Conchoid.

Conchoid with a curve B like base: a curve B, a point O, a segment of length a are fixed in a plane; every straight line s passing through O intersects the curve B on the points M,N,...;we take on s couples of segments MP=MQ=a, NP=NQ=a... The locus of points P and Q when s rotates around O is named conchoid with base B, pole O, interval a.

Mechanical linkage for the conchoid of Nicomede .

The conchoid of Nicomede has a straight line like curve -base B. The cursor M fixed in a point of the rod PQ, moves on the straight slot ff. The rod PQ rotates around the point O fixed on the plane, at distance d from ff. We take two points P and Q on the rod such as MP=MQ=b.The points P and Q describes the conchoid with pole O, base ff and interval b. The conchoid is made up of two branches, one of them has a cusp or a node or an isolated point on O , if b>d, b=d, d>b. This curve is very famous because it is possile to draw it exactly (the " compass" was invented by Nicomede, about 200 a.C. ) and because it helped the solution to the problems of cube duplication and angle trisection.