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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.
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 ...
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.
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)
From January 2008 to December 2012, if you bought shares in companies when Robert D. Beyer joined the board, and sold them when he left, you would have a -3.9 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
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.
From January 2008 to May 2009, if you bought shares in companies when Michael H. Sutton joined the board, and sold them when he left, you would have a -96.7 percent return on your investment, compared to a -38.2 percent return from the S&P 500.