What does epitrochoid mean?
An epitrochoid is a mathematical curve produced by a point fixed to one circle as that circle rolls, without slipping, around the outside of a second, stationary circle. Depending on where the tracing point sits on or within the rolling circle and on the ratio between the two radii, the resulting curve may be looped, wavy, or nearly circular; if the point lies exactly on the rolling circle's edge, the special case called an epicycloid results. Epitrochoids belong to a broader family of curves studied since antiquity under the theory of roulettes and epicycles. Though primarily a term of geometry, the word has practical currency in engineering: the profile of the Wankel rotary engine's combustion chamber is epitrochoidal, and some gear-tooth profiles exploit similar shapes. Related terms include hypotrochoid (rolling inside rather than outside) and trochoid (rolling along a straight line).
nounA plane curve traced by a point rigidly attached to a circle rolling around the outside of another fixed circle. When the tracing point lies on the circumference of the rolling circle, the curve is the special case known as an epicycloid.
- A plane curve generated by a point attached to a circle that rolls without slipping around the outside of a fixed circle; a special case of a roulette.
"The gears were machined with an epitrochoidal profile to ensure smooth meshing."
"Mathematicians classify the epitrochoid according to the ratio of the radii of the rolling and fixed circles."
"In a Wankel rotary engine, each apex of the triangular rotor traces out an epitrochoid against the housing wall."
Standard regular English plural; used when referring to the family of curves generated by different radius ratios or tracing-point positions.
"Different ratios of the two radii yield distinct epitrochoids, some with loops and others with gentle undulations."
The Spirograph toy you played with as a child was quietly drawing epitrochoids — and so are the rotors spinning inside a Mazda rotary engine.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does epitrochoid come from?
The word derives from Greek elements via New Latin scientific coinage: 'epi-' meaning 'upon' or 'over', and 'trochoid', from Greek 'trochos' ('wheel') plus '-eides' ('-like'). It was formed in analogy with 'epicycloid', following the pattern of curve names established by early modern geometers studying rolling circles. Its siblings in the same family include hypotrochoid, hypocycloid, and trochoid itself, all built from the same Greek root for wheel.
Related word forms
How epitrochoid is actually used
A technical term confined almost entirely to mathematics, mechanical engineering, and physics. In formal writing it is typically italicized or set as a headword only in specialist contexts; general readers will most often encounter it in discussions of gear design or the Wankel engine. The plural 'epitrochoids' is standard and unremarkable.
Easily confused with epitrochoid
An epicycloid is traced by a point on the rim of the rolling circle, whereas an epitrochoid is traced by any point attached to it, inside or outside the circumference.
A hypotrochoid results from a circle rolling around the inside of a fixed circle, while an epitrochoid arises from a circle rolling around the outside.