The Geometry of the Scroll Compressor

Abstract

The scroll compressor is an ingenious machine used for compressing air or refrigerant; it was originally invented in 1905 by Léon Creux. The classical design consists of two nested identical scrolls given by circle involutes, one of which is rotated through $\text{180}^{\circ}$ 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.