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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. [1] The evolute of an involute is the original curve.
The evolute of a curve (blue parabola) is the locus of all its centers of curvature (red). The evolute of a curve (in this case, an ellipse) is the envelope of its normals. In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point ...
Because the evolute of a nephroid is another nephroid, the involute of the nephroid is also another nephroid. The original nephroid in the image is the involute of the smaller nephroid. inversion (green) of a nephroid (red) across the blue circle
Logarithmic spiral (pitch 10°) A section of the Mandelbrot set following a logarithmic spiralA logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature.
Permian genera include Parastenopoceras, a smooth, involute form with a semiellptical whorl section and ventral saddle; Plummeroceras, a form similar to Domatoceras but more evolute and with a deep ventral lobe; Pselioceras, a smooth evolute form with a perforate umbilicus, ovoid whorl section, and suture crossing straight over the venter; and ...
The involute gear profile, sometimes credited to Leonhard Euler, [1] was a fundamental advance in machine design, since unlike with other gear systems, the tooth profile of an involute gear depends only on the number of teeth on the gear, pressure angle, and pitch. That is, a gear's profile does not depend on the gear it mates with.
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