involuteˈɪn vəˌlut; ˌɪn vəˈlut
involute
English Definitions:
involute, rolled (adj)
especially of petals or leaves in bud; having margins rolled inward
involute (adj)
(of some shells) closely coiled so that the axis is obscured
involute (Noun)
A curve that cuts all tangents of another curve at right angles; traced by a point on a string that unwinds from a curved object.
involute (Verb)
To roll or curl inwards.
involute (Adjective)
Difficult to understand; complicated.
involute (Adjective)
Having the edges rolled with the adaxial side outward.
involute (Adjective)
Having a complex pattern of coils.
Involute
In the differential geometry of curves, an involute 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, 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.
Involute
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve.The evolute of an involute is the original curve. It is generalized by the roulette family of curves. That is, the involutes of a curve are the roulettes of the curve generated by a straight line. 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), where he showed that the involute of a cycloid is still a cycloid, thus providing a method for constructing the cycloidal pendulum, which has the useful property that its period is independent of the amplitude of oscillation.
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"involute." Kamus.net. STANDS4 LLC, 2024. Web. 23 Apr. 2024. <https://www.kamus.net/english/involute>.
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