The geometry of the Moineau pump

The Moineau pump was invented in 1931 by the French engineer René Moineau and exhibits an intriguing geometry. The original design is based on hypo- and epi-cycloids and all except one design has cusps or points with infinite curvature. By using the support function to represent planar curves it is possible to give an explicit analysis of a general design and we can show that points of infinite curvature are unavoidable.