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.

Mathematical review of the involute curve and its significance to mechanical gear systems. 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 involute gear profile is the most commonly used system for gearing today, with cycloid gearing still used for some specialties such as clocks. In an involute gear, the profiles of the teeth are involutes of a circle.

5 days ago · Attach a string to a point on a curve. 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.

Figure 3.5 illustrates how an involute gear tooth profile is generated. It shows how the pitch line of a rack cutter rolling on a pitch circle generates a spur gear. Gear shapers with pinion cutters can also be used to generate involute gears.

The involute function is a function that takes as argument an angle — the pressure angle — and returns a value that corresponds to the width of the involute curve at that point. The formula for the involute function is φ = tan(α) − α .

Involute of an angle calculator and finding an angle by the given involute. Plunging into the theme of gears and their calculations, I've encountered involute and evolvent terms. I thought that's interesting, and they deserve separate calculators, see them below.

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.

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.

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