Cycloid plates of golden age violins are closely modeled by curtate cycloid curves. Later work indicates that curtate cycloids do not serve as general models for these curves, which vary considerably. 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
Torsion of a curve development of the subject. The radius of torsion, often denoted by σ, is defined as Geometric relevance: The torsion formula_9 measures the turnaround of the binormal vector. The larger the torsion is, the faster the binormal vector rotates around the axis given by the tangent vector (see ). In the animated figure the rotation of the binormal vector is clearly visible at the peaks of the torsion function. Let r = r("t") be the parametric equation of a space curve. Assume that this is a regular parametrization and that the curvature of the curve does not vanish. Analytically, r("t") is