where ( r_b ) is the base circle radius and ( \theta ) is the roll angle. For helical gears, the transverse pressure angle ( \alpha_t ) relates to the normal pressure angle:
The lead ( L ) of the helix is:
[ L = \frac\pi \cdot d\tan \beta ]
[ x = r_b \cdot (\cos \theta + \theta \sin \theta) ] [ y = r_b \cdot (\sin \theta - \theta \cos \theta) ] helical gear generator