How many gears to rotate a 34mm dial 28.07 degrees?

[bcrary3]

Okay, I am no math genius here, so this may sound like a stupid question, but I am curious to know, how do I find how many teeth a gear will need and how big or small it should be to rotate a 34mm dial 28.07 degrees?
Cheers

 

[Ryoko]

That all depends on how much force will be applied and how fast you want to turn it. Maybe if you explained what you're trying to do.

 

[bcrary3]

Sorry for the vague description.
Basically what I am trying to make is this:

It will be a rectangular prism approx. 63x36x36 (LxWxD) with two 10mm shafts that will protrude from either end, this two shafts will have gears attached to them which will rotate a numbered dial 34mm in diameter. I am guessing a 90degree rotation of either shaft will take you to the next number (the dial will be numbered 0-12). Hopefully this is a little better description of it.

 

[jedishrfu]

okay so 90 degrees on the shaft gear will cause 30 degrees on the number gear. Hence one complete shaft gear rotation ie 360 degrees will rotate the number gear by 120 degrees.

The shaft gear would need a tooth every 3 degrees meaning it should have 120 teeth and the number gear would have 360 teeth. You can reduce this down to:
- 60 teeth and 180 teeth (too many teeth on the number gear)
- 30 teeth and 90 teeth
- 20 teeth and 60 teeth
- 12 teeth and 36 teeth
...
I think 4 teeth and 12 teeth would be too rough so I'd go with the 12 teeth and 36 teeth pair or higher.

Anyway this is my guess.

 

[bcrary3]

Jedishrfu, that seems like it makes sense to me.

Sorry if this seems stupid, but what diameter did you use for each gear to figure this out?
Thanks. :D

Also, I would assume that a 30:90 gear ratio would be best for smoothness?

 

[xxChrisxx]

From the context is not acutally clear what you want to do. I'd also like to point out that 30degrees is not 28.07 degrees. The latter indicates a much tighter accuracy and tolerance.

How far you want to rotate is largely irrelevant to how many teeth you need. Unless you are limited by input rotation. Precision and acccuracy would determine the amount of teeth needed.

For example:

Why do you need a gear at all? Just turn it manually by hand. To 28 degrees.
You have to judge by eye 28 degrees - low precision.

With a larger reduction ratio, the more turns you need to get the desired output rotation.
So a reduction ratio of 3:1 means, 3 turns of the input gear = 1 turn of the output gear.
A reduction of 12.8:1 = means that 1 turn (360degrees) = 28.125 degrees of the output gear.

The way you wrote your angular rotation indicates a tolarance of ±0.005deg (±18 arcsec)


Diamater will depend on gear tooth module. A large module will mean a large diameter. Ie:
1 module 90 teeth = 90mm reference diameter.
2 module 90 teeth = 180mm reference diamater