Reduction Gears: Solving Math Problem for 34mm Dial

In summary, the conversation discusses the need for a set of reduction gears to rotate a 34mm dial with a precision of 1.356mm. The desired gear ratio is 90 degrees of rotation for 5 degrees of movement on the dial. The conversation also touches on the calculation of the angle needed to turn the dial to the next number and the importance of considering tolerances in precision. Ultimately, it is determined that the dial will need to move 2.60615mm, and the gear ratio needed is 28.07 degrees for each number on the dial.
  • #1
bcrary3
9
0
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!
 
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  • #2
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
 
  • #3
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?
 
  • #4
My apologies, my initial calculation was off a tad, it would need to move 2.60615mm not 1.356
 
  • #5
bcrary3 said:
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...

bcrary3 said:
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.
 
  • #6
Mech_Engineer said:
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.

Mech_Engineer said:
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?
 
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What are reduction gears?

Reduction gears are a type of mechanical device used to reduce the speed of a motor or engine while increasing its torque. They consist of a set of interlocking gears with different sizes that work together to transfer power and change the rotational speed of a system.

How do reduction gears work?

Reduction gears work by using a smaller gear (known as the pinion) to drive a larger gear (known as the wheel). The pinion rotates at a faster speed, transferring more power to the larger gear and increasing its torque. This allows the system to operate at a slower speed with more force.

What is the purpose of reduction gears?

The main purpose of reduction gears is to decrease the speed of a motor or engine while increasing its force. This is useful in various applications such as automobiles, industrial machinery, and even clocks. It also allows for better control and efficiency in power transmission.

How do you solve a math problem for 34mm dial using reduction gears?

To solve a math problem for a 34mm dial using reduction gears, you first need to determine the gear ratio. This can be done by dividing the diameter of the wheel by the diameter of the pinion. Once the gear ratio is known, you can use it to calculate the number of rotations the pinion needs to make in order to move the dial a certain distance.

What are some common applications of reduction gears?

Reduction gears have a wide range of applications, including in automobiles, industrial machinery, and household appliances. They are also commonly used in clocks, watches, and other timekeeping devices. In addition, they are used in various types of engines, such as aircraft engines and marine engines, to adjust the speed and torque of the propeller.

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