How to cut a Gear

CNC Machining or Laser Cutting

Designing Gear Trains

For the purposes of this project, we will be using a cycloid gear tooth profile,
instead of the standard involute profile used in industry.  Cycloid gers are just easier to cut, and have been used
in clocks, some of the oldest gear trains still running!

Since you have yet to take learn about gear trains in your course work, a few definitions are in order.
The big gear is called a gear, the small gear is called a pinion.
Two gears should be sparated my the half of the sum of the two pitch circle diameters.


We have found that gears of a diametral pitch of 10 is about the minimum size possible with the MDF board.
(diametral pitch is the number of teeth on a gear per inch of its diameter)
All gears drawn to the same diametral pitch will mesh properly with each other.
This makes calculations easy, if you want a 36 tooth gear, its pitch circle diameter is 36/10=3.6".
Thus for the above figure, with a 36 tooth gear and a 11 tooth pinion, they should be separated by:

Gear pitch dia.  36 tooth /10 diametral pitch = 3.6"
Pinion pitch dia.  11 tooth /10 diametral pitch = 1.1"

Shaft to shaft distance = (3.6"/2) + (1.1"/2) = 2.35"

Gear Ratios

For the above gear train, each revolution of the 11 tooth pinion, will, of course, move the 36 tooth gear through 11 teeth.
11/36 = .31 of a revolution
.31 x 360 degrees = 110 degrees

Drawing Gears Simplified

For this simplified cycloid gear profile;
the distance from the pitch circle to the top of the gear tooth is the addendum,
the distance from the pitch circle to the bottom of the gear tooth is the dedendum.

Begin by drawing the pitch circle.
(number of teeth/10 = circle diameter)
Now draw the the top tooth.

Notice that the center of the tooth radius is at the intersection between the tooth thickness and the pitch circle.
For simplicity, a radius of 0.0625" is used at the root of the tooth.
If you are drawing in AutoCAD, draw one tooth at the 12 o'clock position as shown.
Make sure that all the lines end and start at the same point.
Use the "PEDIT" command to transform all the individual lines into one long "Polyline".
Then, use the "ARRAY" command, in Polar mode to copy your teeth around the gear.
Finally, join all the gear teeth together with the "PEDIT" command.

The tables below list the appropriate values for gears and pinions of 10 diametral pitch.

Addendum 0.135"
Dedendum 0.157"
Tooth Radius 0.157"
Tooth Thickness 0.157"


Addendum 0.086"
Dedendum   6 tooth 0.151"
                    7 tooth 0.159"
                    8 tooth 0.167"
                > 10 teeth 0.179"
Tooth Radius 0.105"
Tooth Thickness 0.105"

Gear Calculator
*** NOTE ***
For CNC machining, I would suggest using a 10 dimetral pitch gear.
For laser cutting out of 1/8" plexi, probably no smaller than a 16 dimetral pitch.

If you want to use gears of a different pitch, you can
use my gear calculator for cyloid gears:
 Cycloid Gear Calcualtor (javascript)

Prof. Chan's Rubber Band Car

These gears have a 10 dimetral pitch.

Devin's Rubber Band Car

Page created: Jan 5, 2001,  Updated Jan 30th, 2014 by: Vincent Chan, Associate Professor, Department of Mechanical Engineering,
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