Our Involute Function Calculator is an essential tool for engineers, designers, and students working with gear geometry and cam profiles. Quickly compute the involute function value (inv(t)) and derive Cartesian coordinates (x, y) of a point on an involute curve, given the base circle radius and a specific roll angle. Achieve precision in your mechanical designs and analyses.
Formula:
The Involute Function (inv(t)) is defined as:
inv(t) = tan(t) - t (where t is in radians)
The parametric equations for an involute curve from a base circle of radius Rb are:
x = Rb * (cos(t) + t * sin(t))y = Rb * (sin(t) - t * cos(t))
Where:
Rb= Base Circle Radiust= Roll Angle (in radians), which is the angle between the generating line and the y-axis, or the angle through which the tangent to the base circle has rolled.