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A curve that is obtained by attaching a string which is imaginary and then winding and unwinding it tautly on the curve given is called involute in differential geometry. Involute or evolvent is the locus of the free end of this string
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.
Nov 26, 2024 · Extend the string so that it is tangent to the curve at the point of attachment. Then wind the string up, keeping it always taut. The locus of points traced out by the end of the string is called the involute of the original curve, and the original curve is called the evolute of its involute.
An involute, specifically a circle involute, is a geometric curve that can be described by the trace of unwrapping a taut string which is tangent to a circle, known as the base circle. The circle involute has attributes that are critically important to the application of mechanical gears.
The set of all centers of curvature of the curve \(\gamma\) is called the evolute of the curve. If the curve \({\gamma_1}\) is the evolute of the curve \(\gamma,\) then the initial curve \(\gamma\) is called the involute of the curve \({\gamma_1}.\)
Involutes are typically described as the points that a string traces when it is unwrapped from a circle or other curve. More useful is the property that every point on the involute is tangent to the involute and tangent to some ray of the generating circle.
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What is an Involute Curve? §An Involute is described as the path of a point on a straight line, called the generatrix, as it rolls along a convex base curve (the evolute). §The Involute Curve is most often used as the basis for the profile of a spline or gear tooth.
