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
Torsion of a curve a three times differentiable function of "t" with values in R and the vectors are linearly independent. Then the torsion can be computed from the following formula: Here the primes denote the derivatives with respect to "t" and the cross denotes the cross product. For "r" = ("x", "y", "z"), the formula in components is Torsion of a curve In the elementary differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the plane of curvature. Taken together, the curvature and the torsion of a space curve are analogous to