1. Move the point A along the circle[br]2. The point A' moves along a curve (of degree 6, a sextic). The bottom of the curve "looks like" a straight segment, but it is not. [br][br]Such linkages are used in car engines (and others) to transform linear into circular motion and in reverse direction. The fact that an almost (only) straight part explains why mechanical parts have to be changed from time to time.[br][br]The proof that the obtained geometric locus is a sextic has been obtained with GeoGebra Discovery:[br]a. The obtained equation is x^(6) - (24 * x^(5)) + ((3 * x^(4)) * y^(2)) + (16 * x^(4)) - ((48 * x^(3)) * y^(2)) + (2304 * x^(3)) + ((3 * x^(2)) * y^(4)) - ((96 * x^(2)) * y^(2)) - (5120 * x^(2)) - ((24 * x) * y^(4)) + ((2304 * x) * y^(2)) - (49152 * x) + y^(6) - (112 * y^(4)) + (768 * y^(2)) + 147456=0 [br]b. This equation describes the union of 2 disjoint loops, which cannot be distinguished by algebraic means as the polynomial is irreducible.