There are a total of 100 gears in this machine, with each gear pair having a reduction of 1 to 10, so for every 10 revolutions, the gear next in line makes one rotation, and so forth. So for the last gear to spin one time, the first has to revolve a googol number of times.
My question is, will the last gear start turning as soon as the first one does?
No, right? Because there is too much slop in the gears. Do we have the capability but build one with tolerances that would allow that?
You could minimize gear lash.
At some point, you have to contend with the elasticity of the gear and shaft materials.
I believe that in theory, something would confound you because truly intantaneous transfer of movement would violate the speed of light.
I prefer this version.
Does anyone know how much torque is applied at the end of that thing? I would think it is a lot.
Tolerances aren’t really the issue. It’s how much slop is in the gear train and how it’s distributed.
The last gear will start turning promptly after the first one does if there is no slack between the meshed teeth all along the gear train.
One can easily remove all the slack in a very finite time by simply turning the 99th gear by hand to be snug against the 100th in the driving direction. Then turn the 98th to be snug against the 99th in the driving direction. Then the 97th to be snug against the 98th. Etc., all the way back to snugging #1 against #2.
After just a couple of minutes’ work, tops, you’ll have removed all the slack from the entire gear train. At that point when you start to turn gear #1, gear #100 will turn promptly. since there’s no more slack to be taken up.
So what’s promptly?
The physical motion propagates through the gears and teeth at the speed of sound in the material they’re made of. If we assume steel for simplicity, that’s on the order of 10,000 feet per second. Each double gear is a couple of inches from the small driving pinion to the out driven perimeter. So we’ve got on the order of 100 gears * 2" each = 200 inches of total distance to propagate the motion. Call it 240 inches or 20 feet to make the numbers simple. 10,000/20 = 500. So after 1/500th of a second, or 2 milliseconds, the 100th gear will start to turn. Very slowly, but very promptly.
I saw an art piece that was similar to this (I don’t think the ratio was quite this high). The shaft on the final gear was cemented into a block of concrete. The first gear had a motor spinning it at fairly high speed.
It would certainly be possible to preload all the gears so that there was no backlash, but I suspect that would end up breaking the first gear at some point. It could still take a long time, though.
Don’t you have to account for Material deformation as well. Teeth bending/abrading away mostly.
Edited: Screwed up the quoting stuff
I’m not an engineer, but here’s what I’m thinking.
The first cog rotates, say 10 cm.
The second cog rotates 1 cm
The third cog rotates 1 mm
The fourth cog rotates 1 tenth of a mm
The fifth cog rotates 1 hundredth of a mm
The sixth cog rotates 1 thousandth of a mm, or 1 micron.
I don’t think the seventh cog moves at all.
There could be a 2-micron distance between teeth of adjacent cogs. Thus a 1-micron movement won’t even make contact.
There is some elasticity in any material. When two cogs press against each other, both compress slightly. If the compression is greater than a micron, the cog won’t move.
And I’m sure there are many other factors, such as inertia.
Assuming perfectly rigid materials, a very small torque on the input side would generate a very large torque on the output side. Real materials are not perfectly rigid, though. You’d have to spin the input end an awful lot in order to strain all the parts of the machine enough to develop significant torque at the output end.
Probably this one:
One can remove most of the slack that way. What if, as you’re taking your finger away, you nudge the gear back a nanometer the other way? Now there’s slack again, because you’d have to move the first gear 10^91 meters before the last one would move a nanometer.
Of course, that’s assuming we’re modeling the gears as rigid, but that’s not true, either. A better model would be to treat all solid objects as springs. Push slightly against them, get a slight force. So you’d have to go some distance beyond “touching” to get a torque on the gear greater than the frictional torque on the axle.
It would be whatever torque the materials it’s made of can handle. Which would be a heck of a lot less than 10^100 times the input torque.
Mounting Odin on the last gear was a nice touch, there. And man, that guy found nearly every way to make a gear ratio possible in Lego.
I especially liked the planetary gears.
OK, I’m not a mechanical engineer, but is it possible to do the ratio in the other direction? I love the idea of barely touching one gear and having the gear at the other end spin and close to the speed of light or something.
Thinking as I write this, among the problems is the amount of force it would take to turn the far gear. I suppose that first machine could operate that way, but you’d need 1e100 times as much force to turn that last gear, and obviously the materials couldn’t take it.
I’m no engineer either, but I know a waste of Legos when I see it.
It’s all just torque.
Obviously you just need two gear trains that work in opposite directions. The first gear train gears down googol-fold to give you enough torque to turn the first wheel on the train that gears up googol-fold.
To get the fast end spinning fast means it has a lot of kinetic energy, and you’re the source. If you’re only barely touching the slow end, you’ll have to sustain your input torque for a very long time to deliver the energy needed to reach Ludicrous Speed (and even longer if you want to go to plaid).
Based on my experience with Lego gear trains, a 5:1 or 25:1 speed increaser you can drive with ease, a 125:1 gets pretty difficult, and a 625:1, you can usually keep it moving once it’s started, but it’s nearly impossible to start it driving at the slow end, and that only if you’re holding it just right to minimize friction.
I’ve never made a 3125:1.
(and these are all powers of five because I generally make them with 8-tooth and 40-tooth gears)
Ok, that’s funny.
When that logo flashed on the screen at the end I thought that was the gears exploding at first!
I think there are two at SF’s Exploratorium. One that might be the one in Machine_Elf’s post, and one where the gear chain drives a drill going into the original motor. It’s killing itself…slowly.