What is the working principle of hexagonal flying cutter lathe?

Because B turns clockwise 1 and A turns counterclockwise 2 (the angular velocity of the cutter head is twice that of the workpiece) in actual machining, I use the inversion method. Assuming that the workpiece B is stationary, let A turn counterclockwise 1 (revolution) around the center of B, and let A turn counterclockwise 2 at the same time, and then draw a point. By repeating the above method, three incomplete trajectories in the graph are obtained. I drew the sparse points with 5 and 10. If all of them are drawn, the trajectory will leave an approximate hexagonal trajectory on B. It needs to be declared that the diameters of my A and B are arbitrarily selected. If they are properly configured, the trajectory will be closer to a hexagon, but they are close after all and should not be a real straight line.