Return of the plane evolute

We consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree d ≥ 2 , we provide lower bounds for the following four numerical invariants: (1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d ; (2) the maximal number of real cusps which can occur on the evolute of a real-algebraic curve of degree d ; (3) the maximal number of crunodes which can occur on the dual curve to the evolute of a real-algebraic curve of degree d ; (4) the maximal number of crunodes which can occur on the evolute of a real-algebraic curve of degree d .