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- Involute : If C is a curve and C ' is its evolute, then C is called an involute of C '. Any parallel curve to C is also an involute of C '.
mathshistory.st-andrews.ac.uk/Curves/Definitions/
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.
Involute or evolvent is the locus of the free end of this string. The evolute of an involute of a curve is referred to that original curve. In other words, the locus of the center of curvature of a curve is called evolute and the traced curve itself is known as the involute of its evolute.
Aug 6, 2022 · Involute: Given a regular parametric curve $\gamma$, an involute for $\gamma$ is another parametric curve $\gamma^*$ defined on the same interval such that i) $\gamma^*(t)$ lie on $T(t)$ (tangent to $\gamma$ at $t$). ii) $T(t)$ and $T^*(t)$ (corresponding tangent vectors) are orthogonal.
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.
Involute : If C is a curve and C' is its evolute, then C is called an involute of C'. Any parallel curve to C is also an involute of C '. Hence a curve has a unique evolute but infinitely many involutes.
Oct 28, 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.
Involute : If C is a curve and C' is its evolute, then C is called an involute of C'. Any parallel curve to C is also an involute of C '. Hence a curve has a unique evolute but infinitely many involutes.
