When a circle rolls on the circumference of another circle, each point on the rolling circle can describe a curve, called the cycloidal curve. If the circle rolls outside another circle, the describing curve is an epicycloid; if the circle rolls inside another circle, the describing curve is a hypocycloid. The cycloidal curves are commonly applied in the generation of gear tooth profiles and the design of displacement curves of cam mechanisms. It has the advantages of no interference and undercutting problems for gear design and having smoother acceleration curves, compared with simple harmonic motion curve, for cam design. The shown mechanism is used to demonstrate an application of the cycloidal curves. It consists of a spur gear pair, a connecting rod, a driving crank, and a frame. The internal gear is served as the frame; the external gear is driven by the input crank which is located behind the model; the connecting rod is connected to the external gear on its pitch circle with a revolute joint and is adjacent to the frame with a prismatic joint. Since the radius of the pitch circle of the internal gear is double of that of the external gear, the center of the connecting joint on the pitch circle of the external gear will draw a straight line along the diameter of the pitch circle of the internal gear. Hence, when the external gear is driven, the connecting rod is forced to reciprocally slide on the frame. Since the external gear rolls inside the internal gear, the generating straight line belongs to a hypocycloid.