What does epicycloid mean?
An epicycloid is a mathematical curve produced by a point fixed on the rim of one circle as that circle rolls, without slipping, around the outside of another, stationary circle. The shape of the curve depends on the ratio of the two radii: when the rolling circle's radius divides evenly into the fixed circle's, the epicycloid closes into a pattern of arches or cusps, and in special cases it degenerates into familiar forms such as the cardioid or nephroid. The word entered English from the Greek-derived terms 'epicycle' and 'cycloid', reflecting its roots in ancient astronomical theory and later analytic geometry. Though rarely encountered outside mathematics, physics, and mechanical engineering, the epicycloid is practically significant: cycloidal gears, certain cam profiles, and even the rotary engine's housing geometry draw on epicycloidal curves. Its everyday cultural presence is perhaps best seen in the spirograph drawing toy, whose looping patterns are essentially epicycloids.
nounA plane curve traced by a point on the circumference of a circle that rolls without slipping around the outside of a fixed circle.
- The curve generated by a point on the circumference of one circle as it rolls without slipping around the exterior of another fixed circle.
"The gear teeth of the cycloidal drive are cut along an epicycloid."
"When the rolling circle has half the radius of the fixed one, the resulting epicycloid is a straight-line segment known as the Tusi couple's diameter path."
"Engineers chose an epicycloid profile for the rotor housing because it maintains a tight seal against the rotating apexes."
Standard regular plural.
"Different ratios of radii produce epicycloids with varying numbers of cusps."
The spirograph toy you played with as a child was secretly drawing epicycloids all along.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does epicycloid come from?
Epicycloid derives from 'epicycle', from Greek epi- ('upon') plus kyklos ('circle'), combined with the '-oid' suffix meaning 'resembling'. The underlying concept comes from ancient Greek astronomy, where epicycles were circles moving upon larger circles to explain planetary motion. The word was coined in the early development of modern analytic geometry, likely during the 17th century, when mathematicians such as Ole Rømer and others began systematically studying curves generated by rolling circles.
Related word forms
How epicycloid is actually used
A technical term used almost exclusively in mathematics, engineering, and mechanical design; it is not part of everyday vocabulary. In technical writing it is often paired with its counterpart, the hypocycloid.
Easily confused with epicycloid
An epicycloid is traced by a circle rolling on the outside of a fixed circle, whereas a hypocycloid is traced by a circle rolling on the inside of it.
A cycloid is traced by a point on a circle rolling along a straight line, while an epicycloid involves rolling around the outside of a circle.