^{1} Department of Mathematics, Technical University of Denmark^{2} Department of Applied Mathematics and Computer Science, Technical University of Denmark

Abstract:

The scroll compressor is an ingenious machine used for compressing air or refrigerant, which was originally invented in 1905 by Léon Creux. The classical design consist of two nested identical scrolls given by circle involutes, one of which is rotated through 180° 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.