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.

   

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.



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.

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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.


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.


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


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.


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.


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.


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.


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


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!

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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.

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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.


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.


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.

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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.

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.


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.


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.


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.

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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.

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 November 11, 20195 yr by Didumos69

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.

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?

This is a nice and easy to read article, thanks for sharing!

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 .

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)

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

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. 

1 minute ago, nerdsforprez said:

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

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.

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

 

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 .

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.

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 November 10, 20195 yr by Didumos69

31 minutes ago, Didumos69 said:

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 November 10, 20195 yr by nerdsforprez

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 November 10, 20195 yr by Didumos69

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.

Edited November 11, 20195 yr by Didumos69

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

Like one in the Chiron?

nope like this:

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 June 22, 20204 yr by SNIPE

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 November 11, 20195 yr by Didumos69

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.

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: 

 

Thank you @Didumos69 for the explanation! While I understand how gearboxes work, I have a problem that I've been trying to figure out for so long, and haven't found anything on the Internet about it. Most gear boxes I've built, whether new, used or mocs, (Porsche, Land Rover, Lambo, other's mocs, etc.), have had extreme friction problems with higher speeds, in ONLY ONE direction. The friction ends up being so bad, that the whole drivetrain binds up and barely moves. For example, my Lambo works fine, except for pushing it backwards in 7th gear. And ONLY while pushing these in one direction does this happen. It can't be a bracing problem, as the Lambo and some of the other's mocs braced their gearboxes well enough, and it still happened. This has happened to me way too many times with Technic transmissions and I want to figure it out. Keep in mind that with all these, I've built them twice, gave gears space, and swapped parts (Like the new and old bevel gears), AND even new parts - like the Lambo's - wouldn't make a difference. Now, upon observing these problems, I've watered everything down to the 24t gear with the 8t gear. As soon as this combination is added, whether a sinple 4-speed or 8-speed, the gearboxes suffer in one direction. It's a very weird phenomenon and I thought you - being somewhat of an expert at Lego Technic - could help me figure out this issue. 

3 hours ago, Filthy Fox said:

Thank you @Didumos69 for the explanation! While I understand how gearboxes work, I have a problem that I've been trying to figure out for so long, and haven't found anything on the Internet about it. Most gear boxes I've built, whether new, used or mocs, (Porsche, Land Rover, Lambo, other's mocs, etc.), have had extreme friction problems with higher speeds, in ONLY ONE direction. The friction ends up being so bad, that the whole drivetrain binds up and barely moves. For example, my Lambo works fine, except for pushing it backwards in 7th gear. And ONLY while pushing these in one direction does this happen. It can't be a bracing problem, as the Lambo and some of the other's mocs braced their gearboxes well enough, and it still happened. This has happened to me way too many times with Technic transmissions and I want to figure it out. Keep in mind that with all these, I've built them twice, gave gears space, and swapped parts (Like the new and old bevel gears), AND even new parts - like the Lambo's - wouldn't make a difference. Now, upon observing these problems, I've watered everything down to the 24t gear with the 8t gear. As soon as this combination is added, whether a sinple 4-speed or 8-speed, the gearboxes suffer in one direction. It's a very weird phenomenon and I thought you - being somewhat of an expert at Lego Technic - could help me figure out this issue. 

This is a tricky issue that I have come across in many gearbox designs. I too couldn't find any literature on it and it took a while to figure out. The problem really is too many idler gears transmitting torque on too many axles, which is a problem that is inherent to the appalling design of Lego gearboxes. I understand the problem but it's kinda hard to fully explain.

Lets say we are using the gearbox in the above image in a manual model. When in 1st gear the torque generated by the wheels when you push the model forwards comes in to gear 1, is transferred up to gear 2 and so on till we get to gear 7 which drives the engine. Because Technic has no proper bearings friction can be a real issue in their inefficiently designed gearboxes. Even though this is a fairly simple example of a 6 speed gearbox by Technic standards, the path of torque still has to pass through 6 gears rotating on 4 axles, where as a real life gearbox would only have 2 gears on 2 axles. This is the main issue however, in many cases the gearbox doesn't lock up completely and can still be forced to rotate and most people won't notice how hideously inefficient TLGs gearboxes are, until the Sian breaks an 8t gear of course!

However, in many cases where people want to design their own gearboxes they run into the problem of the gearbox locking up completely. In the case of this gearbox example it locks up in first because of gear 2 (that's the gear with the number 2 on it, not second gear), which is transmitting torque to gear 3, and is also spinning on an axle that is geared to spin faster, and it is also not meshed with a gear to it's right side when looking up at it from this angle. This is significant because when gear one rotates in a direction that pushes gear 2 towards gear 3, the equal and opposite reaction generated from gear 2 trying to drive gear 3 pushes them back apart, so those two forces somewhat cancel out and gear 2 will rotate on it's axle (though with a lot of friction). However if you rotate gear 1 in the other direction, such that gear 2 is being forced away from gear 3, now the two forces add up and create even more friction between gear 2 and it's axle. Now you have multiple points of friction adding up and in this case this gearbox will lock up. The friction has become so great that it is enough to stop it turning, and the more torque you apply to try to force the gears to turn, the more the friction increases, like a Chinese finger trap I suppose, or more accurately like trying to reverse drive a Technic worm gear. In real life you can indeed back drive worm gears, but with Lego you cannot simply because the slope angle of the worm is too shallow to overcome the friction of the sliding plastic.

So this is why Technic gearboxes lock up. Too many shafts, too many gears and too much needless complication when they could just do it like a real car gearbox. These gearboxes ALL have way too much friction to the point where small oversights as described above cause it to lock up entirely. There are work arounds, like redesigning your gearbox to re-route the torque paths so that they avoid these problem areas in all gears in both directions, but this usually leads to even larger and even more convoluted gearboxes, and how a child is supposed to problem solve all that and then redesign it to come up with a solution I don't really know.

 

Edited June 21, 20204 yr by allanp

@allanp Thank you for your extensive response! Yeah, it's too bad that Lego gear parts aren't designed very optimally. The gearbox in your image is actually almost the exact same one I just built recently (Sheepo's Manual Jeep Rubicon), and was having the "only works in one direction problem," except there was a 8t gear with the two 24t, and had a high/low selector. I also wonder why many Technic fans don't complain about the "good" transmissions in many mocs grinding then. (The Pimp Up my Land Rover mod didn't work for me and Sariel and Racing Brick didn't complain about too much friction in the Sian's drivetrain.) Maybe they didn't test push the car enough? And maybe it was because I used some used parts for the Rover mod. The biggest question I still have though, is why these big gearboxes I've built only work in one direction, but not the other. Because the highest speeds work perfectly for me pushing it one direction, but not the other. (Keep in mind this has only happened to me with transmissions 4 speeds or more).

16 hours ago, allanp said:

So this is why Technic gearboxes lock up. Too many shafts, too many gears and too much needless complication when they could just do it like a real car gearbox. These gearboxes ALL have way too much friction to the point where small oversights as described above cause it to lock up entirely. There are work arounds, like redesigning your gearbox to re-route the torque paths so that they avoid these problem areas in all gears in both directions, but this usually leads to even larger and even more convoluted gearboxes, and how a child is supposed to problem solve all that and then redesign it to come up with a solution I don't really know.

Thanks @allanp for this elaborate explanation. It makes total sense to me and confirms my own line of reasoning. This is why I always avoid idler gears transmitting torque. In my designs (except for some mods for Bugatti and Lamborghini) clutch gears are either engaged with a driving ring or they are just making dummy rotations and not transmitting torque. For instance in this 8-speed transmission tunnel. The gearboxes of the Bugatti and the Lamborghini have the high-low gearbox and the 4-speed gearbox layed out next to each other, with several idler gears transmitting torque from one gearbox to the other. In this 8-speed tunnel I layed out the same gearboxes longitudinally which allows them to be connected without using torque transmitting idler gears.

Edited June 22, 20204 yr by Didumos69

@Filthy Fox, @allanp, the stock Lamborghini gearbox has 4 idlers transmitting torque, of which one is very suspicious. I really don't understand why they made it so complex, because the same ratios can be obtained with much less gear meshes.

39 minutes ago, Didumos69 said:

@Filthy Fox, @allanp, the stock Lamborghini gearbox has 4 idlers transmitting torque, of which one is very suspicious. I really don't understand why they made it so complex, because the same ratios can be obtained with much less gear meshes.

Yeah, it's pretty bad. On 7th gear pushing backwards, the engine can't even move. And I made sure everything had space. I guess I'll just have to accept that any Lego transmission will not work in high gears unless it's designed properly??

Do you know any gearboxes that actually work smoothly on all gears? I would like to experience it lmao.

46 minutes ago, Filthy Fox said:

Do you know any gearboxes that actually work smoothly on all gears? I would like to experience it lmao.

One that I'm pretty sure about is this 4-speed (without idlers transmitting torque). Instructions are in the link:

And the one discussed in this topic should also work properly.

On 11/10/2019 at 12:14 AM, Didumos69 said:

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.

 

@Didumos69 Thanks! I was following your Rugged Supercar project for years,  but I never have had enough dog hone pieces (I don't wish to take apart my Sian). sill still don't have enough for your gearbox

Could I also post a video of the problem I'm having?

Edited June 22, 20204 yr by Filthy Fox