NonCircular Gear Calculator
The following online calculator computes
the raw outlines of two meshing noncircular gears based on the polar equation of Gear_{1},
the desired Gear_{1}toGear_{2} pitch length ratio, and desired number of teeth.
Two meshing noncircular gears can conceptually be represented by two
touching curves, called pitch or reference curves. The calculator allows the curve for Gear
_{1}
to be specified in the form of an arbitrary mathematical function
f(u) in the polar coordinate system.
The function must define a closed, nonintersecting and smooth curve.
Below are two examples of functions which meet these requirements and are therefore suitable for noncircular gear design:
The polar equation for Gear_{1} is to be entered in a syntax used by all programming languages: parentheses are required with mathematical
functions, and the multiplication symbol (*) must not be omitted. Incorrect: sin 2u. Correct: sin(2*u).
The N and M parameters together specify the ratio of the lengths of Gear_{1}'s and Gear_{2}'s pitch curves.
To put it differently, when Gear_{1} makes N full rotations, Gear_{2} makes M full rotations.
The following diagram illustrates the effect of 4 different N/M combinations for this ellipsedefining function: 10 / sqrt( sin(u) * sin(u) + 5 * cos(u) * cos(u)).
Note that the N and M values cannot be picked at random. They must reflect the periodicity of the main gear function.
The ratio N/M times the number of periods of the function must be an integer. In the example above, the periodicity of the function is 2
and therefore (N=1, M=2) and (N=3, M=2) are valid combinations. If the periodicity were, say, 1, they would not be.
The Number of Teeth (Z) must be divisible by both N and M. The actual number of teeth in Gear_{1} is Z / N, and in Gear_{2} Z / M.
The Tooth Angle (α) specifies the slanting angle of the tooth flanks. It is 20° by default.
The Tooth Height Ratio specifies the height of each tooth relative to the distance between the teeth. It is 1 by default.
NonCircular Gear Generating Script

Related: How to Model NonCircular Gears in Blender 2.8+