Reduction Gears: Solving Math Problem for 34mm Dial

[bcrary3]

Okay, so I am having a problem, I'm not the greatest at math, here is the problem:
I need a set of reduction gears, my plan is to have a gear attached to a shaft (base diameter of this first gear is 33mm) with 50 teeth (maybe?) To turn a reduction gear that will be on another shaft that will rotate a 34mm dial 1.356mm. What size does my reduction gear need to be? Am I at all on the right track? Thanks all!

 

[Mech_Engineer]

When you say "rotate a 34 mm dial 1.356 mm" what do you mean exactly? Tangential distance? How much are you going to turn the input shaft?

Generally you can find the reduction you're looking for by specifying the ratio between the input and output shafts. As an example, if you want to move the first shaft 90 degrees, and you want the output shaft to turn 5 degrees, you need a gear ratio of 90 / 5 = 18.0. This ratio can be used to find the required number of teeth (which will be proportional to the gear diameter, related by the tooth pitch).

For a very precise positioning requirement it may be tricky to find the EXACT correct reduction for a given displacement, because your gear needs to have an integer number of teeth for obvious reasons.

http://en.wikipedia.org/wiki/Gear_ratio

 

[bcrary3]

Basically what I am looking to do is create a devise that will keep track of score in a game. So the distance the input shaft will need to be turned to move the dial to the next number isn't terribly important, however I would assume probably 90 degrees would be ideal.

If I have a cylinder that is 34mm in diameter with a circumference of 106.760mm and the space between the numbers is 1.356mm how do I find the angle needed to turn it to the next number?

 

[bcrary3]

My apologies, my initial calculation was off a tad, it would need to move 2.60615mm not 1.356

 

[Mech_Engineer]

If I have a cylinder that is 34mm in diameter with a circumference of 106.760mm and the space between the numbers is 1.356mm how do I find the angle needed to turn it to the next number?

For a start, a 34mm diameter cylinder should have a circumference of 106.81 mm ([calculation link])... But with that being said, if the numbers you're referring to are equally spaced around a circular dial you probably don't need to calculate tangential (millimeter) distance at all; just consider how many numbers are around the circle and divide that number into 360 degrees...

My apologies, my initial calculation was off a tad, it would need to move 2.60615mm not 1.356

There's no need to calculate to 5 decimal places, especially in millimeters. For this 3 is more than adequate, 2 is probably enough considering standard machine tolerances. Keep in mind .001 mm is 1 micron and much, much smaller than the diameter of a human hair or the thickness of a sheet of paper.

 

[bcrary3]

For a start, a 34mm diameter cylinder should have a circumference of 106.81 mm ([calculation link]

Like I said, not the greatest at math, and am not looking at my notes right now.

consider how many numbers are around the circle and divide that number into 360 degrees..

So, from this, I am wanting the dial to go from 0-12 (a total of 13 digits) so, it would be 28.07 degrees?