A menudo se traza sin saberlo: cuando un hilo tenso o un cable se desenrollan de una bobina circular sus puntos describen la evolvente de la circunferencia de esa bobina. Fue estudiada originalmente por Christian Huygens, que trataba de diseñar relojes de péndulo para uso marino. Huygens utilizó la cicloide para forzar la oscilación regular del péndulo. Cuando un hilo tenso se enrolla en una cicloide cada uno de sus puntos describe un cicloide, es decir, la curva de desarrollo de una cicloide es una cicloide, como la de una circunferencia es una evolvente. La aplicación a los perfiles de las ruedas dentadas fue propuesta por Leonhard Euler.

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In the differential geometry of curves, an involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its free end as it is wound onto that given curve; or in reverse, unwound. It is a roulette wherein the rolling curve is a straight line containing the generating point. For example, an involute approximates the path followed by a tetherball as the connecting tether is wound around the center pole. If the center pole has a circular cross-section, then the curve is an involute of a circle. Alternatively, another way to construct the involute of a curve is to replace the taut string by a line segment that is tangent to the curve on one end, while the other end traces out the involute. The length of the line segment is changed by an amount equal to the arc length traversed by the tangent point as it moves along the curve. The evolute of an involute is the original curve, less portions of zero or undefined curvature. Compare Media:Evolute2.gif and Media:Involute.gif If the function is a natural parametrization of the curve (i.e., for all s), then : parametrizes the involute. The notions of the involute and evolute of a curve were introduced by Christiaan Huygens in his work titled Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae (1673).

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