Definition

1. Noun:
   • A curve traced by a point on the circumference of a circle that rolls without slipping on the outside of another fixed circle. It is a specific type of roulette or cycloid.

Usage and Examples

• Noun:
  • The path traced by a point on a rolling coin is an epicycloid.
  • In geometry class, we learned how to construct an epicycloid.
  • The shape of certain gear teeth is based on an epicycloid to ensure smooth motion.

Advanced Usage

• Mathematical Context: In mathematics and engineering, the epicycloid is studied for its properties in gear design and planetary motion models.
  • The epicycloid's arc length can be calculated using integral calculus.

Variants and Related Words

• Hypocycloid (n): A curve traced by a point on a circle rolling another circle.
• Cycloid (n): A curve traced by a point on a circle rolling along a straight line.
• Epicyclic (adj): Relating to or involving epicycles or epicycloids, often used in "epicyclic gear train."

Synonyms

• Roulette (in a mathematical context): A curve generated by a point attached to one curve rolling on another.
• Curve: A general term for a line that is not straight.

Related Terms and Concepts

• Planetary Motion: Historically, epicycloids were used in models to describe the apparent retrograde motion of planets.
• Gear Design: Epicycloidal curves are used in the design of gear tooth profiles for certain types of gears.

Noun

1. a line generated by a point on a circle rolling around another circle