View Full Version : Need Help with some Gear Measurements

09-13-2008, 07:01 PM
I am looking for someone who knows how to measure gears.

I need this rack to be pulled down by these series of gears.

Each system is the same in the picture I am providing but I need the gears of each system to be able to pull down separately the distance of 1 inch, 2 inches and 3 inches.

Also if you can please provide the equations you used and any suggestions to make the system more efficient, thanks.

Here's a link to the picture of the system:


The pole connecting to the Worm Gear will be connected to an arm that will be turning an arm connected to it 3/4 an inch in distance.

Here's a picture of what I mean:


I also would need calculations for the gear measurements to be able to bring that rack down those distances if the arm were only turned 1/2 an inch.

The circle will be 6 inches in circumference for the arm that turns 3/4 an inch and 4 inches in circumference for the arm turning 1/2 inches.

Also, please let me know if the circle needs to be bigger to compensate for the possible size of the gears.

09-14-2008, 01:49 AM

I tried to look at the pics you posted, but I get a message that they've been moved or deleted. Anyway, I'll give you what I can about gears.

The operative measurement of a gear is called the Pitch Circle Diameter. This is the effective diameter of the gear. It is not the outer diameter, nor is it the diameter at the base. It is the diameter of interaction of other gears of the same pitch. The pitch for imperial gears is stated in teeth per inch. For instance, at a pitch of 48TPI, a gear with 48 teeth has a PCD of 1 inch, a gear with 24 teeth has a PCD of 1/2 inch.

When working with racks, you'll probably need to know the circumferential pitch of the round gear. This is easily calculated from the PCD. The circumference of a circle is 2*pi*radius or pi* diameter. So the circumference of a 24 tooth geat at 48TPI is pi * 1/2" that is the effective working length of the round gear.

For imperial pitch gears, the standard pitches are 120TPI, 96, 80,72,64, 48, 32, 24, 20, 16. Ther are some larger pitches than 16, but 16TPI has pretty big teeth. Also, the teeth on a 120TPI gear are just about microscopic. A little math will tell you that the higher the pitch, the more teeth you get in less space. Higher pitches are better in gauges where forces are small. Bigger pitches are better in things like flight controls etc. As a rough rule of thumb, if you're building a gauge, you will probably want to work with 64 or 48TPI. If you're building controls, then 32-20TPI will be good.

I hope this helps with what you're trying to do, but if you need to you can PM me and we'll work out what will do what you want.

09-14-2008, 02:01 PM
There's more to it then just a gear pulling down a rack. Going to put up a bunch of links. Hopefully one of them works.

This is the overhead view:


This is the side view:


09-14-2008, 04:13 PM

Here's some things to consider:

a) If the arm is 6" long and moves 3/4" at it's end then the rotation of the worm will be (.75 / (2 * pi * 6)) * 360. that is 3/4" divided by the total circumference gives the percentage of the circumference of movement, then that multiplied by 360 is the number of degrees the worm will turn. This probably won't be exact as the circumference is measures around the circle and the arm movement is most likely measured in a straight line, but it will be close enough.

b) The pitch of the worm should match the pitch of the gears. This is not straightforward. I'm not familiar with the calculations on this aspect, but I've found that for a 48TPI gear a metric 1.75mm pitch screw fits quite nicely. In any case, if the worm has only one starting (that is it doesn't have multiple threads interwoven) then the ratio between the worm and the gear is set by the number of teeth on the gear. For example: Since there is only one thread on the worm, one turn moves one thread groove. If there is a gear meshed with the thread, it will turn by one tooth. So if the gear has 20 teeth, when the worm turns one turn, the gear turns one tooth or 1/20 of a turn so the ratio is 20:1 reduction (20 turns of the worm to one turn of the gear).

c) Since you want the rack to move 1" for a 3/4" input, you're going to have to get a speed increase, and a worm gives a speed decrease. So you're going to have to do some heavy gearing UP. Doing gear ratios between round gears is easy though. It's just the ratio of the numbers of teeth. So a 20 tooth gear driving a 10 tooth gear gives a speed increase of 2:1.

There are a lot of variables that you need to solve to do what you're trying to do. The maths is not difficult, there's just a lot of it to do. I'd suggest that since worm gears give such high rates of speed reduction and you need speed increase, that a worm might not be the best solution if it can be avoided. Given the limited amount of travel of the input arm, maybe some kind of linkage would be better.

Hope this has been helpful.

09-15-2008, 06:54 AM
Well I figured a worm gear would be the best way to get to a gear in that position but what would you suggest. Perhaps you could draw me a simple picture of what gear setup would work more efficiently.

09-16-2008, 07:31 PM
Okay, let's try this set up then with the same measurement requirements I needed in the previous post. (I replaced the worm gear with bevel gears)

This being the overhead view:


This being the side view:

09-16-2008, 08:48 PM

The more I look at this, the more I think that gears is not going to be the easiest/best solution. What about using a cable attached to another arm which is attached to the pole. Then the cable runs around a pulley and pulls the slider (rack) in the direction required. The length of the arm that the cable is attached to will then set the distance that the slider moves.

09-17-2008, 05:34 AM
I'm a visual person but your drawings have me totally confused.
What is it you are trying to do? What part of the aircraft? Or is it even an aircraft?

09-17-2008, 05:10 PM

The more I look at this, the more I think that gears is not going to be the easiest/best solution. What about using a cable attached to another arm which is attached to the pole. Then the cable runs around a pulley and pulls the slider (rack) in the direction required. The length of the arm that the cable is attached to will then set the distance that the slider moves.

The pole only goes in one directional rotation.

A cable won't work unless the cable is attached to a pulley ring with a gear on it's side and that gear is attached to a gear on the pole and then you can have a system of pulleys which can attach to the rack but bare in mine the rack has to pop back up into position that's why I had the last gear on that gear train have missing teeth to allow the rack to pop back up every 3/4 an inch the arm moves.

The picture is just a part of the whole system.

There is suppose to be a rack every 3/4 of an inch from each other going around that circle.

It's kind of funny you mentioned a pulley system, since that was my originally idea. I just didn't think it would provide the ratio required for a 3/4 inch turn to pull down a rack 1, 2, or 3 inches.

09-27-2008, 09:01 PM
The Machinist Handbook is an EXCELLENT resource, not just for machinists, but for people like us. It also describes the diametric pitch of gears, how to measure, etc.