[HELP] Gear Reduction Ratio

[Lego Otaku]

For conventional gears like 8t to 24t it's easy to figure out the ratio (1:3 BTW) but when I use a worm gear how do I figure the ratio? It seems that one full revolution of the worm gear = one tooth moved. So if I used 8t gear, would 8:1 be correct, that is 8 revolutions on the worm gear to one turn of 8t?

Or am I wrong? If so, help me?

[jantjeuh]

8:1 is correct.

[allanp]

That's correct. A Lego worm gear has one tooth. Use it with a 24t gear and you have a 24:1 ratio, with a 40t gear you have a 40:1 ratio and so on. In real life there are some worm gears that have more than one tooth.

[Lego Otaku]

Ok so with this theory I put together in LDD, and assume the M motor is about 275 RPM, the turntable would be at about 11 RPM (5 seconds per turn)

M motor drives the worm gear, the worm gear turns the 8t gear (reduced to about 34 RPM)

The 8t gear drives the shaft that turns another 8t gear. There's 2 planar 8t gears that revolves and turns around the center 8tg, which should be running at the same rate inside the technic turntable. The planar gears turns the technic turntable (24t) and that turns the turntable at about 11 rpm.

http://www.brickshelf.com/gallery/Lego-0taku/ldd/turntable.lxf

Am I right with math so far? I left school 20 years ago and I rarely need to use any math other than adding and subtacting.

Also if you can check my LDD, any problem I might run into with that design? Ignore the loose parts floating around, it's an experiment in design to see if I can build something.

[Junpei]

That's correct. A Lego worm gear has one tooth. Use it with a 24t gear and you have a 24:1 ratio, with a 40t gear you have a 40:1 ratio and so on. In real life there are some worm gears that have more than one tooth.

A worm gear with more than one tooth?

I can't check your LDD file, but it sounds like it should be correct.

[DrJB]

In your LXF file, you're using a 'planetary' gear system. The center 8t gear will spin at 1/8 the speed of the worm-gear. However, there is no way to calculate the exact RPMs of both the turntable and the 3L liftarm (under the turntable) that is holding the 2 planetary 8t gears. Which one will spin and how fast depends on the load on the two and how much friction is present. If however you fix the 3L liftarm (prevent it from rotating), then the turntable will spin at 1/3 the RPM of the center 8t gear. This is because the turntable has 24 teeth on its inner gear, and 24/8=3. Thus, still immobilizing the 3L liftarm, the turntable will spin at 1/3×1/8=1/24 times the RPM of the worm gear. Hope this helps, else, ask again.

[Lego Otaku]

I see what you mean, I fixed the planetary gears so the turntable will turn as expected.

Revised version: http://www.brickshel...rntable2.lxf I also changed the turntable and got a few more parts added. Something went out of alignment because now I can't change much on the bottom, and the 3 walls won't line up properly so I can't finish the 3rd hinged piece. LDD can be a tad touchy with alignment and it can't gracefully shift pieces to make everything fit properly. The real thing, if I ever go that far, should fit better.

I haven't quite figured how to better secure the center walls since LEGO didn't make many pieces that comes in 60-degree angle. if you have an idea how to secure better, LMK please. LDD may not care about gravity but if I build the real one, unsupported side may sag a bit.

If you guessed my moc looked like a carnival ride, give yourself a pat on your back. While someone else did the ride: http://www.eurobrick...showtopic=46430 mine is more minimal and resembles more the version designed for easy transport (ie less lights, doesn't swing up and down, etc) and not the more elegant version found at permanent location like someone else's LEGO carnival ride. Beside it's fun to experiment

Edited October 21, 2013 by Lego Otaku

[DrJB]

It is a bit better now, but we have another problem.

1. The bottom part (dark gray) of the turntable is fixed, and thus it will NOT rotate.

2. When the center 8t gear rotates a speed X, the 3L liftarm will rotate with speed X/4.

3. Because the 3L liftarm is secured to the top part (black) of the turntable, such part will also rotate with speed X/4.

4. Thus, we have the longvertical center axle that will rotate at X, and the 'superstruture' (aka yellw bricks) will rotate with speed X/4

5. The bottom 3 horizontal axles will NOT rotate (about their own axis)

6. However, because of the speed difference in #4 above, the mid 3-axis (at 120 degrees) will rotate about their own axis with speed (X-X/4)×Gear_Ratio = (3X/4)×12/8 = 9X/8.

7. All of this is fine, assuming this is what you intended to do ... but there is a small hiccup ...

8. Because the 3L liftarm now rotates about the vertical axis, it will INTERFERE with the worm gear.

9. The fix here should be simple, all you need to do is lower the worm gear (+8t gear) by one 1L.

Let us know how this evolves ... the contraption looks nice.,. and playing with planetaries is 'never' trivial.

[jantjeuh]

In real life there are some worm gears that have more than one tooth.

I'm curious about this as well, got some more information?

[Lego Otaku]

It is a bit better now, but we have another problem.

1. The bottom part (dark gray) of the turntable is fixed, and thus it will NOT rotate.

2. When the center 8t gear rotates a speed X, the 3L liftarm will rotate with speed X/4.

3. Because the 3L liftarm is secured to the top part (black) of the turntable, such part will also rotate with speed X/4.

4. Thus, we have the longvertical center axle that will rotate at X, and the 'superstruture' (aka yellw bricks) will rotate with speed X/4

5. The bottom 3 horizontal axles will NOT rotate (about their own axis)

6. However, because of the speed difference in #4 above, the mid 3-axis (at 120 degrees) will rotate about their own axis with speed (X-X/4)×Gear_Ratio = (3X/4)×12/8 = 9X/8.

7. All of this is fine, assuming this is what you intended to do ... but there is a small hiccup ...

8. Because the 3L liftarm now rotates about the vertical axis, it will INTERFERE with the worm gear.

9. The fix here should be simple, all you need to do is lower the worm gear (+8t gear) by one 1L.

Let us know how this evolves ... the contraption looks nice.,. and playing with planetaries is 'never' trivial.

In the yellow brick structure, the horizontal rods are supposed to rotate the same rate as the yellow brick. The middle horizontal rods are connected via gear to the center rod to get different rotational speed. The design is that there will be 3 sets of rotating seats that will be held in place by bottom and top horizontal support while middle support would be the one to spin the seats.

Didn't notice that 3L would hit the worm gear. I'd have to tweak it a bit.

[JTS]

A worm gear with more than one tooth?

I'm curious about this as well, got some more information?

They are called Multiple Thread Worms. The one in the image above is a 3z MTW, meaning it has three threads (teeth).

The pro of this is a 30:1 speed reduction ratio now becomes 10:1

The con is that due to the "steepness" of the threads, it requires more torque for the threads to turn the teeth of the meshing gear (becoming more inneficiant)

So if a 3z MTW meshes with a 30z gear, the theoretical increase in torque would be 10:1, but in reality is much less than this.

The applications of MTWs in real life is when a rotation reduction or torque increase is needed in the drivetrain at 90 degrees, but cannot be achieved by altering the speed/.torque of the input or changing the size of the meshing gears.

For example in a flour mill powered by a waterwheel, the speed of the waterwheel cannot be changed and the meshing gears need to be as large as possible to produce as much flour as possible. By using an MTW, the speed of the meshing gear is increased at the cost of efficiency.

I hope this helps

[zux]

Just to help JTS's explanation.

Single threaded worm has only one beginning and finishing "contacts" at the end of worm gear like LEGO ones have.

Multiple threaded worms are easy to distinguish as they have more than one starting point, like you can see here and here.

[Lego Otaku]

And FYI LEGO worm gear is just one thread. I don't think any variation of worm gear (ie part of steering rack) has more than one thread.

http://www.brickshelf.com/gallery/Lego-0taku/ldd/turntable3.lxf

Updated mine with some changes. I had to rebuild the base as something was out of alignment and not letting me add or change part. The blue plate is there to make sure nothing shifted behind my back! Also I did away with 3L liftarm and secured planetary gears in a different way so the worm gear has clearance, and added a few more parts to get an idea of what the whole thing would look. i did find another issue: the seats would be hitting the yellow structure so I'd need to extend the arms a bit and move

if I got the gearing right, the seat assemblies should be rotating at about 2/3 the RPM of the center shaft. I could change gears to get different speed but I need to build this first since LDD can't animate or rotate multiple gears.

[1963maniac]

Guys & Dolls, I've produced a gear ratio chart. I hope there are no errors.

LEGO Gear Ratio Table (rounded up to the next hundredth)

Follower gears along the top driver gears along the side

# of teeth

1

8

12

14

16

20

24

28

36

40

56

1

1:1

1:8

1:12

1:14

1:16

1:20

1:24

1:28

1:36

1:40

1:56

8

8:1

1:1

1:1.5

1:1.75

1:2

1:2.5

1:3

1:3.5

1:4.5

1:5

1:7

12

12:1

1.5:1

1:1

1:1.16

1:1.33

1:1.67

1:2

1:2.33

1:3

1:3.33

1:4.67

14

14:1

1.75:1

1.16:1

1:1

1:1.14

1:1.42

1:1.71

1:2

1:2.57

1:2.86

1:4

16

16:1

2:1

1.33:1

1.14:1

1:1

1:1.25

1:1.5

1:1.75

1:2.25

1:2.5

1:3.5

20

20:1

2.5:1

1.67:1

1.42:1

1.25:1

1:1

1:1.2

1:1.4

1:1.8

1:2

1:2.8

24

24:1

3:1

2:1

1.71:1

1.5:1

1.2:1

1:1

1:1.17

1:1.55

1:1.67

1:2.33

28

28:1

3.5:1

2.33:1

2:1

1.75:1

1.4:1

1.17:1

1:1

1:1.29

1:1.43

1:2

36

36:1

4.5:1

3:1

2.57:1

2.25:1

1.8:1

1.55:1

1.29:1

1:1

1:1.11

1:1.55

40

40:1

5:1

3.33:1

2.86:1

2.5:1

2:1

1.67:1

1.43:1

1.11:1

1:1

1:1.4

56

56:1

7:1

4.67:1

4:1

3.5:1

2.8:1

2.33:1

2:1

1.55:1

1.4:1

1:1

Guys & Dolls, I've produced a gear ratio chart. I hope there are no errors.

LEGO Gear Ratio Table (rounded up to the next hundredth)

Follower gears along the top driver gears along the side

# of teeth

1

8

12

14

16

20

24

28

36

40

56

1

1:1

1:8

1:12

1:14

1:16

1:20

1:24

1:28

1:36

1:40

1:56

8

8:1

1:1

1:1.5

1:1.75

1:2

1:2.5

1:3

1:3.5

1:4.5

1:5

1:7

12

12:1

1.5:1

1:1

1:1.16

1:1.33

1:1.67

1:2

1:2.33

1:3

1:3.33

1:4.67

14

14:1

1.75:1

1.16:1

1:1

1:1.14

1:1.42

1:1.71

1:2

1:2.57

1:2.86

1:4

16

16:1

2:1

1.33:1

1.14:1

1:1

1:1.25

1:1.5

1:1.75

1:2.25

1:2.5

1:3.5

20

20:1

2.5:1

1.67:1

1.42:1

1.25:1

1:1

1:1.2

1:1.4

1:1.8

1:2

1:2.8

24

24:1

3:1

2:1

1.71:1

1.5:1

1.2:1

1:1

1:1.17

1:1.55

1:1.67

1:2.33

28

28:1

3.5:1

2.33:1

2:1

1.75:1

1.4:1

1.17:1

1:1

1:1.29

1:1.43

1:2

36

36:1

4.5:1

3:1

2.57:1

2.25:1

1.8:1

1.55:1

1.29:1

1:1

1:1.11

1:1.55

40

40:1

5:1

3.33:1

2.86:1

2.5:1

2:1

1.67:1

1.43:1

1.11:1

1:1

1:1.4

56

56:1

7:1

4.67:1

4:1

3.5:1

2.8:1

2.33:1

2:1

1.55:1

1.4:1

1:1

Sorry, this didn't post properly.

[1963maniac]

Last try:...

[DrJB]

much much better ... I was wondering what that series of numbers meant ...

You can go back, edit your post, and modify it. No need to repost.

Edited February 26, 2014 by DrJB

[legolijntje]

You can also use Sariel's online tool to calculate gear ratio's, the speeds with different motors and the placement of gears

It's nice to see it in one big table though, if you need a certain speed, you can find it very quickly.