# Gear Train solution

#### leod

Joined Dec 21, 2020
18
Hello

I am looking to find solution for gear train set, with below conditions, because I dont understand well, I appreciate your help:

- first gear circumference 100 cm
- first gear has spool winch, on which is attached string with 100 kg weight
- first spool winch circumference not defined yet

- second gear circumference not defined yet
- second gear has a spool winch, on which is attached string with 20 kg weight
- second spool winch circumference not defined yet

Question:
- what should be first spool winch, second gear and second spool winch circumference, so both weight would be in equilibrium?

Thanks

Leo

#### ericgibbs

Joined Jan 29, 2010
14,645
hi leod,
Is this a College course assignment.?
E

#### leod

Joined Dec 21, 2020
18
hi leod,
Is this a College course assignment.?
E
Hello, no, it is my hobby. I already tried in practice, but because of no results I wanted to try here too.

#### drc_567

Joined Dec 29, 2008
1,156
Is there a purpose or particular application to this arrangement?
For simple equilibrium, the radius of the first spool, that is 1/2 of the spool diameter, times the load weight, 100 kg, must be equal to the radius of the second spool, times the second load, or 20 kg.
$$R_1*W_1=R_2*W_2$$
$$15.92 cm * 100 kg = R_2 * 20 kg$$
$$R_2 = 79.6 cm$$
... This assumes that the diameter of the first spool is equal to the diameter of the first gear.

Last edited:

#### leod

Joined Dec 21, 2020
18
Is there a purpose or particular application to this arrangement?
For simple equilibrium, the radius of the first spool, that is 1/2 of the spool diameter, times the load weight, 200 kg, must be equal to the radius of the second spool, times the second load, or 20 kg.
$$R_1*W_1=R_2*W_2$$
$$15.92 cm * 100 kg = R_2 * 20 kg$$
$$R_2 = 79.6 cm$$
... This assumes that the diameter of the first spool is equal to the diameter of the first gear.
Thanks.

I would like to make gears and spools, where attached weight on first spool of first gear is 5x bigger than weight
Is there a purpose or particular application to this arrangement?
For simple equilibrium, the radius of the first spool, that is 1/2 of the spool diameter, times the load weight, 200 kg, must be equal to the radius of the second spool, times the second load, or 20 kg.
$$R_1*W_1=R_2*W_2$$
$$15.92 cm * 100 kg = R_2 * 20 kg$$
$$R_2 = 79.6 cm$$
... This assumes that the diameter of the first spool is equal to the diameter of the first gear.
Thanks.

If like this, when first gear makes 1 revolution (100 cm), for how many cm second gear and second spool moves?

#### drc_567

Joined Dec 29, 2008
1,156
For one complete rotation of the first gear/spool, of 100 cm. circumference, the second larger spool, of 500 cm circumference, would also travel 100 cm. However, the rotation angle of the second spool would only be 1/5 of a full rotation, or 72 degrees.
... Not quite sure what you are looking for.

#### leod

Joined Dec 21, 2020
18
For one complete rotation of the first gear/spool, of 100 cm. circumference, the second larger spool, of 500 cm circumference, would also travel 100 cm. However, the rotation angle of the second spool would only be 1/5 of a full rotation, or 72 degrees.
... Not quite sure what you are looking for.
Thanks.

So first gear circumference 100 cm, first spool circumference 100 cm, second spool circumference 500 cm, what about second gear?

#### drc_567

Joined Dec 29, 2008
1,156
... I am assuming that the second, larger gear circumference is the same as the second spool.
However, as far as costs and economics, it may be better to reduce the diameter of the first gear, and then the second gear would be a smaller diameter.
... Is there a specific reason that the circumference of the first gear is specified as 100 cm? That makes the second gear and spool almost 1.8 meters in diameter, which may not be acceptable.

pp

#### drc_567

Joined Dec 29, 2008
1,156
... ok... rethinking this...
What if the second gear was the same diameter as the first gear ... That is make the first and also the second gear diameter equal to 31.84 cm., or 100 cm. in circumference. Then arrange for the second spool diameter to be 5 times the diameter of the first spool? That should provide the equilibrium necessary for the specified weights.
... If you want the output gear to go faster than the input gear, then you make the output gear smaller. If you want the output gear to go slower than the input gear, you make the output gear larger. If the output gear is the same diameter as the input gear, the will both be going at the same speed.

Last edited:

#### leod

Joined Dec 21, 2020
18
... ok... rethinking this...
What if the second gear was the same diameter as the first gear ... That is make the first and also the second gear diameter equal to 31.84 cm., or 100 cm. in circumference. Then arrange for the second spool diameter to be 5 times the diameter of the first spool? That should provide the equilibrium necessary for the specified weights.
Yes, but then when first one makes 1 rotation, second one also makes 1 rotation, but we need second spool to make only 1/5 of 1 rotation...
In case more gear(s) added between them, possible to keep same equilibrium and also ratio of rotation 1:1/5?

#### drc_567

Joined Dec 29, 2008
1,156
... If the relative rotation between the two gears is important, then it will be necessary to have a ratio of 5 to 1 for the diameter of the large gear to the diameter of the small gear. A 1.8 meter diameter large gear could be expensive. Maybe it would be possible to use a smaller diameter gear for the first one.