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An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle and base line C into a number of equal parts, draw through the division point the ordinates and abscissas, make aa' = 1d, bb' = 2'e, cc = 3f, then ab' and c' are points in the cycloid. In the Epicycloid and Hypocycloid the abscissas are circles and the ordinates are radii to one common center."

Construction Of A Cycloid

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle…

"In geometry, a curve generated by the motion of a point on the circumference of a circle which rolls upon the convex side of a fixed circle." -Whitney, 1911

Epicycloid

"In geometry, a curve generated by the motion of a point on the circumference of a circle which rolls…

"Epicycloidal teeth, teeth for gearing cut in the form of an epicycloid." -Whitney, 1911

Epicycloidal Teeth

"Epicycloidal teeth, teeth for gearing cut in the form of an epicycloid." -Whitney, 1911

"Epicycloidal wheel, a wheel or ring fixed to a framework, toothed on its inner side, and having in gear with it another toothed wheel, of half the diameter of the first, fitted so as to revolve about the center of the latter. It is used for converting circular into alternate motion, or alternate into circular." -Whitney, 1911

Epicycloidal Wheel

"Epicycloidal wheel, a wheel or ring fixed to a framework, toothed on its inner side, and having in…