Gear help (cogs)

[Twitch010]

Thought of something for a personal project. I can picture it and think of it in my head but can't figure out if it will work or not.

So my idea is to have a bunch of cogs link together to create a pretty fast RPM with minimal effort. Take a bike for example, you have a big sprocket in the front where you peddle and a chain is used to spin the small sprocket in the back. If you bolted another big sprocket to the small sprocket in the back and then ran a chain to another small sprocket in the front that moves freely and had another big sprocket bolted to the small one in the front would each big sprocket spin faster then the last? The way I'm picturing it the big sprocket you are peddling would go say 25rpm then the next big one would go say 40 - 50rpm and the last one would go even faster.

My main question is is this correct or would they all go the same speed?

Thanks in advance and wasn't sure where else to post this so if it needs moved feel free to please.

 

[pappus]

Thought of something for a personal project. I can picture it and think of it in my head but can't figure out if it will work or not.

So my idea is to have a bunch of cogs link together to create a pretty fast RPM with minimal effort. Take a bike for example, you have a big sprocket in the front where you peddle and a chain is used to spin the small sprocket in the back. If you bolted another big sprocket to the small sprocket in the back and then ran a chain to another small sprocket in the front that moves freely and had another big sprocket bolted to the small one in the front would each big sprocket spin faster then the last? The way I'm picturing it the big sprocket you are peddling would go say 25rpm then the next big one would go say 40 - 50rpm and the last one would go even faster.

My main question is is this correct or would they all go the same speed?

Thanks in advance and wasn't sure where else to post this so if it needs moved feel free to please.

Your considerations are OK.

But keep an eye on the torque which is necessary to run your machine.

 

[Twitch010]

Was hoping I was right, Thanks very much for your response. Hopefully it will not require much torque because it needs to be able to be powered by peddling. So I guess I need to figure out the easiest gear ratio while still producing very high rpm.

 

[soroban]

Hello, Twitch010!

Thought of something for a personal project.
I can picture it and think of it in my head, but can't figure out if it will work or not.

So my idea is to have a bunch of cogs link together to create a pretty fast RPM with minimal effort.
Take a bike for example, you have a big sprocket in the front where you pedal
and a chain is used to spin the small sprocket in the back.
If you bolted another big sprocket to the small sprocket in the back and then ran a chain to another small
sprocket in the front that moves freely and had another big sprocket bolted to the small one in the front,
would each big sprocket spin faster then the last? . Yes

The way I'm picturing it, the big sprocket you are pedaling would go say 25rpm,
then the next big one would go say 40 - 50rpm, and the last one would go even faster.

My main question is is this correct or would they all go the same speed?

The set-up might look like this:

              o o *                     o o *                     o o o
          o           o *           o           o *           o           o
        o               o     *   o               o     *   o               o
       o                 o       o  *              o       o  *              o
                                          *                         *
      o                   o     o       o   o       o     o       o   o       o
      o         .         o     o      o  .  o      o     o      o  .  o      o
      o                   o     o       o   o       o     o       o   o       o
                                          *                         *
       o                 o       o  *              o       o  *              o
        o               o     *   o               o     *   o               o
          o           o *           o           o *           o           o
              o o *                     o o *                     o o o

             Pedals                   Back Wheel               Front Wheel

Suppose the ratio of the radii of the large gear to the small gear is \(\displaystyle 3:1.\)
(Note: These are not the wheels; they are the gears.)

Then the Back Wheel will turn 3 times faster than the Pedals.
And the Front Wheel will turn 3 times faster than the Back Wheel.

We have a problem:
. . The Front Wheel will travel 3 times as far as the Back Wheel.

Either the bicycle will tear itself apart
. . or the Back Wheel will have a braking effect.

Solution: make the Back Wheel three times the size of the Front Wheel.


Since this is a "thought experiment", we can extend it freely.

Consider a chain of thousands of these gears in a row.
Conceivably, you could turn the pedals once,
. . and a point on the circumference of the last wheel
. . would have a velocity exceeding the speed of light.

Yeah, right!