Calculating Optimal Gear Ratio for Efficient Job Performance | Diagram Included

[Yanko693]

I have a basic understanding of how to calculate gear rpm, but have no idea as to how one could figure out what size and number of teeth you would need if you want to give X turn to the drive gear to get a rack to slide Y inchs. Obviously I would want to contain the entire assembly in the the smallest place possible. I doubt I explained very well so here is a diagram of what I would like to do, excuse the not so technical drawing:

From what I've read I want 4x as many teeth (as the second gear) on my drive so 1/4 turn gives a full rotation on my second gear, my third will be the same amount of teeth as gear 2, now I just need to figure out how many teeth on the final gear that actually moves the final piece.
PS: I hope this is in the correct section

 

[Travis_King]

First: Are you sure you need those last two gears? If you can make it work with just the driver and the second gear, would that be ok? If the third gear is just there to ensure proper direction of the rack when the driven gear is turned, and the fourth gear is likely only to be a small reduction, why not just size the first and second gears appropriately?

Second: You are right. If your driver gear has 100 teeth, and you want to rotate your second gear 4 times for every 1 turn of your driver, then you will want 25 teeth on the second gear.
N1/N2 = gear ratio; 100/25 = 4:1

Your other question is the more tricky of the lot, but not altogether that difficult.
As an approximation, say the driver gear is directly connected to the rack. 1/4 turn of the driver gear will move the rack a distance, x of x = .25 * (Pi * Diameter of driver) or a quarter of the circumference.

To better understand this picture it like this (sorry I don't have the capacity to upload photos right now):
Picture the gear's top tooth meshing exactly in the tooth recess of the rack. The centerline of the tooth on the gear lines up directly with the centerline of the recess on the rack.

Rotate the gear so that the next tooth becomes the top most tooth. The centerline of this tooth will then have matched up with the centerline of the next recess on the rack.

So, every time the gear is rotated by one tooth, the rack is moved a distance equal to the difference between adjacent centerlines on the rack (tooth or recess, it doesn't matter, generally).

Do you see what I mean?

 

[Mech_Engineer]

The easiest way to figure out how far a gear will move a rack is to look at the "tooth pitch" which is usually specificed for the specific gear in something like "teeth per inch." This means for example if you have a gear/rack combo with a tooth pitch of 10 teeth/inch and the gear has 20 teeth, a half revolution of the gear (180 degrees, 10 teeth) will move the rack one inch.

 

[Yanko693]

Thank you for the helpful replies.

Yes the extra gears are to ensure direction. I would go directly off the drive gear, but the same drive will be running the diagram x 4. two will move to the right like the diagram and two will move left (one more gear for those two) So it looks like I will get my desired distance by sizing the single driver and the first followers for each direction with the rest being the same size to maintain the same ratio and just there to ensure direction.

So I think I will do 10 teeth per inch, 20 in circumference on the driver, 5 inch circumference on the follower to get my ratio of 1 to 4. now to take the 5" circumference and make it turn the final gear of X" circumference so that it will move a total of 2". I'd prefer to keep 10 teeth per inch for the sake of simplicity.

 

[Travis_King]

you aren't going to buy gears on a circumferential basis. Do some research into common gear sizes and teeth numbers.

What I meant about the last two gears is that if they are all the same size, you are wasting space and money and efficiency. With just one driven gear meshed with the driver you will get the right direction. ie you would have Rack->small gear->Driver gear

 

[Yanko693]

you aren't going to buy gears on a circumferential basis. Do some research into common gear sizes and teeth numbers.

What I meant about the last two gears is that if they are all the same size, you are wasting space and money and efficiency. With just one driven gear meshed with the driver you will get the right direction. ie you would have Rack->small gear->Driver gear

I will be making them myself with the laser at work. I just got to draw them up in cad and wait until we do some jobs on 1/4 inch stainless. The hard part is I'm not entirely sure what size/shape the teeth should be. this is not a real tight tolerance project, the teeth just need to be as beefy as possible. Also the extras are needed as there where be quite a bit of space between the racks. unless I did a belt of some sort but I'd prefer not to.I will upload a better drawing of the total idea to give a better understanding of what I mean.

Who does sell gears though? It could help to get one for reference.

 

[Mech_Engineer]

Gear tooth profiles are a pretty deep subject... you may be in for a surprise if you're hoping to cut a precision gear on a laser cutter with no real profile to it. 10 teeth per inch is actually a pretty small profile, how much force do you want out of it?

That being said, W.M. Berg sells a good variety of precision gears if you're curious...

http://precisionparts.wmberg.com/gears/
http://precisionparts.wmberg.com/images/overview/pgears[1].jpg

 

[Yanko693]

Gear tooth profiles are a pretty deep subject... you may be in for a surprise if you're hoping to cut a precision gear on a laser cutter with no real profile to it. 10 teeth per inch is actually a pretty small profile, how much force do you want out of it?

That being said, W.M. Berg sells a good variety of precision gears if you're curious...

http://precisionparts.wmberg.com/gears/
http://precisionparts.wmberg.com/images/overview/pgears[1].jpg

I don't know exactly how much force will be on it, but it will be simply hand turned. It is actually a locking mechanism, think of the rack as a deadbolt. It needs to stand up to someone attempting to force it, but normal use will be a simple quarter turn by hand. I know we have cut a gear for a company before, but it didn't work correctly. That being said what they needed was .005 tolerance. My use has much looser tolerance.