Train of gears |
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A simple train of gears is shown here, and the explanation of what happens and how is below.
Okay what does this train of gears serve in this particular example? Well one thing as there is an odd number of gears the direction of rotation will be the same as you started with. But let's look at the ratio change. First we will take the first wheel (20teeth) and the last wheel (60teeth) and to make it meaningful we will give the starting speed at A to be 500rpm. So 20/60 = 0.333r and if we multiply this by the speed we get the final speed of 166.666, we shall use this as a comparison at the end of this explanation. So now lets take each pair seperately and apply the same sum to it..... 1) 20/30 = 0.666r x 500 = 333.333r 2) 30/40 = 0.750 x 333.333r = 249.999 3) 40/50 = 0.8 x 249.999 = 199.999 4) 50/60 = 0.833r x 199.999 = 166.666 And that as you can see is exactly the same as the original 20/60x500 and proves once and for all that the only changes to the ratio are cause by the first and last gears. One other thing that appears to cause some confusion is lathes with a fitted gear or teeth cut into the mandrel and tumblers for reverse direction attached. Well taking the above as our proof that only the first and last effect a change, then provided that the number of teeth on the mandrel is the same as the number of teeth on the final gear then nothing has changed and you just use that number in your equation, as shown in the picture below....
So here we have 20 teeth both prior to the tumbler and also as the output to the change wheels, so the two other gears ie the 13 or the 16 have no effect on the outcome other than to change the direction. In case one both are in the drive train giving four gears which reverses the direction or in the other case one is in mesh giving a train of three gears giving the same direction. |
