Deltoid and Rolling Curves drawn with the same Stick

The deltoid is defined by these equations:
  c(t) = RR * [ cos(t)+0.5*cos(-2t), sin(t)+0.5*sin(-2t) ]
Of course it is a special case of the Hypocycloids with frequency = -2 and stick = 1. It is shown separately because its rolling construction has beautiful additional properties:
The tangent intersects the deltoid in a segment of constant length and this "needle" is rotated through 180 degrees while one radius of the rolling circle draws the deltoid once. The midpoint of the needle is also center of a larger rolling circle which intersects the deltoid at the endpoints of the needle. And, this midpoint also lies on the rolling circle.