Gears. You find them in your engines, in your transmissions, your shop tools,
in your toys. They're located in your garage, your shed, even your kitchen.
But perhaps most importantly, you'll find them in your bicycles. Always remember,
especialy when driving your Prius, that the bicycle is the most efficient
form of transportation that we have, fueled bysimple things like Taco Bell and Mountain Dew.
But anyway, let's Lrn Fzx. The basics, The most basics,
of gears, mechanical advantage, what's a torque multiplier, what's a speed multiplier.
Two simple meshed gears. If the big one is the input driven by my hand, and the small
one is the output, this is clearly a speed multiplier because the output is
moving faster than the input. Switch it up - the drive gear is the small one
the driven gear is the big one.
It's moving slower so this machine multiplies torque. When analyzing gears,
first just play with the system, then clearly identify which is the input -
often called the drive - and which is the output - often called the driven.
We'll need to calculate a ratio and you can useeither radius to radius,
diameter to diameter, circumference to circumference. Or, often very conveniently
the number of teeth to the number of teeth because teeth represent circumference.
so 36 teeth to 12 teeth, that little one is spinning three times as fast, 36 over 12.
That's a mechanical advantage of one-third. Here's a 36 tooth 24 tooth combination, which means
that the little one is spinning one-and-a-half times as fast and the mechanical
advantage is two-thirds. Remember that any mechanical advantage less than one
is a speed multiplier and mechanical advantage greater than one in these
cases is a torque multiplier. Note also the change in direction. If one turns
clockwise the other one turns counterclockwise always with these enmeshed gears.
Switch the input and the output
and you now have a speed divider. But more importantly because it divides speed
it multiplies torque so the output torque is gonna be larger than the input
torque. Mechanical advantage in this case 36/24 = 1.5. Now we're back to that 36 x 12
combination switch the input the output and you now have a torque multiplier,
clearly a speed divider identified visually. So it is a torque multiplier of three.
The mechanical advantage is 3. Note that a counter-clockwise input gives you a
clockwise output. It is still switching directions. So what do you do if you want
to have them both spin in the same direction? One option is putting
what we call an idler gear in between the two. You can see that both the input and the output
are spinning clockwise and the two shafts are now separated a larger distance.
Now let's talk mechanical advantage and calculations. Watch the number of turns.
Output turns one. Output turns two. And output turns three. We know that
that's a speed multiplier, it's a torque divider, the mechanical advantage has to be less
than one so it is one-third. To get that value the equation turns out to be the
driven over the drive, the output over the input. Again you can use
circumference or diameter or the number of teeth or radius. And that idler gear?
Crazy thing, doesn't even matter what size it is because if you watch the output
output travels one rotation, output travels two rotations, output travels three rotations
for one input just as what we had before.
The mechanical advantage equation is driven over drive, we'll be using the number of
teeth so 12 teeth 24 teeth and 36 teeth is what we have, so that three gear
combination is 12 over 24 and then 24 over 36. The 24s end up canceling out,
the middle gear size does not matter
the idler size does not matter.
Another example. This one is a torque multiplier because it's a speed divider
and it takes one and a half turns input for one turn of the output so the
mechanical advantage is one and a half or three halves or 1.5. In addition to
using an idler gear there's another method we can use to make sure that the
input and output are spinning in the same direction and that is use a belt drive
or a chain drive. Not only do the pulleys turn in the same direction, the system
compared to the idler pulley system tends to be lighter and you can place
those shafts any distance apart as long as you have the proper length chain.
Now let's find the mechanical advantage. First you determine by looking at it whether
or not it's a speed displacement multiplier or a force multiplier.
Output is spinning faster must be a speed multiplier. Therefore the mechanical advantage
is less than one. Then you spin and spin and spin and count the
number of rotations. The input spins eleven, output spins fourteen. Therefore
the mechanical advantage being less than one must be 11 over 14. In decimal
form it's about 0.79. Switch em, you get a torque multiplier 14/11 or 1.27.
One final example. This is called a worm gear usually used for lifting heavy things.
Just count. Input vs output. One two three just keep on going.
Note that this definitely does divide speed. Therefore being a speed divider it
is a torque multiplier. And if you counted all those you get twenty.
The mechanical advantage is 20. So absent friction, that machine will take your
puny little input torque and multiply by twenty. Gears the basics you just
learned physics