Cycloid Cycloid A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity, and is also the form of a curve for which the period of an object in descent on the curve does not depend on the object's starting position. The cycloid has been
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