Technic gear ratio help

Huw

I'm working on a GBC module and want to turn a wheel made from four of the yellow quarter-rack things from the Bucket Wheel Excavator (https://brickset.com/parts/6151167/1-4-circle-gear-rack-11x11) exactly one eighth of the speed of another wheel.

So, I need some gearing. Trouble is, the yellow wheel has 140 teeth so 1/8th is 17.5 and of course there are no 17.5 teeth gear wheels so it can't be done simply.

I suspect I'm out of luck but thought I'd ask here in case anyone better at maths than I can work out how to do it with a combination of 8, 12, 16, 20, 24, 36 and 40 tooth gears.

Driving it by a wheel or pulley is also possible. Its diameter is 166mm so circumference is 521.5mm which thus would need a wheel of 20.75mm diameter to drive it at 1/8th of the speed.

TIA!

TechnicNick

Well that's awkward.... I keep getting seven and a half or eight and a third. I'll keep trying and post here if I find anything. It should be do-able!

theLEGOman

Remember different motors run at different speeds, so maybe you can use the different motors together with the gears to make it the right speed.

alaskaguy

Huw said:

I'm working on a GBC module and want to turn a wheel made from four of the yellow quarter-rack things from the Bucket Wheel Excavator (https://brickset.com/parts/6151167/1-4-circle-gear-rack-11x11) exactly one eighth of the speed of another wheel.

So, I need some gearing. Trouble is, the yellow wheel has 140 teeth so 1/8th is 17.5 and of course there are no 17.5 teeth gear wheels so it can't be done simply.

I suspect I'm out of luck but thought I'd ask here in case anyone better at maths than I can work out how to do it with a combination of 8, 12, 16, 20, 24, 36 and 40 tooth gears.

Driving it by a wheel or pulley is also possible. Its diameter is 166mm so circumference is 521.5mm which thus would need a wheel of 20.75mm diameter to drive it at 1/8th of the speed.

You want it to run output at 1/8th input, right?

So your key is to use the 8 and 16 tooth gears.  8:16 is 1/2, which is a multiple of 1/8th.  In fact, 1/2 is 4 * 1/8.

Rig it up so you've got a 8:16 gear set up. Then rig that to another 8:16 gear set up. Then rig THAT to another 8:16 gear set up. So now you're running (1/2)*(1/2)*(1/2). You know what (1/2)*(1/2)*(1/2) equals? Why yes, 1/8th!  Connect all that to your 140 tooth gear, and now the 140 is running at 1/8th of the input.

You don't have to use the 8 and 16 tooth gears. Those are just the smallest ones you can use.  You can use any combination that is 1:2. So that would be the 12 and 24 tooth gears or the 20 and 40 tooth gears.

TechnicNick

The worm gear is effectively a single tooth gear - that with an 8 tooth and you're done. 

Huw

Thanks. I had intended to drive the wheel via its teeth, in which case what you both propose would not work because for every revolution of the axle driving it the wheel would need to move a distance of 17.5 teeth and not simply 1/8th of the speed.

However having just read this article on the excellent website Brickset (!) there may be a way to drive it from the centre as you would a regular gear in which case either of those methods should work.

Back to the building table...

Paperballpark

Yes, you can drive it from the centre - I built a contraption when I was trying to use it for a Robot Wars robot (which I eventually scrapped).

I'm having a play with a spreadsheet to see if I can find some kind of way that normal gearing would work. There's certainly no easy way. The closest I've come so far is 8.10185 (going 8:40, then 24:8, 24:20 and 24:140. I'll keep trying...

Oops, just realised that 8.1 would make it that much faster than the other one...

CCC

Are you running both from the same motor? If not, the speeds are likely to vary eventually and so it will go out of sync at some stage.

I think most successful long running GBC machines tend to allow for misses / misalignment, so that if a ball misses the slot it is meant to go in, it will wait for the next one. That way, if out of sync it doesn't matter too much.

Paperballpark

^ Sometimes though, you need one action to align exactly with another action. Having it slightly out of sync will make the whole thing 'not work'.

Closest I've got so far is 8:1.06 - going 8:20, 40:36, 40:140.

Huw

Yes, from the same motor, and ^ yes, that is the case here.

Paperballpark

Oops, I meant 8:1.016

Paperballpark

If you cut a tooth off a 36-tooth gear, you could go 8:16, 35:140, and that would work... maybe ;)

Honestly, I'm quite surprised that Lego gave this gear 140 teeth. It just doesn't work as a multiple of any of the other gears. 4 more teeth on it would have worked beautifully.

Paperballpark

I've actually come to the conclusion that it can't be done. The main problem is that the 140 tooth gear isn't a multiple of any of the others (apart from 20-tooth, but a multiple of 7 is no use at all).

It just doesn't work. Nothing works, and all because it's 140-tooth. If it was 144-tooth it would be a piece of cake (8:16, 36:144).

I suspect this is a rare case of Lego not actually thinking a new part through properly.

Paperballpark

Bloody hell I've done it! There is an important caveat though.

The caveat is that I've used a gear which you don't list. Well actually, there's two different ones you could use, but I'm not sure if one of them would work or not.

You'd need either this old 14-tooth gear or this 28-tooth differential gear (which I'm not sure you could use, given it's not got an axle-hole)

For the 14-tooth, you'd go 40:16, 20:40, 14:140. For the 28-tooth, you'd go 20:16, 20:40, 28:140.

alaskaguy

Huw said:

Thanks. I had intended to drive the wheel via its teeth, in which case what you both propose would not work because for every revolution of the axle driving it the wheel would need to move a distance of 17.5 teeth and not simply 1/8th of the speed.

What I suggest does work if you drive it from the center.  You just connect the (1/8)^2 system to the final axle with the 140 tooth gear with a 16 tooth gear, making that last axle spin at 1/8 of the whole assembly at a 1:1 rate with the previous gear. 

CCC

I haven't got any parts with me to test this, but can you not set it up as a planetary gear style setup. If you use a 20 tooth driving ring and the 140 tooth outer ring, this will give a ratio of 8:1 (for planetary systems ratio is 1+ 140/20 = 8).


In fact, see Sariel's gear calculator http://gears.sariel.pl ... in the example there, red is 20 tooth and yellow is 140 tooth. Then instead of fixing the yellow ring and allowing the grey bar to be the rotator, fix the grey bar and the yellow ring will rotate at 1:8 speed of the red. I haven't got the parts with me to test what fits for the blue.

Paperballpark

^ I think the 140-tooth gear is just too large for that. I could be wrong, as I haven't got parts in front of me, but I don't think it'd work.

Anyway, surely it'd be a 7:1 ratio? For every 7 times you turned the 20-tooth gear, the 140-tooth gear would turn once.

CCC

Planetary systems are a bit tricky when it comes to gear ratios. It might be that you have to attach another ring to the "planets" to get the 1:8 ratio, holding the initial ring fixed. If you do, it is probably just easier to construct the frame and drive it from the centre.

Huw

Thanks, and well done, Jamie! I've rebuilt to drive from the centre but should that not work out I'll see if your plan does.

Paperballpark

Excellent! I look forward to seeing what you've done with the finished module! :) I'm currently working on two myself, with a third in the planning stages.

WJC1

Huw,

If the centre drive doesn't work and you did want to use the old 28 tooth differential like a regular gear (part 73071) as suggested by Paperballpark.  The easiest way to fix it to an axle is to insert the three internal bevel gears and slide a single axle through the whole assembly. 

You could have a drive train 140:28 to 16:8 to 16:8 to 16:40 giving a ratio of 5 x 2 x 2 x .4 = 8.

Will