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- Dictionaryinvolute/ˈɪnvəl(j)uːt/
adjective
- 1. involved or intricate: formal "the art novel has grown increasingly involute"
- 2. curled spirally. technical
noun
- 1. the locus of a point considered as the end of a taut string being unwound from a given curve in the plane of that curve.
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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.
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.
1. a. : curled spirally. b (1) : curled or curved inward. (2) : having the edges rolled over the upper surface toward the midrib. an involute leaf. c. : having the form of an involute. a gear with involute teeth. 2. : involved, intricate. involute. 2 of 3. noun. : a curve traced by a point on a thread kept taut as it is unwound from another curve.
Oct 28, 2024 · Involute. Download Wolfram Notebook. 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.
This EzEd video explains WHAT is an INVOLUTE and step by step method on how to CONSTRUCT an INVOLUTE of a circle of DIAMETER 30mm. String length is equal to...
If the curve \({\gamma_1}\) is the evolute of the curve \(\gamma,\) then the initial curve \(\gamma\) is called the involute of the curve \({\gamma_1}.\) We denote the center of curvature by the point \(C\) with coordinates \(\left( {\xi ,\eta } \right).\) If the curve \(\gamma\) is given in parametric form
In an involute gear, the profiles of the teeth are involutes of a circle. The involute of a circle is the spiraling curve traced by the end of an imaginary taut string unwinding itself from that stationary circle called the base circle, or (equivalently) a triangle wave projected on the circumference of a circle.
An involute (also known as an evolvent) is a form of curve in mathematics that is dependent on another shape or curve. The location of a point on a taut string as it is either unwrapped from or wrapped around a curve is called an involute of a curve. It’s a type of curve that belongs to the roulette family of curves.
The involute of a circle is a curve that is tangent to the circle at the point of contact and is generated by a point on the circle that moves so that its distance from the center of the circle always equal to the radius of the circle.
