# Cam curvature and undercut screening
# Scope: Polar pitch-curve local curvature from supplied derivatives with respect to radians.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

radius = 40 mm
firstDerivative = 5 mm
secondDerivative = 10 mm
rollerRadius = 5 mm

curvatureRadius := (radius^2+firstDerivative^2)^1.5/(radius^2+2*firstDerivative^2-radius*secondDerivative) [mm]

check roller below pitch curvature: rollerRadius < curvatureRadius

scenario alternative: radius = 32 mm