Supposing we need to make a
1 to 10 gear reduction.
The smallest we really want any gear to be is about 7 teeth.
So, we can make that a 7 to
70. Which is a bit unwieldy.
So, we'd be better off
making this as 2 stages
and 10 can be factored in
as 2 times 5.
So we can make a 1 to 2 reduction.
And a 1 to 5 reduction.
And that would give us the 1 to 10.
But let's suppose we want those two ratios to be a
little bit more close to the same ratio.
So, we could start with a 1 to 3 reduction.
And then we'd need a 3 to 10 reduction to get our 1 to 10.
And then we could multiply this by 7 to 21
And this one here we'd multiply that by 3
give this 9 to 30.
So that would work quite nicely. And we have a total of
67 teeth for those.
But let's suppose we want to get a ratio that's a bit more even than that.
Let's write our 7 to 70.
And, let's imagine between the little wee gear
we have another gear and then a bigger gear.
The gear ratio for those 3 is still gonna be the same.
Except that the final gear rotates in the opposite direction.
So, 7 to 20 to 70
We can write that as 7 to 20 and 20 to 70.
Trying to reduce those a bit we don't want to go smaller than 7 on here.
But the 20 to 70. We could write that as 2 to 7.
And then, let's see multiply that by 4.
That gives us 8 to 28.
So our 1 to 10 is equal to
a 7:20 plus
a 8 to 28 reduction.
And that gives us a total of 63 teeth
for these ones. Whereas the 70 to 77
is 84 teeth.
If I didn't have any more even gear ratio we'd have 63 teeth.
Versus this other try where we had 67 teeth.
Let's try another example. Suppose we want a
1 to 12 reduction
for a clock to go from the minute hand to the hour hand.
So, we could write that as
multiplying both sides by 8. We'd have 8 to 96.
Now, if you want to divide that into two separate gear ratios
and we want those ratios to be about the same.
We want the gear ratio to be roughly
the root of 12.
For each set of gears and that is equal to about
3.464
So, 8 times 3.464
is 27.7, so we have 8 to 27.7
And, of course we can't make 27.7.
So, let's say we make that one 8 to 28.
And then we need a 28 to 96
We can divide the right side by 4
and that gives us 7 to 24.
So, we went down below 8.
But this works out really nicely because the next one up would be much bigger.
So, basically we need an 8 to 28 gear reduction
and a 7 to 24 gear reduction.
It doesn't always work so nicely. Sometimes you have to pick and intermediate value
that is something else so if 28 hadn't worked out
I would have tried 26, 27, 28, 29.
And see whatever divides nicely.
Now, for a clock the hours hand and the minute hand
have to be concentric so
our gears here and then another set of gears here
like so. They have to have
exactly the same shaft spacing that is between the two centers of the shaft.
Now, if both sets of gears use the same size teeth
the shaft spacing does not end up the same.
And, to adjust for that we can use my gear generator program.
And, I'm just gonna enter a value of 8 centimeters for the shaft spacing.
And the program automatically recalculates the size of the teeth
to get that shaft spacing.
The two sets of gears came out to almost the same size but
slightly different tooth counts.
One two three
4, 5, 6, 7, 8, 9, 10, 11, 12.
Exactly where we started.
Well, here's what could be a clock face.
The hands move in the correct motion with each other.