Gear drawing program

How about a _small_ CAD program?

Softkey "Key Cad Complete" for instance. I got mine from a clearance bin at Office Depot for $7. The list price is $20 or so. It looks like it can accept what it calls 'XYZ' files, which I assume means just lists of point coordinates in ASCII.

That sort of list could be generated using a spreadsheet. You can get a good one for free as part of a (huge) download of Open Office at OpenOffice.org, or buy the CD pretty cheap.

You'd have to do a fair amount of computing in the spreadsheet to figure out a tooth profile, array it to make a gear profile, and convert that from polar to rectangular coordinates. But it's the sort of thing that spreadsheets do well, and that way you get to pick your tooth profile. I think wooden clocks traditionally use cycloidal gears because the teeth are strong.

Okay, it's a _lot_ more work than just plugging numbers into a 'gear drawing program', but it could be a lot more fun, too.

-Mike-

Hi Richard:

Actually you should just lay the gear out the old-fashioned way and skip the fancy CAD program.

I'm assuming these gears are for mostly ornamental purposes, but still need to roll on each other properly. Since they probably don't have to mate with existing gears of standard pitch, you have a lot of leeway to design them.

First, you need to decide what size you want to make your gears. The first gear is easy because for any desired diameter and number of teeth you can calculate a pitch. The pitch might be some bizarre number like 12.2359, so you wouldn't want to use it in a standard machine, but if you only want to mate it to another gear that you're making, who cares what the pitch is?

Let's say you want to make a 6" dia. gear. Now, you can have any number of teeth you want (within reason). The more teeth you want, the smaller those teeth will be. Let's say you want 24 teeth. Your pitch (actually "diametral pitch") is just the number of teeth divided by the diameter (actually "pitch diameter"). So, in our case, the DP would be 24 / 6 = 4 [incidentally this is actually a standard pitch].

A gear has to have a "pressure angle". This is the angle of the tangent point where the gear teeth just kiss each other. The common standard angles are 14-1/2 deg. and 20 deg., but again you can really use any reasonable angle you want between about 10 and 30. Let's use 20 deg. since it's a nice round number.

Now let's draw our gear teeth on the wood. The contours of an involute gear tooth are generated by a string unwrapping from a "base circle". So the first thing we need to do is make a base circle. The diameter of this circle is just our pitch diameter (6 inches) multilplied be the cosine of our pressure angle. Using a calculator we calculate this to be

D = 6 x cos20 = 5.638 inches

So start by marking such a circle with a compass and cut it out of some material (preferably something thick that you can wrap a string around). Lay this disk onto the wood that you are going to make your gear out of and drive a nail through the center (where you stuck your compass) to attach it to the wood . Tape the end of a piece of string to the outer rim of the disk and wrap it around it about one turn. Attach a pencil to the end of the string (tie it near the tip of the pencil). Now strike an arc outward from the disk for a couple of inches. Since we want 24 teeth you should mark one of these lines (an involute) every 15 degrees (that's 360 divided by 24 teeth). Just rotate your disk 15 degrees each time and draw another curve. These are the contours of one side of each gear tooth.

Remove the disk temporarily and draw your "pitch" circle with your compass (a 6-inch circle, remember?). Now we need to draw the other side of the tooth. The new arc should cross the pitch (6") circle exactly half way between any two of the arcs you already drew. If your gear is big and your teeth are many, you can just measure the midpoint with a ruler. Otherwise you can draw a line at 7-1/2 degrees from where one of the old curves intersects the 6-inch circle (7-1/2 is half of 15) and this will give you your midpoint. Nail the disk back on and wind the string around it in the

*opposite* direction. Rotate it until the pencil is right on that point we just found and the string is taut. Strike your arc. Now rotate the disk 15 degrees and strike the rest of the curves like before.

OK, now all you need is the tops and bottoms of the teeth. The distance out from the 6-inch circle to the top of the tooth is the "addendum"; the distance inward to the bottom of a tooth is the "dedendum". In a perfect world these distances are just the reciprocal of the pitch (1/4 inch). In reality they need to be a little more to provide a little clearance for the gears to rotate freely. If you made them exactly 1/4 inch, the tops of the teeth of one gear would just touch the bottoms of the other. So let's add about a sixteenth and call the addendum/dedendum about 5/16" So you need to get your compass again and draw two circles: one will be 6.625 dia. and the other 5.375 dia.

Now you have drawn your whole gear profile! Just jigsaw it out!

But what about the other gear? Believe it or not, you can make it any size or number of teeth you want! As long as the other gear has the same DP (4) and the same pressure angle (20 deg.) they will mate perfectly. So you can either make another identical gear, or one of a different size. This time you have to pick either a number of teeth N, or a pitch diameter D. If you pick one, the other can be calculated

N = D x DP or D = N / DP

So if you wanted the second gear to have 30 teeth, the pitch dia. would then be 30 / 4 = 7.500 inches. Then you just do the same thing over again.

Good luck!

Don

From: "Richard" Newsgroups: sci.engr.mech Sent: Monday, November 10, 2003 7:48 AM Subject: Gear drawing program

This was a very readable tutorial on the basics of gear design.. (something I've wondered about for a while now...) The Handbooks that I've browsed haven't made it as easy to understand as you just did. Thanks.

Al...

look up GEARGEN - free gear drawing code in DOS. Lots of sources listed on GOOGLE.