Calculating Gear Ratios

Homework?

No, not homework. I am retired !

I am simply trying to resolve a problem I have with driving a turntable on which is mouted a large sculpture which I wish to return to its starting position every 24 hrs.

So... let's get this straight.

Your gear 165 tooth is the driver. And, your 32 tooth gear is final driven. And, end result, final driven gear needs to complete rotation divisible by 360^0. How am I doing so far?

What possible difference, given your project, could it make where gears Driver, 2^nd driven and 3^rd driven are (in rotational relationship with start) after 24 hours, as long as final driven gear is in correct orientation?

This does sound like a homework question I had about a hunnerd years ago. Can you convince us otherwise?

Also the gear train has 165-45-40-32 teeth

The final ratio will be 165/32 = 5.15625 a bit odd ratio.

all other intermediates are immaterial

ratio : 165/45 * 45/42 * 40/32

Why not directly 165 and 32 teeth (forgetting all other ?)

BTW your answer is 495 for the first gear.

I think you guys have misinterpreted the question. This is a LCM problem. For instance the first ratio is 165 or 11x15 to 3x15 or 11 to 3. It will take 33 revolutions for the first two gears to get back to the original position. The big wheel will turn 3 times while the small wheel turns 11 times. A even number of turns will not occur before that. My wxMaxima tells me that for all 4 gears it will take lcm(165,45,40,32)/165; lcm(165,45,40,32)/45; lcm(165,45,40,32)/40; lcm(165,45,40,32)/32; or 96 352 396 495 revolutions

Look above in the last line.

But the question is why? It looks to glaringly like homework so answer was given but not the method. Wanted to be convinced that we are not doing his homework

If it is not homework, answer is enough. If it is, let him find it.

I am willing to take Revision at his word and his request is well defined and simple. If Revision is a student he will need to look up the LCM function.

They are correct it's a lowest common multiple problem. So:-

165 = 3X5X11
45 = 3X3X5
40 = 2X2X2X5
32 = 2X2X2X2X2

The only number not "covered" by the first and last cog is the extra 3 in 45 so total number of "teeth" is 165X32X3, and total number of revs. of first cog is 165X32X3/165 = 96

One revolution every 15 minutes.

Please send us a picture of the finished sculpture using the little green camera:-

Incidentally you can simulate this problem fairly easily in phun

Sorry you can only just see the marker on the second gear in these screen captures:-

Phun is a free toy so setting up will not be easy. You will need to draw several gears about the right size for say the 32 toooth cog then "fine tune" to get it right; then, use a (real) ruler against the screen to create the other cogs.

The sculpture is carved in wood, is approx 2m high and is in the form of a propeller, hence the need for it to turn, but slowly. It is not finished yet but when it is I will post a picture of it

The 165 cog will make 0.27, 0.24, and 0.19 revolutions for the 45 cog, 40 cog and 32 cog wheels to make one revolution respectivley.

The first 10 replies all assumed that you have all four gears in a row. Since you didn't specify otherwise, that is probably true. Likewise, they all assumed the gears are assembled in the order given, and that is also likey true, but you did not specifically say so, although the 'respectively' probably was intended to mean that. So They are all assuming:

As long as the first gear has 32 teeth and the last has 165, in this configuration (all in a row), the order and the number of teeth of the intermediate gears has no effect on the speed of rotation of the last gear, but it would affect the answer to your question.

Here is one of many other possible arrangements that have the same 4 gears in constant mesh, with a very different answer to your question:

You may need to be more specific in your description...

dkwarner "the order and the number of teeth of the intermediate gears has no effect on the speed of rotation of the last gear"

I agree but the question asked was:

"How many revolutions must the largest cog wheel make before each of the cog wheels is back in its starting position ?"

You left off the last part of my statement in your quote: "..., but it would affect the answer to your question."

Now that you mention it, I'm virtually certain the OP meant all, rather than each.

You're right, I did leave off the rest of your comment.

I appologize