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Curve traced by a string as it is unwrapped from another curve
An involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An example of the involute of a curve
Involute
Gear with teeth whose profile is an involute of a circle
specialties such 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
Involute_gear
errors and deflection under load. The base circle of an involute gear is the circle from which involute tooth profiles are derived. The base cylinder corresponds
List_of_gear_nomenclature
Curve traced by a point on a rolling circle
{\displaystyle \left({\frac {dx}{dh}}\right)^{2}={\frac {2r}{h}}-1.} The involute of the cycloid has exactly the same shape as the cycloid it originates
Cycloid
New leaf or frond development in botany
other. This folding mechanism makes the emerging leaf look like a tube. In involute vernation both margins on opposing sides of the leaf are rolled up towards
Vernation
Tumor originating from blood or lymph vessels
hemangioma: non-involuting, and rapidly involuting (beginning in the first year of life). A third variant is also recognised as partially involuting. Congenital
Vascular_tumor
Topics referred to by the same term
inverse Involution algebra, a *-algebra: a type of algebraic structure Involute, a construction in the differential geometry of curves Exponentiation (archaic
Involution
Extinct subclass of cephalopod molluscs
and oxycones: narrow and moderately involute. Discocone – Intermediate between oxycones and spherocones: involute and moderately broad. The modern Nautilus
Ammonoidea
Toothed gear based on epicycloids and hypocycloids
and watches, rather than the involute gear form used for most other gears. Cycloidal gears have advantages over involute gears in such applications in
Cycloid_gear
Rotating circular machine part with teeth that mesh with another toothed part
For involute gears, the teeth always exert force along the line of action, which, for involute gears, is a straight line; and thus, for involute gears
Gear
Simplest type of gear
with either an involute or cycloidal profile. When two gears mesh, it is possible that an involute portion of one contacts a non-involute portion of the
Spur_gear
Recreational mathematics planar boundary and area problem
can not enter the circular area dictates that the grazing area forms an involute. If the goat were instead tethered to a post on the edge of a circular
Goat_grazing_problem
Methods for transmitting power from a source to an application
is commonly referred to as the "540". All new types (2, 3, and 4) use involute splines, whereas Type 1 uses straight splines. Inch-denominated shafts
Power_take-off
Extinct genus of molluscs
Carinonautilus is a genus of extinct, Middle Cretaceous nautilid with a very involute, compressed shell in which the whorl section is higher than wide, umbilicus
Carinonautilus
Type of linear actuator
arc of involute, as in most gears. On the rack, on the other hand, the matching working surfaces are flat. One may interpret them as involute tooth faces
Rack_and_pinion
Centers of curvature of a curve
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
Evolute
Involucres occur in Marchantiophyta, Cycads, fungi, and many other groups. involute Rolled inward, for example when the margins of a leaf are rolled toward
Glossary_of_botanical_terms
Ridges or teeth on a drive shaft that transfer torque to interlocking components
directions, radial and axial. Involute spline where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. The
Spline_(mechanical)
Tool bits used in milling machines
Involute gear cutter – number 4: · 10 diametral pitch cutter · Cuts gears from 26 through to 34 teeth · 14.5 degree pressure angle
Milling_cutter
Process used to cut teeth into gears
the hob, and a drive motor. For a tooth profile which is theoretically involute, the fundamental rack is straight-sided, with sides inclined at the pressure
Hobbing
Semigroup in abstract algebra
In mathematics, particularly in abstract algebra, a semigroup with involution, or a *-semigroup, is a semigroup equipped with an involutive anti-automorphism
Semigroup_with_involution
Medical condition
population, and is an embryologic remnant that results from a failure to involute. In persistent left superior vena cava, the left brachiocephalic vein does
Persistent left superior vena cava
Persistent_left_superior_vena_cava
Extinct genus of molluscs
161 to 5 million years ago). They are characterized by a highly rounded involute shell with slightly sinuous suture patterns. Eutrephoceras typically possess
Eutrephoceras
Family of molluscs
inches). The Nautilidae, both extant and extinct, are characterized by involute or more or less convoluted shells that are generally smooth, with compressed
Nautilus
Genus of flowering plants in the daisy family
the way in which they were folded along their longitudinal axis: flat, involute (curled inwards) or revolute (curling backwards). If the end of the ray
Dahlia
Genus of molluscs (fossil)
largest species measuring around 2 m (6.6 ft). It possesses a moderately involute shell with flat or slightly rounded sides. Distinct primary and secondary
Parapuzosia
Plane curve; an epicycloid with radii differing by 1/2
is another nephroid, the involute of the nephroid is also another nephroid. The original nephroid in the image is the involute of the smaller nephroid
Nephroid
Angle on a gear
pressure angle, and the axial pressure angle. List of gear nomenclature Involute gear Halsey, Frederick Arthur (1913). Handbook for Machine Designers and
Pressure_angle
Mechanical transmission using multiple gears
Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio
Gear_train
to parallel cucullate Forming a hood, margins and tip curved downward involute Rolled upwards (towards the adaxial surface) plicate plicatus With parallel
Glossary_of_leaf_morphology
Genus of ammonites
Cleoniceras is a rather involute, high-whorled hoplitid from the Lower to basal Middle Albian of Europe, Madagascar, and the Transcaspian region. The shell
Cleoniceras
Drivetrain transmitting propulsion power
introduction and general influence factors". ISO. "ANSI/AGMA 2001 - Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth".
Transmission (mechanical device)
Transmission_(mechanical_device)
Central part of the thoracic cavity
lymph nodes The small mediastinal branches of the internal thoracic artery Thymus (involuted in adults) superior and inferior sternopericardial ligaments
Mediastinum
Species of grass
leaf-blades are erect or drooping; flat, or conduplicate (folded lengthwise) or involute (spiral); and from 10 to 45 cm long by 3–6 mm wide. The Latin specific
Cenchrus_alopecuroides
Botanical term for a cluster of flowers
hypanthodium, which bears numerous flowers on the inside of a convex or involuted compound receptacle. The genus Euphorbia has cyathia (sing. cyathium)
Inflorescence
Involution (shrinking) of the thymus after the neonatal period
reptiles, although the thymi of a few species of sharks are known not to involute. This process is genetically regulated, with the nucleic material responsible
Thymic_involution
Economic concept that describes an excess of competition
on the ways of living for youth and contemporary middle-class parents. Involuted King refers to someone who works extremely hard, by fair means or foul
Neijuan
1845 book by Thomas de Quincey
novel. Kimberly A. Garcia (2017). Involute Analysis: Virtual Discourse, Memory Systems and Archive in the Involutes of Thomas De Quincey. academicworks
Suspiria_de_Profundis
Superfamily of single-celled organisms
in varying planes about the longitudinal axis, which later may become involute or uncoil. Advanced forms may have secondary partitions within the chambers
Milioloidea
Genus of perennial plants from South Africa
flat or involute panicle scabrid 1⁄2–1 mm scabrid/viscid, fimbrate mauve C. a. scabridum scabridum linear to falcate, ≥11⁄2 mm glabrous, involute, sometimes
Corymbium
Mathematical curves generated by rolling other curves together
epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. On a basic level, it is the path traced by a curve while rolling on another
Roulette_(curve)
Medical condition
Thymic hypoplasia is a condition where the thymus is underdeveloped or involuted. There are various causes of thymic hypoplasia such as 22q11.2 deletion
Thymic_hypoplasia
the hypotenuse of the prior triangle Approximates the Archimedean spiral Involute 1673 x ( t ) = r ( cos ( t + a ) + t sin ( t + a ) ) , {\displaystyle
List_of_spirals
Symptom, also called "bent spine syndrome"
fibrosis (green) and fatty infiltration. Also observable is irregular distribution of involuted muscle fibers. (Trichrome, original magnification ×9100)
Camptocormia
Powered mechanical device
Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio
Machine
1966 studio album by Bob Dylan
Esquire, Robert Christgau said Dylan had "presented his work at its most involuted, neurotic, and pop—and exhilarating—in Blonde on Blonde." Blonde on Blonde
Blonde_on_Blonde
Eccentric gear reduction mechanism
backlash and high torque capacity while being compact in size, unlike involute gearboxes. They are useful in situations where low speed with high torque
Cycloidal_drive
Superfamily of nautiloids
family in this group. Species in the Nautilaceae are generally smooth and involute with straight to strongly sinuous sutures and a small siphuncle. Some groups
Nautilaceae
Genus of molluscs (fossil)
North America and parts of Europe. The shell of Gastrohoplites is variably involute to evolute. Sides and venter are flat, shoulders sharp. Ribs more or less
Gastrohoplites
Curve that winds around a central point
consists of a sequence of circle arcs. The involute of a circle looks like an Archimedean, but is not: see Involute of a circle. The following considerations
Spiral
Extinct order of molluscs
coiled discoidal shells that may be evolute with inner whorls exposed or involute with only the outer whorl showing. In a few later forms the shell became
Ceratitida
French mathematician (1661–1704)
brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point. L'Hôpital exchanged ideas with
Guillaume_de_l'Hôpital
Device which converts input forces and motion to output forces and motion
is a higher pair called a cam joint. Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints. A kinematic
Mechanism_(engineering)
Catacaustic and Diacaustic Cissoid Conchoid Evolute Glissette Inverse curve Involute Isoptic including Orthoptic Negative pedal curve Fish curve Orthotomic
List_of_curves
Extinct family of molluscs
Cretaceous. Members of the Phylloceratidae are characterized by smooth, involute shells with very thin walls. Many are covered with fine growth lines but
Phylloceratidae
heterotopic brain tissue) Nasolacrimal duct cyst Nevus psiloliparus Non-involuting congenital hemangioma Omphalomesenteric duct cyst (omphalomesenteric duct
List_of_skin_conditions
Vascular tumor derived from blood vessel cell types
birth. They tend to grow quickly for up to a year. Most then shrink or involute without further problem, however some can ulcerate and form scabs which
Hemangioma
Organ found in mammalian skin
cycles of various phases: anagen is the growth phase; catagen is the involuting or regressing phase; and telogen, the resting or quiescent phase (names
Hair_follicle
blood during human embryonic development. Normally, the trigeminal artery involutes after the formation of the posterior communicating artery. However, in
Trigeminal_artery
Industrial action in which employees do no more than the minimum required
2022. Retrieved 24 September 2022. Liu, Yi-Ling (14 May 2021). "China's "Involuted" Generation". The New Yorker. Retrieved 28 March 2022. Wang, Qianni; Ge
Work-to-rule
Genus of molluscs (fossil)
genus of Lower Triassic ammonites characterized by a somewhat strongly involute and greatly compressed shell with a sharp, oxyconic, venter. Beatites was
Beatites
Genus of molluscs (fossil)
Poland, and Israel. Beneckeia shells are compressed smooth oxycones, involute with sharp venters. Sutures are multilobed with small adventitious lobes
Beneckeia
Genus of flowering plants
places, sympatric with) the Cryptocoryne, but is distinguishable for its involute vernation (leaf growth); comparatively, Cryptocoryne tends to exhibit convolute
Lagenandra
Shape with same width in all directions
circular arcs centered at crossings of an arrangement of lines, as the involutes of certain curves, or by intersecting circles centered on a partial curve
Curve_of_constant_width
Species of oak tree
margins, sometimes more or less three-lobed. They come out of the bud involute, bright red, covered with rusty down above and white tomentum below. When
Quercus_imbricaria
Species of tree
veins prominent. The leaves come out of the bud conduplicate with slightly involute margins, pale yellow green, downy; when full grown are thin, bright green
Celtis_occidentalis
Benign skin irregularity which appears near the time of birth
infantile hemangioma, colloquially called a strawberry mark, is a benign self-involuting tumor (swelling or growth) of endothelial cells, the cells that line blood
Birthmark
Leg joint in primates
smaller toward the back. This diminishing radius produces a series of involute midpoints (i.e. located on a spiral). The resulting series of transverse
Knee
Species of tree
are found in the axils of the primary veins. They come out of the bud involute, purplish, when full grown are bright green, smooth above, pale green,
Catalpa_bignonioides
Genus of molluscs (fossil)
to the goniatitid family Reticuloceratidae which are characterized by involute subdiscoidal shells covered by linear or biconvex growth lines that may
Aphantites
Frechiella is an ammonite with a smooth, somewhat globose involute shell that lived during the later part of the Early Jurassic, which has been found in
Frechiella
Extinct genus of molluscs
carnivores are variable in form, depending on species; ranges from evolute to involute, compressed lenticular to globose with rounded to flattened venter and
Cenoceras
Imposed limitations in computer-aided design
such that they share exactly one point A line tangent to an arc in an involute gear Dimensions Points, Lines, Arcs etc. Forces various entities to maintain
Constraint (computer-aided design)
Constraint_(computer-aided_design)
Process of changing from working by hand or with animals to work with machinery
teeth ca. 1650. In the 18th century involute gears, another mathematical derived design, came into use. Involute gears are better for meshing gears of
Mechanization
Extinct genus of molluscs
Ceratitida. The family to which Austrotrachyceras belongs, Trachyceratidae involute, highly ornamented shells and ceratitic to ammonitic sutures. Sepkoski
Austrotrachyceras
Extinct suborder of ammonites
forms, including evolute shells where all whorls are exposed, and strongly involute shells with only the outer whorl visible. Shells may be heavily ribbed
Ammonitina
Self-similar growth curve
Relation to other curves: Logarithmic spirals are congruent to their own involutes, evolutes, and the pedal curves based on their centers. Complex exponential
Logarithmic_spiral
Cone- or frustum-shaped gears for shafts whose axes intersect
with a 1:1 ratio. The cylindrical gear tooth profile corresponds to an involute (i.e. a triangle wave projected on the circumference of a circle), whereas
Bevel_gear
Genus of molluscs (fossil)
to the ammonoid family Psiloceratidae. The shell of Kammerkaroceras is involute, all whorls except for the outermost hidden from view, discoidal with sigmoidal
Kammerkaroceras
Gear in a shape other than a circle
Zarebski I., Salacinski T.: Designing of non-circular gears "Laczik- Involute Profile of Non-Circular Gears" (PDF). Archived from the original (PDF)
Non-circular_gear
Genus of molluscs (fossil)
family to which Boreotrachyceras belongs, Trachyceratidae, has more or less involute, highly ornamented shells and ceratitic to ammonitic sutures. Sepkoski
Boreotrachyceras
Overview of and topical guide to geometry
Frieze group Golden angle Holditch's theorem Interactive geometry software Involutes Goat grazing problem Parallel postulate Polygon Star polygon Pick's theorem
Outline_of_geometry
Extinct family of molluscs
related to octopus and squid. Pseudonautilids are characterized by an involute, generally compressed, nautiliconic shell; highly sinuous "goniatitic"
Pseudonautilidae
Extant subclass of cephalopods
ontogeny of the animal. Modern nautiluses have deeply coiled shells which are involute, meaning that the larger and more recent whorls overlap and obscure older
Nautiloid
Small hole in algae, fungi or plants
also used in higher plants, for example to denote the opening of the involuted syconium (fig inflorescence) through which fig wasps enter to pollinate
Ostiole
Genus of flowering plants
picture bend in the periphery, so the placentation is not parietal but involute." Holstein (2015): "a Ripening fruit of C. hirtella. Note the typical lobulate
Coccinia
Extinct genus of molluscs
Nautilaceae in Kümmel 1964. Aturia is characterized by a smooth, highly involute, discoidal shell with a complex suture and subdorsal siphuncle. The shell
Aturia
Genus of single-celled organisms
genus of foraminifera with an agglutinated, planispirally coiled, semi-involute shell, known from the Egyptian Sinai. It lived during the early part of
Ismailia_(foraminifera)
Genus of molluscs (fossil)
stage of the Middle Triassic belonging to the ammonoid subclass. Shell involute, whorls strongly embraced, venter acutely rounded. Suture curved, subammonitic;
Aristoptychites
Catacaustic and Diacaustic Cissoid Conchoid Evolute Glissette Inverse curve Involute Isoptic including Orthoptic Orthotomic Negative pedal curve Pedal curve
List_of_mathematical_shapes
Species of tree
primary veins grooved above, prominent beneath. They come out of the bud involute, red bronze, tomentose and downy; when full grown are bright dark green
Malus_coronaria
Species of plant
95 ft) tall and 60–90 cm (2.0–3.0 ft) wide. The blades are rolled, flat to involute during maturity and are about 15–35 cm long and 1.3–3.5 mm wide at the
Muhlenbergia_capillaris
Suborder of cephalopods
stock of the suborder, includes the living Nautilus. The Nautilidae are involute or slightly evolute and generally smooth with straight to sinuous sutures
Nautilina
Dutch mathematician and physicist (1629–1695)
principle Huygens's lemniscate Huygens–Steiner theorem Huygens's tritone Involute Injection locking Repetition pitch Magic lantern Pendulum clock Problem
Christiaan_Huygens
Withdrawn DIN 5483-3 DIN 5480-1 Involute splines based on reference diameters – Part 1: Generalities Active DIN 5480-2 Involute splines based on reference
List_of_DIN_standards
Species of carnivorous plant
some growth forms it may be significantly longer. Vernation is geniculate-involute, the lamina first unfolding from the petiole, and the lamina margin and
Drosera_capensis
Extinct genus of molluscs
belonging to the trigonoceratacean family Grypoceratidae, characterized by involute, inflated shells, which at maturity develop narrowly rounded keel-like
Gryponautilus
Book by Walter Benjamin
demonologies of the concept as a theological entity in exponentially involuting footnotes whose demotion to the margins he neglects to perform. He speaks
The Origin of German Tragic Drama
The_Origin_of_German_Tragic_Drama
Device to increase vehicle traction
usually straight, they may have more complex shapes, including spikes and involute curves, depending on the type of terrain and the performance requirements
Grouser
Extinct genus of molluscs
have been found on the island of Timor. The shell of Callaionautilus is involute, coiled such that only the outer whorl is exposed. Early whorls have nodes
Callaionautilus
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INVOLUTE
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INVOLUTE
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