Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
Singular point of a curve origin is a point of inflection of the curve. If the coefficients of "x" and "x" are both 0 then the origin is called "point of undulation" of the curve. This analysis can be applied to any point on the curve by translating the coordinate axes so that the origin is at the given point. If "b" and "b" are both 0 in the above expansion, but at least one of "c", "c", "c" is not 0 then the origin is called a double point of the curve. Again putting "y"="mx", "f" can be written Double points can be classified