How I drew a gear rack

I'm still working on learning Inventor. I haven't touched it in a year, having no project to use as a guinea pig (usually my stuff is 2D for CNC plasma). But I'm working on some revisions to my plasma table and thought I'd try to get better at using Inventor. In the process, I wanted to model (well, draw, anyway) the gear rack. I didn't immediately find exactly what I wanted online so I spent way too much time on this and didn't quit until I got it. I got it.

Well, I think so. I have some of the gear rack in real life and this looks right. Here's what I did:

The actual gear material is steel at 0.5" x 0.5" x length. It is 20 degree pressure angle, 20 pitch. According to the manufacturer (Moore Gear, www.mooregear.com) it has a 0.450 pitch line to back. The problem I couldn't figure out easily was how to figure the pitch; is that 20 TPI? No, it's not, because I have some of this stuff and it's darn sure not 20 TPI. The trick was a formula I found somewhere in my scorched earth search of the 'net. The formula I found was for 16 pitch teeth and gave the tooth spacing very much like wave length (meaning one point in the pattern to the next same point). That formula was:

1/16 * PI

I don't like coincidences so I figured that the 16 there corresponded to the tooth pitch. Using that for my 20 pitch gave me 1/20 * PI (of course). Which I used and worked. I'll have to verify the dimensions from my drawing to the actual gear when I get to my shop tomorrow, but this looks right.

I've attached a sample file. I started by making an extrusion of the base material, no problem. Then I sketched on one side of it the tooth pattern. It should be easy to see what I did by viewing the sketches in the file. The trick to the thing was knowing what the tooth spacing (pitch, "wave length") was. With the little "W" sketch constrained for angles, parallel, et cetera, and the middle of the depth set at the pitch line, the tooth spacing took care of the rest. Hopefully the file will explain this better than I can in text.

I will say that what I found was, to reproduce the teeth along the rack, don't use the pattern tool on the sketch (this I learned from reading other postings here). I tried for WAY too long to get that to work. Just pattern the feature/extrusion/cut.

You'll notice that I set the beginning of the first cut to 1/2 the spacing between teeth (check the sketch for the teeth) to simulate how I use this in real life where I stack these things end to end (although, in real life, I don't use 12" pieces). I then adjusted the length of the first extrusion to match the actual tooth pattern (ending a groove at the correct distance from the end) by dividing the length of the first extrusion (12 inches in this case) by the tooth pitch length "(1/20) * PI" for this 20 pitch rack, take the whole number there and multiply it by the tooth pitch length "(1/20) * PI" to get the actual length of the rack for stacking. For this example, the correct distance is ~11.93805 inches.

There are some gear modeling features in Inventor (maybe lots of them, probably lots of them) which probably makes this modeling/drawing irrelevant and a waste of time. I'm a caveman when it comes to Inventor and I don't know those methods. I'm also hard headed and I wanted to draw it just because. It improved my skills with Inventor so it wasn't a complete waste of time.

I'm no expert at this stuff and the formula for tooth pitch spacing may be wrong and maybe I got completely lucky that it looks right in the drawing. I'm sure if I'm wrong that someone here will correct me.

But hopefully this is right and will help someone.

--HC

_Test Gear Rack.ipt