Gear Train Assembly (1)

Now we're going to learn how to calculate ratios for gear sets.  Each of the gears below have their teeth numbered.  The number of teeth on a gear is perhaps the most important piece of information you have about a gear.

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Whenever any of these gears contact a second gear, there is a speed ratio between them.  The ratio between them can be written in a pictorial equation as shown below:

It's very important that you notice that the word output is on the top on the left side of the equation and on the bottom on the right side.  That's because speed and number of teeth are inversely proportional - "the bigger the output gear, the slower it will go."

What about the gear train below?  It had a lot of gears in between the input and output.  It's actually quite easy.  Lets look at the equation again with a few changes.

 

The Re-written equation is:

 
The same process applies here as the single gear set equation.  Let's look at our gear train.  The jumble of gears looks intimidating, but we can break it apart section by section.

 
We'll start by examining the ratio between the motor and the upward shaft as shown in the image below:

 
The worm (screw gear) doesn't do anything, so we can ignore it (if a gear isn't paired with another gear, it does nothing).  How many pairs do we have?  Including the pulleys, we have 3 sets from input to output. The "gear ratio" of the pulleys is simply their diameter ratio, which is 2:1.  If we use our equation from above, that works out to:

 
So even though we had several gear sets, the only thing that changed the gear speed was the pulleys.  That means that the speed of the input is 2 times faster than the output (the tire was the output).

What if there are three gears chained together so one is an idler (it's not connected to the input or output)? 

input                        output

 
This is a little more tricky, but not bad.  Imagine that the idler is actually configured as shown below.  Now there are two idler gears, but does that change the ratios?  No, because the idler gears are the same size and are fixed to the same shaft.  So now we have two full gear sets.

 
What did the idler do?  If you look at the numbers, the number of teeth actually canceled so it had no effect on the speed!  But, it did affect the direction of the output gear.  So Idler gears affect direction, but not speed.