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Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
An Archimedean spiral is, for example, generated while coiling a carpet. [5] A hyperbolic spiral appears as image of a helix with a special central projection (see diagram). A hyperbolic spiral is some times called reciproke spiral, because it is the image of an Archimedean spiral with a circle-inversion (see below). [6]
In mathematics, a conchospiral a specific type of space spiral on the surface of a cone (a conical spiral), whose floor projection is a logarithmic spiral. Conchospirals are used in biology for modelling snail shells, and flight paths of insects [1] [2] and in electrical engineering for the construction of antennas. [3] [4]
Regularly spiral: Bulloid: bubble-shaped Bulla; Coeloconoid a slightly concave conical shell in which the incremental angle increases steadily during growth (see: Calliostoma) Cone-shaped, obconic. Conus; Contabulate, short, with shouldered whorls; Convolute: aperture as long as the shell, nearly or quite concealing the spire. Cypraea ...
In the adjacent diagram, (a) and (b) are referred to as having an offset below center, while those in (c) and (d) have an offset above center. In determining the direction of offset, it is customary to look at the gear with the pinion at the right. For below center offset the pinion has a left hand spiral, and for above center offset the pinion ...
Hypoid spiral bevel gears. A hypoid is a type of spiral bevel gear whose axis does not intersect with the axis of the meshing gear. The shape of a hypoid gear is a revolved hyperboloid (that is, the pitch surface of the hypoid gear is a hyperbolic surface), whereas the shape of a spiral bevel gear is normally conical.
In cone-beam computed tomography (commonly abbreviated CBCT), the X-ray beam is conical. [11] Helical (or spiral) cone beam computed tomography is a type of three-dimensional computed tomography (CT) in which the source (usually of X-rays) describes a helical trajectory relative to the object while a two-dimensional array of detectors measures ...