This paper deals with a novel flying mechanism. Inspired from parallel manipulators, this flying robot is composed of three quadrotors linked by a rigid articulated architecture composed of three legs and a platform. Associating quadrotor co-manipulation and rigid bodies, this new design offers novel possibilities for aerial robotics and manipulation. Previous work leads to the design of a flying parallel robot with two quadrotors. However, this robot did not allow the full control of the six degrees of freedom of its end-effector. With an additional quadrotor, this study seeks to obtain a full control of the platform position and orientation. To prove this property, the kinematic constraints are verified through screw theory. Then, the dynamic model is established and a decoupling property leads to the design of a specific controller for the platform and legs configurations. ADAMS/SIMULINK co-simulations validate the theoretical developments.