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The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
Epicycloid: variant of a cycloid in which a circle rolls on the outside of another circle instead of a line. Hypotrochoid: generalization of a hypocycloid 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 on the edge of the rolling circle.
The red path is a hypocycloid traced as the smaller black circle rolls around inside the larger black circle (parameters are R=4.0, r=1.0, and so k=4, giving an astroid). In geometry , a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle.
Construction of a two-lobed cycloidal rotor. The red curve is an epicycloid and the blue curve is a hypocycloid. A Roots blower is one extreme, a form of cycloid gear where the ratio of the pitch diameter to the generating circle diameter equals twice the number of lobes. In a two-lobed blower, the generating circle is one-fourth the diameter ...
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
Cycloid - curve generated by a rotating point on a wheel Epitrochoid - Wheel rotating around a wheel . In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes.
Construction of a two-lobed cycloidal rotor. The red curve is an epicycloid and the blue curve is a hypocycloid. The smaller generating circles (red and blue) are one quarter the diameter of the larger generating circle (black). The rotor profile is the thick line. A three-lobed Roots blower (Open animation)
The cyclocycloid (in this case an epicycloid) with R = 3, r = 1 and d = 1/2. A cyclocycloid is a roulette traced by a point attached to a circle of radius r rolling around, a fixed circle of radius R, where the point is at a distance d from the center of the exterior circle.