Involute gears with dh_gear_4

I have questions about Jim Hamilton’s dh_gear_4 plugin. I’ve got it installed and I’m trying to replicate this gear:

It has 17mm outside diameter, 15 teeth, pressure angle 20 degrees, step angle 15 degrees. I’ve set the pitch radius to 8.5mm (half of the outside diameter) and I get a flat (no height) profile of a 15-tooth gear. The shape looks correct but the size is much larger than expected: 19.72mm:

How can I constrict the size to what I need?

By scaling down to 86.2%, I get pretty close to the right size but the minor diameter at the base of the teeth is slightly (about 2.2mm) larger than the original gear:

With some estimating and eyeballing, I can push/pull the gear to the height I need and rotate the top face to approximate the angles but it’s not very precise.

Is there a more accurate way to do this? Am I skipping some additional steps?

I’m using SketchUp Make 2017, btw.

I would suggest modeling as if millimeters are meters after setting Units to Meters.

Pitch diameter is not the same as the outside diameter of a gear. There’s a formular to figure that out. You’ll probably get close enough by scaling it, though.

What angle do you want on the teeth?

Just playing and I have this:

Hi DaveR. I actually have done this in meters to be scaled back down when it’s done. I wasn’t sure about pitch diameter. I set it for 8.7m radius and got about 19.72 OD and I couldn’t find anything that had a circle radius of 8.7 so I assume, as you say, there’s some formula I’m not aware of.

The original gear is from am stl postyed online but the designer says the “slant of teeth” is 15 degrees. That appears to be the case. At first, I tried Push/Pull-ing the profile up half the height to 5m then rotating the top face 15 degrees but that’s not the same as the angle of the teeth. (Then I pulled up another 5mm and rotated the top face the other way 15 degrees.)

What parameters did you use to make that double helix? Yours doesn’t have the triangles on the edges of the teeth like mine.


No. It shouldn’t be the same.

I didn’t know what angle the teeth should be set to so I guessed. I softened the edges after completing the lower half of the gear. Instead of the second Push/Pull step I copied the group up in the blue direction and flipped it. Then I used Outer Sheel to combine the halves.

Hang on and I’ll record a video to show.

I sent you a private DM with a link to the video I recorded.

I’m still waiting for that link to say it’s finished processing. When I click on it, it wants me to signon to Flickr. I’ll have to create a Flickr account.

I just tried the 15m pitch circle and it does give me a gear with 17m OD. How does that work? This gets the job done but I’d like to know for future reference how to set the pitch radius for a desired OD. When you drew the gear earlier, how far did you rotate the top face to get the 15 degree angle on the teeth? I found through trial; and error, that rotating 10.24 degrees got there but I don’t know why. Again, is there a formula for how far to rotate for the desired angle? It sure seems like at some height, the rotation and the tooth angle would be equal. Not, of course, at a height of 5m.

Don’t think about the gears, think about the mating circles instead. Example: for a 3:1 gear-train ratio, one circle needs to be 3X the other circle and have 3X times as many teeth.

Here’s a newer version of the gear plugin:

jimhami42_rack_and_pinion.rbz (3.6 KB)


Aah! I hadn’t seen that second link until just now. I see how you did the angle and the rotation. Very clever. As always, you’ve been a huge help. I’ll practice those techniques. I didn’t know about exporting without first scaling down. I’ve made a mistake that way a few times (with units set to millimeters) and wound up with a huge stl that was hundreds of times too big. So I keep two copies of each component, one full size and one scaled down for exporting. I’ll try what you suggested. Thanks again. I learned a few things today.

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Trying creating involute in Geogebra (traced in green) vs constructing (black+red) curve in SketchUp:

(just reading about gear)

p.s. scale in Geogebra is 2x

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