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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 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.
Mean cone distance in bevel gears is the distance from the apex of the pitch cone to the ... the involute polar angle is the angle between a radius vector to ...
Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
Thymic involution is the shrinking of the thymus with age, resulting in changes in the architecture of the thymus and a decrease in tissue mass. [1] Thymus involution is one of the major characteristics of vertebrate immunology, and occurs in almost all vertebrates, from birds, teleosts, amphibians to reptiles, though the thymi of a few species of sharks are known not to involute.
An involute helical gear is the base pitch in the normal plane. It is the normal distance between parallel helical involute surfaces on the plane of action in the normal plane, or is the length of arc on the normal base helix. It is a constant distance in any helical involute gear. Transverse base pitch, p b, p bt
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Involute spline where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. The curves increase strength by decreasing stress concentrations. Crowned splines where the sides of the equally spaced grooves are usually involute, but the male teeth are modified to allow for misalignment. Serrations