Didumos69

Understanding LEGO 4-speed sequential gearboxes

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I finally took the time to write down the things I have come to understand with regard to LEGO 4-speed sequential gearboxes. I am receiving many questions about gearboxes and I hope these understandings can help you reason about a gearbox layout while you're building one or trying to design one. I hope this also answers a question I received from @nerdsforprez more than a year ago, which I did not answer yet.

Gearbox layout
Let's take a look at this 4-speed sequential gearbox layout. Black is input, red is output and orange is control.

800x450.jpg 800x450.jpg 800x450.jpg 800x450.jpg

The main input is divided over a high input (black) with high input ratio and a low input (white) with low input ratio. The high input ratio is 1:1 (via a 12:12 mash) and the low input ratio is 1:2 (via a 8:16 mash). This makes for a combined ratio of (1:1) : (1:2) = 2:1 between the high and low inputs. I will refer to this ratio as the primary ratio. In fact this ratio is the ratio between the two driving rings.

Both driving rings have a high output (green) with high output ratio and a low output (yellow) with low output ratio. For both driving rings, the high output ratio is 1:1 * 2:1 = 2:1 (via a 16:16 mash and a 16:8 mash) and the low output ratio is 5:3 * 1:2 = 5:6 (via a 20:12 mash and a 8:16 mash). This makes for a combined ratio of (2:1) : (5:6) = 12:5 between the high and low outputs of each driving ring. I will refer to these ratios as the secondary ratios.

Rotary catch and quadrants
Even though I will explain things in terms of the gearbox layout described above, the first understanding I want to address, applies to practically all 4-speed sequential gearboxes with 2 driving rings. Let's take a look at the rotary catch and driving rings from above and divide the layout into four quadrants. Each quadrant represents one of the four gears of the 4-speed gearbox. When we turn the rotary catch clockwise (seen from the left) with 90-degree steps, it will always make the following path through the four quadrants.

400x222.jpg

From the path the rotary catch draws, we can see that it toggles from one driving ring to the other driving ring for every 90-degree step. So if we want to obtain a useful gear sequence (either a 1-2-3-4 sequence or a 4-3-2-1 sequence) along that path, we need to tie gears 1 and 3 to one driving ring and gears 2 and 4 to the other driving ring. Otherwise the rotary catch can never 'toggle' between subsequent gears.

Quote

If we want to obtain a useful gear sequence with a rotary catch making 90-degree steps, then we need to tie gears 1 and 3 to one driving ring and gears 2 and 4 to the other driving ring.

Now let's take a look at all distributions of the four gears over the four quadrants that meet this requirement.

400x222.jpg
Starting top-left, this will produce a 1-4-3-2 sequence. Repeating the sequence will give 1-4-3-2-1-4-3-2-etc., which effectively boils down to a 4-3-2-1 sequence.

400x222.jpg
Starting top-left, this will produce a 1-2-3-4 sequence.

400x222.jpg
Starting top-left, this will produce a 3-4-1-2 sequence. Repeating the sequence will give 3-4-1-2-3-4-1-2-etc., which effectively boils down to a 1-2-3-4 sequence.

400x222.jpg
Starting top-left, this will produce a 3-2-1-4 sequence. Repeating the sequence will give 3-2-1-4-3-2-1-4-etc., which effectively boils down to a 4-3-2-1 sequence.

400x222.jpg
Starting top-left, this will produce a 2-3-4-1 sequence. Repeating the sequence will give 2-3-4-1-2-3-4-1-etc., which effectively boils down to a 1-2-3-4 sequence.

400x222.jpg
Starting top-left, this will produce a 2-1-4-3 sequence. Repeating the sequence will give 2-1-4-3-2-1-4-3-etc., which effectively boils down to a 4-3-2-1 sequence.

400x222.jpg
Starting top-left, this will produce a 4-3-2-1 sequence.

400x222.jpg
Starting top-left, this will produce a 4-1-2-3 sequence. Repeating the sequence will give 4-1-2-3-4-1-2-3-etc., which effectively boils down to a 1-2-3-4 sequence.

Surprisingly, every distribution that meets the requirement, will produce either a 1-2-3-4 sequence or a 4-3-2-1 sequence. What this tells us, is that it's enough to tie gears 1 and 3 to one driving ring and gears 2 and 4 to the other driving ring, to obtain a useful gear sequence. Nothing else matters!

Quote

If we want to obtain a useful gear sequence with a rotary catch making 90-degree steps, it's enough to tie gears 1 and 3 to one driving ring and gears 2 and 4 to the other driving ring.

Primary ratio vs. secondary ratios
The next understanding I want to address, concerns the relation between the primary ratio (the ratio between the high and low input) and the secondary ratios (the ratios between the high and low outputs of both driving rings). We have already seen that in the gearbox layout at hand, the high and low output ratios are the same for both driving rings.

One thing we can say about 4-speed gearboxes in general, is that the ratios between gears 1 and 3 and between gears 2 and 4 need to make a bigger difference than the ratios between gear 1 and 2 and between 3 and 4. Now when we take into account that gears 1 and 3 need to be tied to one driving ring and gears 2 and 4 need to be tied to the other driving ring, and we use the same high and low output ratios for both driving rings, we can say that the secondary ratios, which constitute the ratios between gears 1 and 3 and between gears 2 and 4, need to be bigger than the primary ratio, which constitutes the ratios between gears 1 and 2 and between gears 3 and 4.

Quote

If we want to obtain a useful gear sequence with a rotary catch making 90-degree turns and we use the same high and low output ratios for both driving rings, then the secondary ratios need to be bigger than the primary ratio.

The gearbox discussed in the beginning of this post has a primary ratio of 2:1 and secondary ratios of 12:5, so it meets the above requirement. Check!

Swapping and reversing
If we go back to the distributions we listed above, we can see that half of them generate a 1-2-3-4 sequence and half of them generate a 4-3-2-1 sequence. When we study them more thoroughly, we can see that all 1-2-3-4 distributions have a horizontally flipped counterpart with a 4-3-2-1 sequence. In other words, if we flip the distribution horizontally, we reverse the gear sequence.

400x222.jpg400x222.jpg
Example: Swapping 1-3 with 2-4 in a 4-3-2-1 sequence produces a 3-4-1-2 sequence. Repeating the sequence will give 3-4-1-2-3-4-1-2-etc., which effectively boils down to 1-2-3-4.

400x222.jpg400x222.jpg
Example: Swapping 1-3 with 4-2 in a 1-2-3-4 sequence produces a 4-3-2-1 sequence.

What this tells us, is that when we mirror the gearbox layout left-to-right (top-down in the quadrants), which boils down to swapping the high and low inputs, the effect is that we reverse the gear sequence.

Quote

If we want to obtain a correct gear sequence with a rotary catch making 90-degree turns, then we can reverse the gear sequence by swapping the high and low inputs.


800x450.jpg

Practical value: If you find yourself in a situation where you want to swap the upshifting and downshifting directions, simply swap the high and low inputs, like in the image above.

Finally, if we take one more look at the gear distributions above, we can see that when we swap gears 1 and 3 or gears 2 and 4 in any distribution, we get a distribution with the reversed order. 1-2-3-4 will produce 4-3-2-1 and 4-3-2-1 will produce 1-2-3-4. When we swap both gears 1 and 3, and gears 2 and 4, we reverse the order twice and get again the same order.

400x222.jpg400x222.jpg
Example: Swapping 1 and 3 in a 1-2-3-4 sequence produces a 3-2-1-4 sequence. Repeating the sequence will produce 3-2-1-4-3-2-1-4, which effectively boils down to a 4-3-2-1 sequence.

400x222.jpg400x222.jpg
Example: Swapping 2 and 4 in a 1-2-3-4 sequence produces a 1-4-3-2 sequence. Repeating the sequence will produce 1-4-3-2-1-4-3-2, which effectively boils down to a 4-3-2-1 sequence.

400x222.jpg400x222.jpg
Example: Swapping 1 and 3, and 2 and 4 in a 1-2-3-4 sequence produces a 3-4-1-2 sequence. Repeating the sequence produces 3-4-1-2-3-4-1-2, which effectively boils down to a 1-2-3-4 sequence.

What this tells us, is that when we mirror one side of the gearbox front-to-back (swap the high and low outputs of one driving ring), we will reverse the gear sequence. When we mirror both sides front-to-back (swap the high and low outputs of both driving rings), we won't affect the gear sequence.

Quote

If we want to obtain a correct gear sequence with a rotary catch making 90-degree turns, then we can reverse the gear sequence by swapping the high and low outputs of one driving ring. When we swap the high and low outputs of both outputs, the gear sequence will remain unaffected.


800x450.jpg

Practical value: If it's more convenient for the rest of your build to mirror your gearbox layout front-to-back, like in the image above, you can do so without any consequences. If it's more convenient to mirror only the left side or the right side of your gearbox layout, you need to also swap the upshifting and downshifting directions.

If you want to inspect the gearbox used in this post in 3D, here it is in Stud.io format and here in LDD format.

Edited by Didumos69

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I wonder if we can stack two "single orange shifter & two clutch ring" assemblies on too of one another to make a compact 8 speed gearbox.

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9 hours ago, SNIPE said:

I wonder if we can stack two "single orange shifter & two clutch ring" assemblies on too of one another to make a compact 8 speed gearbox.

Like one in the Chiron?

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The shown scheme might appear clear in its lucidity as the concept. But it´s not very practical to install into a chassis, I mean you need to use halfstud setups in both dimensions horizontal and vertical. Understanding of a 4-speed gearbox usually might be what beginners are looking for to instantly build something around it. The good old traditional 4-speed with changeover catches or the „first half“ of the Bugatti gearbox seem to be more suitable for that. Anyway, very nice explanation :thumbup:.

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That's a really good write-up, thank you very much!

On a side note: i personally don't like to use 8-tooth gears in drivetrains as they seem to add friction.
(unfortunately i couldn't use my testing stand to test this)

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Very useful, and yes, this is in response to a question I had about a year ago :laugh:

I took time this morning to really read this.  Thank you for taking the time to do this.  I think I understand everything written, but honestly additional help from the community would be useful for dolts like me.  I have no formal training in this stuff and gearboxes still throw me.  Simple ones - no problem.  But more complex ones I still have difficulty in following the path in which power is transferred. 

Take for example 42110 gearbox.  I am building it now.  The four speed gear box in the rear is simple enough, and I understand how the primary stage of the gearbox (much like @Didumos69's examples here) meshes with the rear four speed gearbox to produce additional gears.  But the forward versus rear indicator throws me.  It almost seems like there are two inputs, and I am not sure how that works. 

Wondering if there are any good resources out there that show the path in which power is transferred through more complex gearboxes.  I know there are many resources out there for real gearboxes but these are simple enough.  In real life there are enough different sizes of gears so that they don't need to be so needlessly complex.  One would think that as long as one has the principles mastered one could apply them to understand any gearbox; yet this is not the case for me.  I can master most, but then comes along 42110 and I am lost. 

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1 minute ago, nerdsforprez said:

Very useful, and yes, this is in response to a question I had about a year ago :laugh:

I took time this morning to really read this.  Thank you for taking the time to do this.  I think I understand everything written, but honestly additional help from the community would be useful for dolts like me.  I have no formal training in this stuff and gearboxes still throw me.  Simple ones - no problem.  But more complex ones I still have difficulty in following the path in which power is transferred. 

Take for example 42110 gearbox.  I am building it now.  The four speed gear box in the rear is simple enough, and I understand how the primary stage of the gearbox (much like @Didumos69's examples here) meshes with the rear four speed gearbox to produce additional gears.  But the forward versus rear indicator throws me.  It almost seems like there are two inputs, and I am not sure how that works. 

Wondering if there are any good resources out there that show the path in which power is transferred through more complex gearboxes.  I know there are many resources out there for real gearboxes but these are simple enough.  In real life there are enough different sizes of gears so that they don't need to be so needlessly complex.  One would think that as long as one has the principles mastered one could apply them to understand any gearbox; yet this is not the case for me.  I can master most, but then comes along 42110 and I am lost. 

What I would suggest is to replicate the gearbox in LDD or such program and color all the gears in different colors to help visualize how the power is transfered.

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1 hour ago, brunojj1 said:

The shown scheme might appear clear in its lucidity as the concept. But it´s not very practical to install into a chassis, I mean you need to use halfstud setups in both dimensions horizontal and vertical. Understanding of a 4-speed gearbox usually might be what beginners are looking for to instantly build something around it. The good old traditional 4-speed with changeover catches or the „first half“ of the Bugatti gearbox seem to be more suitable for that. Anyway, very nice explanation :thumbup:.

That would have been an easier layout to play with, I agree. What's important though, is that I could have used practically any 4-speed sequential gearbox for this explanation. Anyway, perhaps it is useful if I share the whole gearbox, including the gearbox structure. Exploring it in 3D could be very useful, as @Zerobricks suggested. Here it is in Stud.io format and here in LDD format.

800x450.jpg800x450.jpg800x450.jpg

14 minutes ago, nerdsforprez said:

one would have to first know how power is transferred to color the gears.... no?

 

When looking at it in 3D you can reason how transfer flows by following the engaged clutch gear. Try to reason in which of the 4 gears the gearbox depicted above is.

Edited by Didumos69

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31 minutes ago, Didumos69 said:

800x450.jpg

When looking at it in 3D you can reason how transfer flows by following the engaged clutch gear. Try to reason in which of the 4 gears the gearbox depicted above is.

Upper left.  Yea, I get that much, but for some reason, in complex gearboxes it becomes much more difficult for me.  Perhaps I just need to try the advice though....

Edited by nerdsforprez

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16 minutes ago, nerdsforprez said:

Upper left.

It's in third gear. Transfer follows the low input, so it is in either gear 1 or 3 and it follows the high output, so it is in gear 3.

16 minutes ago, nerdsforprez said:

Perhaps I just need to try the advice though....

And color the axles as you go, to persist your mental image...

Edited by Didumos69

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18 hours ago, brunojj1 said:

The good old traditional 4-speed with changeover catches or the „first half“ of the Bugatti gearbox seem to be more suitable for that.

Here's the 4-speed half of the Bugatti gearbox, with a few simplifications I did for @jb70's pimped up Bugatti. Black is input, red is output and orange is control. Though I don't like it's modest ratios, this is the most simple gearbox you can make with the orange rotary catch and can thus serve as a very good first study subject. LDD-file here and Stud.io file here.

EDIT: In relation to the OP: Why are the ratios of this simple gearbox modest? To keep it simple there are no auxiliary output axles, the clutch gears mash with the main output directly. So having different output ratios is solely based on the use of different clutch gears. Therefore the ratio between the output ratios (= the secondary ratio) is in this case only 5:3, for each driving ring. Based on the OP we know that the secondary ratios need to be bigger than the primary ratio to obtain a useful gear sequence (1-2-3-4 or 4-3-2-1), so the ratio between the input ratios (= primary ratio) needs to be even smaller than 5:3. In this case the input ratios are 1:1 (via a 8:8 mash) and 4:5 (via a 16:20 mash), so the primary ratio is (1:1) : (4:5) = 5:4, indeed smaller than the secondary ratios.

800x450.jpg800x450.jpg

Edited by Didumos69

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On 11/10/2019 at 10:15 AM, Zerobricks said:

Like one in the Chiron?

nope like this:800x450.jpg But another of these and flipped so both of the orange shifters are on the outside. Then remove any un needes gears and link the two orange shifters using knob wheels.

Edited by SNIPE

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1 hour ago, SNIPE said:

But another of these and flipped so both of the orange shifters are on the outside. Then remove any un needes gears and link the two orange shifters using knob wheels.

You could do that, but you can hardly say it would be compact. Also, the added gearbox would need to add a tertiary ratio that is even bigger than the secondary ratio, so it can not just be a reduced version of the 4-speed depicted above.

Edited by Didumos69

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Thanks @Didumos69 for this detailed explanations. I recently got into the https://www.eurobricks.com/forum/index.php?/forums/topic/162031-gearboxes-with-new-orange-selector-20z-clutch-gear/ topic and built all the gearboxes you designed and posted the lxf.

The one explained here took me a full day to understand (I stood on page 2 till i understood how it works, silly me the explanation were on the next pages). and build it 5 times (one complete, and 1 for each gear sequence)

I am still unclear on how the central differential gearbox works...

I was looking for a "tool" that would simply highlight the gears/axles while i rotate them, but i could not find such thing.

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Thanks Didumos69 for this post!! I think my whole problem of not understanding Lego gearboxes/ transmissions might have to do with understanding synchronized versus unsynchronized. This post helped a lot: 

 

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