epicycloid

American  

[ep-uh-sahy-kloid] / ˌɛp əˈsaɪ klɔɪd /

noun

Geometry.

1. a curve generated by the motion of a point on the circumference of a circle that rolls externally, without slipping, on a fixed circle. Equation: x = (a +b ) cos(θ) − b cos[(a +b )θ/ b ] and y = (a +b ) sin(θ) − b sin[(a +b )θ/ b ].

---

epicycloid British  

/ ˌɛpɪˈsaɪklɔɪd /

noun

1. the curve described by a point on the circumference of a circle as this circle rolls around the outside of another fixed circle, the two circles being coplanar Compare hypocycloid cycloid

---

epicycloid Scientific  

/ ĕp′ĭ-sī′kloid′ /

1. 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.

---

Other Word Forms

• epicycloidal
  adjective

Etymology

Origin of epicycloid

First recorded in 1780–90; epicycle + -oid

Example Sentences

See Examples For:

epicycloid

Cycloid External epicycloid, described by a circle rolling about a fixed circle inside of it.

From Scientific American, Volume 22, No. 1, January 1, 1870 A Weekly Journal of Practical Information, Art, Science, Mechanics, Chemistry, and Manufactures. by Various

In epicycloidal teeth the curve forming the face of the tooth is designated an epicycloid, and that forming the flank an hypocycloid.

From Modern Machine-Shop Practice, Volumes I and II by Rose, Joshua

The Study and Construction of Toothed Gear.—Involute, cycloid, and epicycloid.

From Scientific American, Volume 40, No. 13, March 29, 1879 A Weekly Journal of Practical Information, Art, Science, Mechanics, Chemistry, and Manufactures by Various

When c = a or = ∞ the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

From Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 5 "Cat" to "Celt" by Various

Suppose b a tracing point on b, then as b rolls on a it will describe the epicycloid a b.

From Modern Machine-Shop Practice, Volumes I and II by Rose, Joshua