Answers.Body: <p>Here's a solution I found in Yoshihito Isogawa's <strong>LEGO Power Functions Idea Book Vol. 1 - Machines and Mechanisms</strong>:</p>
  
  <p><a href="https://i.sstatic.net/iPcv9.jpg" rel="noreferrer"><img src="https://i.sstatic.net/iPcv9.jpg" alt="enter image description here"></a></p>
  
  <hr>
  
  <p><strong>EDIT</strong>
  based on Eric's comment:</p>
  
  <p><a href="https://i.sstatic.net/OxLOe.jpg" rel="noreferrer"><img src="https://i.sstatic.net/OxLOe.jpg" alt="enter image description here"></a></p>
  
  <hr>
  
  <p>And here's using the black piece from JohnnyB's tweak:</p>
  
  <p><a href="https://i.sstatic.net/BUdyv.jpg" rel="noreferrer"><img src="https://i.sstatic.net/BUdyv.jpg" alt="enter image description here"></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T05:22:17.873Z
Answers.Text: Pair this with a 12:12 gear pair, and you can bring your axles back to whole stud boundaries
Answers.UserDisplayName: Eric
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T09:23:02.907Z
Answers.Text: @Eric Thanks. I've added a picture to illustrate your comment...
Answers.UserDisplayName: Uli
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T14:10:07.903Z
Answers.Text: +1 for resourcefulness & inspiration :)
Answers.UserDisplayName: JohnnyB
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-02T23:28:57.800Z
Answers.LastActivityDate: 2019-09-03T12:46:53.753Z
Answers.LastEditDate: 2019-09-03T12:46:53.753Z
Answers.UserDisplayName: Uli
Answers.Body: <p>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.  </p>
  
  <p><a href="https://i.sstatic.net/0rl0T.jpg" rel="noreferrer"><img src="https://i.sstatic.net/0rl0T.jpg" alt="enter image description here"></a>  </p>
  
  <p>I also threw together a few more 1:2 ratio gear configurations for reference:  </p>
  
  <p><a href="https://i.sstatic.net/wOA9Y.jpg" rel="noreferrer"><img src="https://i.sstatic.net/wOA9Y.jpg" alt="enter image description here"></a>  </p>
  
  <p>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.  </p>
  
  <p><a href="https://i.sstatic.net/cJv0c.jpg" rel="noreferrer"><img src="https://i.sstatic.net/cJv0c.jpg" alt="enter image description here"></a>  </p>
  
  <p>Inspired by the answer that Eilon gave regarding Technic chain, I evidently proved myself wrong and came up with this.  </p>
  
  <p><a href="https://i.sstatic.net/DLBMV.jpg" rel="noreferrer"><img src="https://i.sstatic.net/DLBMV.jpg" alt="enter image description here"></a>  </p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-05T07:18:22.590Z
Answers.LastActivityDate: 2019-09-05T07:18:22.590Z
Answers.UserDisplayName: JohnnyB
Answers.Body: <p>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.</p>
  <p>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.</p>
  <p>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.
  <a href="https://i.sstatic.net/USjoJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/USjoJ.png" alt="Differential assembly with one input fixed" /></a></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-05-12T19:48:28.540Z
Answers.Text: Adding a picture of your solution would greatly improve your answer.
Answers.UserDisplayName: Alex
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-05-12T18:16:23.537Z
Answers.LastActivityDate: 2022-05-12T20:50:54.480Z
Answers.LastEditDate: 2022-05-12T20:50:54.480Z
Answers.UserDisplayName: Katie
Answers.Body: <p>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).</p>
  
  <p>Here's a diagram:</p>
  
  <p><a href="https://i.sstatic.net/Dx4Og.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Dx4Og.png" alt="T8 and T16 gear connected with chain"></a></p>
  
  <p>(I wasn't sure how to make a chain appear, nor axles, but I think it's clear.)</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T16:24:19.363Z
Answers.Text: 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.
Answers.UserDisplayName: JohnnyB
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T17:22:04.513Z
Answers.Text: 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!
Answers.UserDisplayName: jncraton
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T19:02:37.563Z
Answers.Text: Agreed it has limitations, but no torque requirement of any kind was specified. Hopefully this helps someone.
Answers.UserDisplayName: Eilon
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-04T02:26:44.533Z
Answers.Text: 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.
Answers.UserDisplayName: JohnnyB
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-04T04:39:39.007Z
Answers.Text: No worries, I re-read my comment and would say the same about my own text :) I do realize now that my suggestion might be appropriate "for emergency use only"!
Answers.UserDisplayName: Eilon
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-05T07:24:29.933Z
Answers.Text: You might find the last bit of my new answer of interest ;)
Answers.UserDisplayName: JohnnyB
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-05T16:02:59.733Z
Answers.Text: Your latest bit is.... insane!  I think it's worth putting it in its own answer even.
Answers.UserDisplayName: Eilon
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-05T16:31:34.883Z
Answers.Text: You are welcome to add it to your answer as an example if you would like, no worries on my part :)
Answers.UserDisplayName: JohnnyB
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-09-03T15:51:46.747Z
Answers.LastActivityDate: 2019-09-03T16:01:13.020Z
Answers.LastEditDate: 2019-09-03T16:01:13.020Z
Answers.UserDisplayName: Eilon
Body: <p>Is there a recognised technique to create a 2:1 gear ratio in stud-less Lego Technic?</p>
  
  <p>Neither of the two methods suggested <a href="http://lego.jtooker.com/gear_ratios/" rel="noreferrer">here</a> (studded though) work.</p>
  
  <p><a href="https://i.sstatic.net/0OKEh.jpg" rel="noreferrer"><img src="https://i.sstatic.net/0OKEh.jpg" alt="enter image description here"></a></p>
  
  <p>24T/12T with a 2L x 1L axle offset does rotate, but is too stiff to be functional.</p>
  
  <p>16T/8T with a 1L x 1L axle offset is totally jammed.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-09-03T05:20:50.323Z
Comments.Text: 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`.
Comments.UserDisplayName: Eric
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-09-05T00:51:19.907Z
Comments.Text: 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.
Comments.UserDisplayName: JohnnyB
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-09-05T01:25:21.737Z
Comments.Text: 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! :)
Comments.UserDisplayName: JohnnyB
Tags: <technic><design><gears>
Title: 2:1 gear ratio in stud-less Lego Technic
UserDisplayName: Peregrine
ThreadText: # 2:1 gear ratio in stud-less Lego Technic
  
  (Asked by: username_0 on 2019-09-02)
  
  Is there a recognised technique to create a 2:1 gear ratio in stud-less Lego Technic?
  
  Neither of the two methods suggested [here](http://lego.jtooker.com/gear_ratios/) (studded though) work.
  
  [![enter image description here](https://i.sstatic.net/0OKEh.jpg)](https://i.sstatic.net/0OKEh.jpg)
  
  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.
  
  **Tags:** technic, design, gears
  
  > **Comments:**
  > **username_1**: 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`.  
  > **username_2**: 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.  
  > **username_2**: The solution from the formula presented by username_1 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! :)  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_3 on 2019-09-02. Score: 9
  
  Here's a solution I found in Yoshihito Isogawa's **LEGO Power Functions Idea Book Vol. 1 - Machines and Mechanisms**:
  
  [![enter image description here](https://i.sstatic.net/iPcv9.jpg)](https://i.sstatic.net/iPcv9.jpg)
  
  ---
  
  **EDIT**
  based on username_1's comment:
  
  [![enter image description here](https://i.sstatic.net/OxLOe.jpg)](https://i.sstatic.net/OxLOe.jpg)
  
  ---
  
  And here's using the black piece from username_2's tweak:
  
  [![enter image description here](https://i.sstatic.net/BUdyv.jpg)](https://i.sstatic.net/BUdyv.jpg)
  
  > **Comments:**
  > **username_1**: Pair this with a 12:12 gear pair, and you can bring your axles back to whole stud boundaries  
  > **username_3**: @username_1 Thanks. I've added a picture to illustrate your comment...  
  > **username_2**: +1 for resourcefulness & inspiration :)  
  
  ---
  
  ### Answer by username_2 on 2019-09-05. Score: 9
  
  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.
  
  [![enter image description here](https://i.sstatic.net/0rl0T.jpg)](https://i.sstatic.net/0rl0T.jpg)
  
  I also threw together a few more 1:2 ratio gear configurations for reference:
  
  [![enter image description here](https://i.sstatic.net/wOA9Y.jpg)](https://i.sstatic.net/wOA9Y.jpg)
  
  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.
  
  [![enter image description here](https://i.sstatic.net/cJv0c.jpg)](https://i.sstatic.net/cJv0c.jpg)
  
  Inspired by the answer that username_6 gave regarding Technic chain, I evidently proved myself wrong and came up with this.
  
  [![enter image description here](https://i.sstatic.net/DLBMV.jpg)](https://i.sstatic.net/DLBMV.jpg)
  
  
  ---
  
  ### Answer by username_4 on 2022-05-12. Score: 4
  
  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.
  [![Differential assembly with one input fixed](https://i.sstatic.net/USjoJ.png)](https://i.sstatic.net/USjoJ.png)
  
  > **Comments:**
  > **username_5**: Adding a picture of your solution would greatly improve your answer.  
  
  ---
  
  ### Answer by username_6 on 2019-09-03. Score: 2
  
  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:
  
  [![T8 and T16 gear connected with chain](https://i.sstatic.net/Dx4Og.png)](https://i.sstatic.net/Dx4Og.png)
  
  (I wasn't sure how to make a chain appear, nor axles, but I think it's clear.)
  
  > **Comments:**
  > **username_2**: 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.  
  > **username_7**: Welcome to Bricks.SE! A chain could be a possible solution, though it does have its limits as noted by @username_2 Thanks for your contribution!  
  > **username_6**: Agreed it has limitations, but no torque requirement of any kind was specified. Hopefully this helps someone.  
  > **username_2**: 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.  
  > **username_6**: No worries, I re-read my comment and would say the same about my own text :) I do realize now that my suggestion might be appropriate "for emergency use only"!  
  > **username_2**: You might find the last bit of my new answer of interest ;)  
  > **username_6**: Your latest bit is.... insane!  I think it's worth putting it in its own answer even.  
  > **username_2**: You are welcome to add it to your answer as an example if you would like, no worries on my part :)  
  
  ---
  
  