning would be required to get the best result, but this is a good starting point.

I hope that someone else finds this interesting!

 

 

Ahhhrrgh. I can't delete the table below! Please ignore....

 

Edited February 1, 2021 by Peter Nolan

[pdw]

4 hours ago, Peter Nolan said:

SO the big question is, why would I be interested in such things?

I read the subject line of your post and thought "spirograph"!

I was inspired by some of the recent spirograph posts on here, and built something similar to what you have and quickly discovered the limitations of the standard gears so it's very interesting to see what you've done here.

 

Edited February 1, 2021 by pdw

[Lira_Bricks]

14 hours ago, Peter Nolan said:

Ahhhrrgh. I can't delete the table below! Please ignore....

The editor here is such a PITA, I don't understand why they do not enable HTML-mode or something... but whatever. What happens if you click on the image to select it, and then press backspace or delete?

[Peter Nolan]

5 hours ago, Lira_Bricks said:

The editor here is such a PITA, I don't understand why they do not enable HTML-mode or something... but whatever. What happens if you click on the image to select it, and then press backspace or delete?

Thanks for the suggestions, but even when you delete the image (both the inline version and the attachment) it just reappears after you accept the edit.