[font=Trebuchet MS][size=150][b]The first application is folding door of bus.[br][br][color=#ff7700]Mechanism of folding door is until 45 degrees, it follows the envelope curve.[br]After then, it follows the rim of a circle.[br][/color][br]The proof of parametric equation of it is written below.[/b][/size][/font]

[font=Trebuchet MS][b][color=#ff7700][size=150]This parametric equation is same with the Astroid[br](particular type of hypocycloid)[/size][/color][/b][/font]