Trochoidal Curve

Trochoidal Curve

 

a plane curve described by a point fixed on the radius (or extended radius) of a circle or on a straight line when the circle or line rolls without sliding along a fixed circle or line. In the special case where a line rolls along a circle, each point of the line describes an involute of the circle. If a circle rolls along a straight line, each point on the circle describes a cycloid. In the general case of a circle rolling along a circle, a distinction is made between hypotrochoids and epitrochoids and between hy-pocycloids and epicycloids. The paths of the planets with respect to the earth are approximately trochoidal. Trochoidal curves play an important role in the kinematics of mechanisms; in particular, such curves are of importance in the cutting of gears.