Explore: Involute Curve

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

as clocks. 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 curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. On

These curves can also be constructed using circular arcs centered at crossings of an arrangement of lines, as the involutes of certain curves, or by

evolute of M. Evolutes are closely connected to involutes: A curve is the evolute of any of its involutes. Apollonius (c. 200 BC) discussed evolutes in

Twisted cubic Viviani's curve Caustic including Catacaustic and Diacaustic Cissoid Conchoid Evolute Glissette Inverse curve Involute Isoptic including Orthoptic

example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under

involute polar angle is the angle between a radius vector to a point, P, on an involute curve and a radial line to the intersection, A, of the curve with

based on the cycloid and involute curves. Cycloidal gears were more common until the late 1800s. Since then, the involute has largely superseded it,

gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola. The curve appears in the design of certain