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Plane curve formed by rolling a circle on the outside of another
In geometry, an epitrochoid (/ɛpɪˈtrɒkɔɪd/ or /ɛpɪˈtroʊkɔɪd/) is a roulette traced by a point attached to a circle of radius r rolling around the outside
Epitrochoid
means Elliptic integral K(m) Epitrochoid Epicycloid (special case of the epitrochoid) Limaçon (special case of the epitrochoid) Hypotrochoid Hypocycloid
List_of_periodic_functions
Method for estimating new data within known data points
An interpolation of a finite set of points on an epitrochoid. The points in red are connected by blue interpolated spline curves deduced only from the
Interpolation
Mathematical curves generated by rolling other curves together
curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. On a basic level, it is the path traced
Roulette_(curve)
US engine manufacturer
only successful pistonless rotary engine to date, a figure-eight-like epitrochoid housing surrounds a curved sided triangular rotor. The rotor revolves
X-engine
Curve traced by a point outside a circle rolling within another circle
Tusi couple). The classic Spirograph toy traces out hypotrochoid and epitrochoid curves. Hypotrochoids describe the support of the eigenvalues of some
Hypotrochoid
Curve traced by a circle rolling along a line
around ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} (the hypotrochoid/epitrochoid case), x ′ = x 0 + r 2 cos ( ω 2 t + ϕ 2 ) , y ′ = y 0 + r 2 sin
Trochoid
curve Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rose curve Bicuspid curve
Gallery_of_curves
Plane curve traced by a point on a circle rolled around another circle
19/5 k = 5.5 = 11/2 k = 7.2 = 36/5 The epicycloid is a special kind of epitrochoid. An epicycle with one cusp is a cardioid, two cusps is a nephroid. An
Epicycloid
Curve traced by a point on a circle rolling within another circle
German painter and German Renaissance theorist Albrecht Dürer described epitrochoids in 1525, and later Roemer and Bernoulli concentrated on some specific
Hypocycloid
Curve traced by a point on a rolling circle
where the generating point may not be on the edge of the rolling circle. Epitrochoid: generalization of an epicycloid where the generating point may not be
Cycloid
l'Hospital Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rational normal curve Rose
List_of_mathematical_shapes
Geometric drawing device
roulette curves of the variety technically known as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher
Spirograph
Radical shift in Western cosmology
Mars. For simplicity, Mars's period of revolution is depicted as 2 years instead of 1.88, and orbits are depicted as perfectly circular or epitrochoid.
Copernican_Revolution
Motor vehicle
material used for the three rotor tips (apex seals) for the oval-like epitrochoid-shaped rotor housing that sealed the combustion chambers. A feature of
NSU_Ro_80
Quartic plane curve
can be specified by other curves particularly as a rose, conchoid or epitrochoid. The curve is one among a number of plane curve trisectrixes that includes
Limaçon_trisectrix
Geometric curve formed by a circle rolling along another circle
rolls without slipping along a fixed circle. The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center
Centered_trochoid
Combustion engine using an eccentric rotary design
of "oversize" of the rotor housing shape relative to the theoretical epitrochoid, to minimize radial apex seal motion, and cylindrical gas-loaded apex
Wankel_engine
Planetary motions in archaic models of the Solar System
The orbits of planets in this system are similar to epitrochoids, but are not exactly epitrochoids because the angle of the epicycle is not a linear function
Deferent_and_epicycle
clover Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Hypotrochoid Lissajous curve Poinsot's spirals Rational normal
List_of_curves
The Moon's circuit around Earth
Earth, tilts of orbits and axes, courtesy of U. of Arkansas Spirograph-Epitrochoid Earth and Moon, interactive visualization of orbital parameters on GeoGebra
Orbit_of_the_Moon
τροχαῖος (trochaîos), τροχαϊκός (trochaïkós), τροχοειδής ditrochee, epitrochoid, hypotrochoid, trochaic, trochanter, trochee, trochelminth, trochlea
List of Greek and Latin roots in English/P–Z
List_of_Greek_and_Latin_roots_in_English/P–Z
Non-functional combustion engine concept
engine shares its basic design, a triangular-like rotor in an oval, epitrochoid-shaped housing, with a regular Wankel engine. The key difference is that
Wankel_Diesel_engine
Type of roulette curve
family of curves called centered trochoids; more specifically, they are epitrochoids. The cardioid is the special case in which the point generating the roulette
Limaçon
Device for storing charged particles
particles to move in the radial plane with a motion which traces out an epitrochoid. The orbital motion of ions in the radial plane is composed of two modes
Penning_trap
the original orbit, so its trajectory resembles a curve known as an epitrochoid. This could explain how the planet seems to move as viewed from Earth
Timeline of cosmological theories
Timeline_of_cosmological_theories
trochoid – Geometric curve formed by a circle rolling along another circle Epitrochoid – Plane curve formed by rolling a circle on the outside of another Epicycloid –
List_of_circle_topics
Three-shaft planetary gearset
the planet gear of an epicyclic gear train. This curve is called an epitrochoid.[citation needed] Epicyclic gearing was used in the Antikythera Mechanism
Epicyclic_gearing
Earth, it also orbits the original orbit, so its trajectory resembles an epitrochoid, as shown in the illustration at left. This could explain how the planet
Historical models of the Solar System
Historical_models_of_the_Solar_System
Japanese Wankel engine motorcycle
rotor that spins on an eccentric shaft in a peritrochoid (Mazda uses an epitrochoid) housing. Since the stationary/rotor gears ratio is 2:3, the rotor rotates
Suzuki_RE5
curve tangent to a family of curves. See Salmon (1879, p. 65). epitrochoid An epitrochoid is the curve traced by a point of a disc rolling along another
Glossary of classical algebraic geometry
Glossary_of_classical_algebraic_geometry
τροχαῖος (trochaîos), τροχαϊκός (trochaïkós), τροχοειδής ditrochee, epitrochoid, hypotrochoid, trochaic, trochanter, trochee, trochelminth, trochlea
List of Greek and Latin roots in English/T
List_of_Greek_and_Latin_roots_in_English/T
Planetary nebula in the constellation Lepus
toy that produces geometric patterns (specifically, hypotrochoids and epitrochoids) on paper. The origin of the Spirograph pattern is unknown. "IC 418"
IC_418
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