Cycloids and Trochoids of an Elliptic Base Curve
Cycloids and Trochoids of an Elliptic Base Curve
Trochoids and cycloids are glisettes: curves generated when a closed curve rolls inside or outside a fixed base curve.
In this Demonstration, the rolling curve is a circle, which rolls without slipping on an elliptic base curve; the generated curve is called a hypotrochoid or an epitrochoid, according to whether the circle rolls on the inside or the outside of the ellipse. The generator point (or pole) that draws the curve is at a variable distance from the center of the rolling circle. If is equal to the circle radius, the trochoids become cycloids.
d
d
The circle radius is computed such that the circle performs an integer number of revolutions around itself while completing a loop around the ellipse. The number of cusps formed in the completed curve is for a hypotrochoid and for an epitrochoid.
n
n+1
n-1