The geometry of the scroll compressor

The scroll compressor is an ingenious machine used for compressing air or refrigerant; it was originally invented in 1905 by Leon Creux. The classical design consists of two nested identical scrolls given by circle involutes, one of which is rotated through 180 degrees with respect to the other. By specifying not a parametrization of the curve, but instead the radius of curvature as a function of tangent direction and using the intrinsic equation of a planar curve, the design can be changed in a way that allows all relevant geometrical quantities to be calculated in closed analytical form.