Hypotrochoid
A hypotrochoid is traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. Use the sliders to adjust the radius R of the fixed circle, the radius r of the interior circle, and the distance d of the point to the center of the interior of the circle.
Note the type of curve with different combinations of R, r, and d. When are there cusps and when is the curve smooth. The case where d=r is called a hypocycloid and if R=2r the curve is an ellipse.
Move the slider to adjust the value of t to see the curve traced out - you can also click the play button in the lower left to animate.
To change the viewing window, hold the shift button and left-click to drag the graph or use the scroll wheel to zoom in/out. You can also adjust the axes by holding the shift button and left-click on the axis you want to change.