A new 3:2 design

We start with a positively curved arc (the red curve).
It is moved by the motion generated by letting the blue circle with radius 1 roll inside of the black circle with radius 2.
We then determine the (green and cyan) envelope of the red family of curves. This is the outer part of the design
We now move the green curve around by the opposite motion.
The missing inner part of the design is determined as the envelope of the green family of curves.
The final design.