Motional Cycloid and It's Application in Security Pattern Design

We extend the definition of traditional cycloid such that the cycloidal point is no longer a fixed point on the motional circle but has its own moving track Φ. The cycloidal point will move along its track concurrently while the motional circle rolls along the inside of the fixed circle without slip. Based on the convex and concave characteristics of the approximate polygon of Φ, we further define two moving rules for the cycloidal point to achieve more meaningful and variable tracks. Finally, we illustrate the applications of motional cycloidal track in the security pattern design.