Definition

Noun: * A specific type of curve in geometry: A prolate cycloid is the path traced by a fixed point attached to, but located outside of, a circle as that circle rolls without slipping along a straight line. It is characterized by loops or cusps that point away from the direction of the rolling circle.

Examples of Usage

• Noun:
  • The mathematician plotted the equation to visualize the shape of the prolate cycloid.
  • In this mechanical design, the cam's profile is based on a prolate cycloid to create a specific intermittent motion.
  • The path of a point on the flange of a train wheel relative to the rail approximates a prolate cycloid.

Advanced Usage

• Mathematical Context: The prolate cycloid is one of three main types of cycloids, distinct from the common cycloid (point on the rim) and the curtate cycloid (point inside the circle). Its parametric equations are derived from the circle's radius and the distance of the fixed point from the circle's center.
  • The study compared the kinetic energy profiles of systems using prolate cycloid and common cycloid gears.

Variants and Related Words

• Cycloid (n): The general family of curves traced by a point on a rolling circle.
• Curtate Cycloid (n): A cycloid generated by a point the rolling circle.
• Trochoid (n): A more general term that encompasses prolate cycloids, curtate cycloids, and common cycloids.
• Prolate (adj): Having an elongated shape along the polar axis (often used in describing spheroids).

Synonyms

• Extended cycloid (less common technical synonym).
• Looping cycloid (descriptive synonym referring to its shape).

Related Concepts (Not Phrasal Verbs or Idioms)

• Parametric Equation: The mathematical representation used to define a prolate cycloid.
• Locus: The set of all points satisfying the conditions that generate the prolate cycloid.
• Roulette: A curve generated by tracing a point attached to one curve as it rolls upon another; a cycloid is a roulette.

Noun

1. a cycloid generated by a point outside the rolling circle