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Involute curve also known as evolvent curve is a kind of differential curve. In mechanical engineering this curve is used a lot in gear design. This curve is used to get the gear tooth profile and when two gears of this profile mesh, the instantaneous contact point is only one and it moves along the curve profile. This property is known as line of action or line of Contact or pressure Line and this is why it is used extensively in gear design.

There are many ways to define an involute curve. I take a simple trigonometry method in cartesian coordinates system to explain this. To start let me explain how we define an involute curve.

Just see the picture on the left side. There is pole at the center and a sting is attached to it.
This topic explains how to create a metric (module) helical gear in pro engineer / Creo using relations and formulas. Helical gears are widely used gear types after spur gears. The nomenclature of spur and helical gears are all same except for the helix angle and its relevant parameters.

In spur gears the gear teeth is straight and parallel to the axis of rotation but in helical gears the gear teeth is at an angle to the axis of rotation and follows a helical path (aka Helicoid) along the pitch circle diameter.

Formulas for helical gear:

Transverse_module = normal_module / cos (helix_angle)

Normal_circular_pitch = pi * normal_module

Transverse_circular_pitch = pi * transverse_module

Transverse_pressure_angle = atan ((tan (normal_pressure_angle))/(cos (helix_angle)))

Outer_Diameter = pitch_diameter + (2 * normal_module)

Root_diameter = pitch_diameter - (2 * 1.25 * normal_module)

Base_diameter = pitch_diameter * cos (transverse_pressure_angle)

Normal_tooth_thickness = (pi * normal_module) / 2

Transverse_tooth_thickness = (pi * transverse_module) / 2

Lead = pi * Pitch_diameter / tan (Helix_angle)