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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. It is generalized by the roulette family of curves. That is, the involutes of a curve are the roulettes of the curve generated by a straight line.
The involute function is mathematically expressed as a function of pressure angle. inv α= tanα−α inv α = tan α − α. The involute function can also be used to express the relationship between pressure angle and roll angle. The previous figure illustrates the involute function in the context of the roll angle and pressure angle.
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. This is part of a special branch of geometry called ...
Apr 1, 2006 · The applications of these two entities are indispensable to the vast majority of parallel axis gearing, cams, splines, and serrations in use today. (Figure 1) Figure 1: The involute curve is determined by the locus of points that are generated by a line unwound on it’s base circle.
- Gear Solutions Magazine
7.3.1 Generation of the Involute Curve. Figure 7-3 Involute curve. 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. It may also be defined as a path traced by the end of a string which ...
An involute curve is a curve that is traced by a point on a taut string as it is unwound from a stationary circle. The curve is formed by the intersection of the string with a plane that is tangent to the circle. The key feature of the involute curve is that it is self-similar, meaning that its shape remains unchanged when it is scaled up or ...
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3 days ago · Involute. 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.
