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trochoid

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Trochoid - Wikipedia
In geometry, a trochoid (from Greek trochos 'wheel') is a roulette curve formed by a circle rolling along a line . It is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line. en.wikipedia.org
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Trochoid -- from Wolfram MathWorld
A trochoid is the locus of a point at a distance b from the center of a circle of radius a rolling on a fixed line. A trochoid has parametric equations x ... mathworld.wolfram.com
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Trochoid - MATHCURVE.COM
Trochoid refers to the curve described by a point linked to a disk with radius R rolling without slipping on a line (D). mathcurve.com
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trochoid
trochoid, n. and a. (ˈtrɒkɔɪd, ˈtrəʊkɔɪd) [ad. Gr. τροχοειδής round like a wheel, f. τροχός wheel + εἶδος form: see -oid; cf. F. trochoïde (1658 in Hatz.-Darm.).] A. n. 1. Geom. A curve traced by a point on or connected with a rolling circle; orig. = cycloid 1: now usually restricted to the curtate ... Oxford English Dictionary
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TROCHOID Definition & Meaning - Merriam-Webster
The meaning of TROCHOID is the curve generated by a point on the radius of a circle or the radius extended as the circle rolls on a fixed straight line. www.merriam-webster.com
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What is a Trochoid ? - YouTube
What is a Trochoid ? · Comments. 12. Add a comment... 6:26 · Go to channel · Construction of an Inferior Trochoid. Manas Patnaik•24K views · 23 ... www.youtube.com
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【Product info】Trochoid® pump - Nippon Oil Pump Ltd.
Trochoid® pump is a kind of gear pump that captures fluid between an external gear and an internal gear and transfers it by rotating its gear. www.nopgroup.com
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Trochoid and its Parametric Equations - YouTube
At time 1:51, Note the distance of the roll from the origin (that is the length of the segment) is equal to the arc length which is ... www.youtube.com
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Centered trochoid - Wikipedia
A centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a point attached to a circle as the ... en.wikipedia.org
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Cycloid, Trochoid, Epicycloid, Hypocycloid, Epitrochoid and ...
The Cycloid Family of curves features the most distinguished group of investigators in mathematics. Galileo and Father Mersenne are credited with being the ... nationalcurvebank.org
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Sprial & Trochoid | PDF | Circle | Differential Geometry - Scribd
A trochoid is a curve generated by a point either inside or outside the circumference of a circle that rolls along a straight line without slipping. www.scribd.com
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Centered trochoid
In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle. wikipedia.org
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Prove parametric equations trochoid I have to show that the parametric equations of a trochoid are: $x = r\theta - d\sin\theta$ and $y=r-d\cos\theta$ where r is radius and d is the distance between center of the cir...
hard look at picture take some fixed point anywhere on the circle and when the circle is rolled around the curve drawn by the the fixed point is the TROCHOID
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Arc length of a trochoid Wolfram MathWorld gives parametric expressions for a trochoid in terms of a parameter $\phi$: \begin{eqnarray*} x &=& a\phi - b \sin \phi\\\ y &=& a - b \cos \phi, \end{eqnarray*} but then giv...
Since this is a first time I hear about trochoids, I just computed the arc length using $$\begin{eqnarray*} x &=& a\phi - b \sin (\phi) \implies x'=a -b\cos(\phi)\\\ y &=& a - b \cos (\phi)\implies y'=b \sin (\phi) \end{eqnarray*}$$ $$L=\int \sqrt{(x')^2+(y')^2} \,d\phi=\int \sqrt{a^2+b^2-2 a b \cos...
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Zaphriphyllum
Sutherland proposed the genus Zaphriphyllum for those zaphrentids which still possess a trochoid shape and pronounced cardinal fossula and consistently wikipedia.org
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