- Draw a circle in Rhino which will be the pitch circle of the gear.

The pitch circle is an imaginary circle on a gear that divides the gear teeth into addendums and dedendums (see diagram below).

**For example:**

I drew a circle with diameter equal to 6″.

- Run the Involute Gear Plug-In. You will be asked to select the pitch circle of the gear.

- You select your circle and press Enter. You are provided with the following options:

The plug-in demonstrates a summary of the data of the gear, given the selected circle and the default values of the plug-in. You can edit any of these values.

**teeth:**

the number of teeth of the gear

**module**:

the module of the gear m is the ratio of the diameter d of the reference circle divided by the number of teeth z:

**module = reference diameter/ number of teeth or m = d/z**

**Pitch:**

The circular pitch p (the pitch is the distance between equivalent points on adjacent teeth) of a gear is defined as:

**circular pitch = circumference/ number of teeth or p = ****π*d / z**

**PressAngle:**

** ** Pressure angle is general the angle at a pitch point between the line of pressure which is normal to the tooth surface, and the plane tangent to the pitch surface.** ** Pitch point is the point of intersection of the pitch circle and the profile of the tooth. See diagram below:

source: http://en.wikipedia.org/wiki/File:Pressure_profile.jpg

**Bevel:**

Defines the bevel angle of the gear. By default is set to 0.

** ****Accuracy:**

** **Number of points that define the involute curve of the gear tooth.

- I defined my gear by setting the number of teeth to 20. The gear is generated and the summary of the new data is displayed in the command window.

- If you want to design a second gear that will mess correctly with your first gear you have to make sure that they have the same pitch.

**p _{1} = p_{2}**

If we assume that we have one gear with pitch circle diameter d_{1 }and number of teeth z_{1 }and_{ }another gear with pitch circle diameter d_{2 }and number of teeth z_{2 }then the relation that connects the pitch circle diameter and the number of teeth of the two connected gears is the following:

** If: p _{1} = p_{2}**

**Then:
**

**π* d _{1} / z_{1} = **

**π* d**

_{2}/ z_{2}**d _{1} / z_{1} = d_{2} / z_{2}**

**d _{1} / d_{2} = z_{1} / z_{2}**

- You have to make sure that:

The pitch circle passes through the point where the teeth touch when one gear meshes with another.

The two pitch circles come in contact (See diagram below)

source: http://www.fi.edu/time/Journey/Time/Lessons/printgeomgears.html

- In Rhino:

Generate the pitch circle for the second gear. Run the Involute Gear plug- in. This time, after you have the pitch circle selected, set the pitch value equal to the pitch value of the previously generated gear.

The pitch value of my previous gear was 0.942.

I set the same value for the current gear.

Given the input pitch value, in order to keep a whole number of teeth the system will adjust the diameter of the pitch circle.

Rotate each of the gear so that their pitch point ( point of intersection of the pitch circle and the profile of the tooth) is on the same line.

Bring the pitch circles in contact.