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- The locus of the centre of curvature, as Q varies on the curve, is called the evolute of the curve. The original curve is called an involut e of the new one.
www.cambridge.org/core/books/book-of-curves/evolutes-and-involutes/4B7CB8F6DC7ACDC6002F6D0763407C1C
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.
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.
During rotation each flank moves to a parallel involute. No matter where the two touching flanks have their contact point, the distance to parallel involutes is the same. Therefore: If one wheel rotates with constant speed, then so does the other - no vibrations are excited.
All involutes of a given curve are parallel to each other. This property also makes it easy to see that evolute of a curve is the envelope of its normals. Two involutes of a ellipse. Involute and Evolute. If curve A is the evolute of curve B, then curve B is the involute of curve A.
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.
The curve most commonly used for gear-tooth profiles is the involute of a circle. This involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle.
