# 2:1 gear ratio in stud-less Lego Technic

Is there a recognised technique to create a 2:1 gear ratio in stud-less Lego Technic?

Neither of the two methods suggested here (studded though) work.

24T/12T with a 2L x 1L axle offset does rotate, but is too stiff to be functional.

16T/8T with a 1L x 1L axle offset is totally jammed.

• An explanation of these observations - most lego gears need a pitch of `(n + m) / 16` studs. Your first case needs `36/16=2.250` but you give it `sqrt(5)=2.236`. Your second needs `24/16=1.5` but you give it `1.414`.
– Eric
Sep 3, 2019 at 5:20
• Despite our good intentions with various solutions, the only answer you need is that the first build on the left (12T/24T) is correct. If you are experiencing any stiffness it is from the "L" brackets pinching the gears. This is a case of "real world" application. Anyone who tells you differently obviously hasn't tried it and doesn't know what they're talking about. Sep 5, 2019 at 0:51
• The solution from the formula presented by Eric above is a great example of geometric tolerances in mechanical design. Knowing first-hand that the 12T/24T gears mesh perfectly shows that a difference of .014 is insignificant in this application. Yay tolerances! :) Sep 5, 2019 at 1:25

Here's a solution I found in Yoshihito Isogawa's LEGO Power Functions Idea Book Vol. 1 - Machines and Mechanisms:

EDIT based on Eric's comment:

And here's using the black piece from JohnnyB's tweak:

• Pair this with a 12:12 gear pair, and you can bring your axles back to whole stud boundaries
– Eric
Sep 3, 2019 at 5:22
– Uli
Sep 3, 2019 at 9:23
• +1 for resourcefulness & inspiration :) Sep 3, 2019 at 14:10

I felt my original answer got messy. The simplest answer is that you already had it. I experimented with variations of your 12T/24T build and experienced varying degrees of the stiffness you mentioned. It became evident that the location of the gears was affecting how much the side pieces were pinching the gears even though the actual gear mesh remained well within tolerances. Stabilizing the brackets, thus the distance between them, eliminated any and all stiffness.

I also threw together a few more 1:2 ratio gear configurations for reference:

Inspired by the design from Yoshihito Isogawa posted by Uli, I couldn't resist tweaking it in an attempt to make it stronger and easier to build off of.

Inspired by the answer that Eilon gave regarding Technic chain, I evidently proved myself wrong and came up with this.

Another solution to consider (although it only makes sense in certain scenarios) is to use a differential. It naturally creates a 2:1 ratio, but if your mechanism doesn't require one then it's kinda bulky and silly to introduce one with a fixed input. But if you have one involved, just swapping around how you're using the inputs and housing can introduce a 2:1 ratio where you didn't have one before.

I did this today designing a mechanism for a clamshell excavator. Turning one crank extends both lines at the same rate, turning another crank keeps one line fixed while adjusting the second. But I wanted a block-and-tackle on the suspension line, meaning it would need to turn twice as fast. Just changing how I used the differential got me that ratio for free.

Here's an illustration of the basic concept - the differential housing will rotate at half the rate of the yellow shaft. Like I said, silly and bulky, but could be useful in the right situation.

– Alex
May 12 at 19:48

Consider using a chain with any two gears that have a 2:1 ratio. The chain also helps preserve direction of rotation, if that's important in your case. The chain could even drive other gears if needed (like the serpentine belt in a car).

Here's a diagram:

(I wasn't sure how to make a chain appear, nor axles, but I think it's clear.)

• Lego chain, while fine in some applications, is often temperamental with high torque and high speed. It is especially bad, in my experience, when used on the 8T gear. Sep 3, 2019 at 16:24
• Welcome to Bricks.SE! A chain could be a possible solution, though it does have its limits as noted by @JohnnyB Thanks for your contribution!
– jncraton
Sep 3, 2019 at 17:22
• Agreed it has limitations, but no torque requirement of any kind was specified. Hopefully this helps someone. Sep 3, 2019 at 19:02
• I should have mentioned that since the chain doesn't work on beveled gears, the 8T/16T combination for a 2:1 would be the only option. Because Lego chain can't seat properly on a 8T gear, it's doesn't take hardly any resistance to slip. I physically built this to make sure I had remembered correctly before commenting. I'm not saying you're wrong, it does "work" in a sense, it just slips so easy that it really limits it's usefulness. Apologies if I came off brash, it wasn't my intention. Sep 4, 2019 at 2:26
• You might find the last bit of my new answer of interest ;) Sep 5, 2019 at 7:24