Using the Gear Calculator

The Gear Calculator does not create gears, but helps you figure out gear ratios in order to get the ratio of motion you want from a series of gears.

The Gear Calculator is available under the Help menu. Under “Help”, select “Gear Calculator.”

The gear calculator contains two functions.

First, the gear calculator will help find the smallest fraction which represents a target ratio, and find the prime factors of the numerator and denominator. For example, suppose we want to create a gear system with a target ratio of 24 to 1, because we’re building a 24 hour clock.

Open the Gear Calculator, and enter “24” and “1” under Target Ratio.

Gear Calculator 1

This helpfully shows the prime factors of 24. Since 1 has no prime factors it’s not displayed.

What this shows us is that we need to have 3 stepdowns of 1:2 and a stepdown of 1:3 to get a total stepdown of 1:24.

Suppose instead we want a gear ratio of 25 to 4. Enter 25 and 4 for the target ratio we get:

Gear Calculator 2

This means we need two stepdowns of 1:5 and two stepups of 2:1 to get our target ratio.

Now how we use this information requires a little art. Meaning we need to figure out if we want to use two gears of sized 20 and 8 teeth (for a 5:2 ratio, as 5*4 = 20 and 2*4 = 8), or if we do this with a bunch of 1:5 and 2:1 ratios or how–that requires a bit of art. But at least the heavy lifting of telling you the prime factors of the ratio is done for you.

Where the gear calculator shines is when you want to approximate a specific ratio represented as a decimal number.

For example, a “synodic month” is the period of time between full moons. A synodic month is 29.530587981 days, according to Wikipedia.

So let’s figure out a gear system which can approximate this ratio.

Open the Gear Calculator, select “Target Fraction”, and enter our number of days in a synodic month.

Gear Calculator 3

Notice we get a list of proposed ratios, and prime factors for the selected ratios.

The proposed ratios are integer fractions which come close to approximating our target fraction. Each is displayed with an error. For example, the third ratio is given as:

2924:99               17.213 rev/1 deg

This means for the proposed fractional ratio 2924:99, we have an error of 1 degree for every 17.213 revolutions our month gear revolves. That means over 10 years, our month gear will drift by around 7 degrees. (120 months / 17.213 rev = 6.97° error.)

Selecting that row displays the prime factors for 2924 and 99:

Synodic Month

Again, how we put together a gear chain to represent this is art.

But we can see from the prime factors we need to assemble a string of gears which give the step-ups and step-downs outlined.

One way we can approach the problem is to group the pairs of primes as:

[2:1] [2:1] [17:9] [43:11]

This has the nice property of keeping us having too large a gear (because a 43-tooth gear is pretty large). We can now string gears together starting from the back to the front.

With a little fiddling we wind up with the following gear train:

Synodic Gear Train

You can download the resulting file from here:

We have a number of other tutorials available to help you understand how to use Kythera. Please visit our product page for more information.

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