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The parametric equations of an epicycloid are
x = (a + b) cos θ - b cos ( a + b/b
y = (a + b) sin θ - b sin ( a + b/b


The curve described by a point on the circumference of a circle as the circle rolls on the outside of the circumference of a second, fixed circle.

ep′i·cy·cloid′al (-kloid′l) adj.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
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His first post was with the mechanical engineering company of Kitson and Co in Leeds, where he began manufacture of a high-speed epicycloidal steam engine for electrical power generation which he had conceived whilst at Cambridge.
As a result of the development of this direction some authors suggest to use a circular profile of elements of such gearing, replacing a pusher for a solid of revolution: a ball or a roller that allows to receive, depending on the form of the connected surfaces of internal gearing, (hypo-) epicycloidal (Dumoulin, 1989) or (hypo-) epitrochoidal (Riffel, 1981) engagement of harmonic tooth-cam transmission.