Hi Joy Ride
Autogyros, including the unpowered Focke-Achgelis Fa 330 "Bachsteze" do not have 3 axis control
I did some evaluation and development flying on the Wallis Autogiro in the 80's. It had the "Wallis" patented offset rotorhead which could be controlled in both pitch and roll as well of having rudder of course so it certainly felt like it had 3 axis control in flight.
Colleague Bill Sayer (of the RAF Museum and Shuttleworth's) built and flew successfully a replica Voisin ( Papillon Blanc) which is now in the Brooklands museum. I had long discussions with him on it's flight characteristics, hence my earlier remarks about flying 2 axis control with automatic stability in the 3rd.