The following online calculator computes
the parametric equations of a globoid (throated) worm shaft based on its basic dimensions,
shape and desired number of teeth in the matching gear wheel.
A globoid worm shaft is based on an hourglass shape cut out of a torus (shown in solid red.)
Its dimensions are defined by the radius of its narrowest section (r),
angular size of its arc (β) and the diameter of the corresponding gear wheel (shown in solid blue).
The latter is calculated as the user-specified total number of teeth (z) multiplied by the user-specified module (m).
The module is 1 by default, and is nothing more than a scaling factor for the entire worm/wheel design.
The z and β combination is subject to the following restriction: the number of teeth falling within
the arc, zβ = z * β / 360°, must be an integer number.
The effect of the Falloff Rate checkbox is demonstrated on the image below.
If the box is unchecked the worm's tooth height remains unchanged throughout the entire length of the spiral.
This is useful when the worm's surface is used to model the tooth profile for the matching gear wheel.
If the box is checked, the tooth height falls off gradually at the top and bottom of the spiral to become
flush with the hourglass surface. This option should be used for the final product.
