This paper presents the wrench capability analysis, the controller design, and experimental results of an aerial robot flying gripper. This robot uses four quadrotors to actuate four fingers such as to grasp and manipulate large size objects. The yaw motion of each quadrotor is used to open/close one of the four fingers. A method is proposed to analyze its manipulability considering inequality constraints such as the propellers’ capabilities and equality constraints such as the yaw torque applied by each quadrotor to open or close a finger and the equilibrium conditions of passive joints. This allows concluding on the full manipulability of the robot and evaluating its force and torque capabilities. A dynamic control allocation algorithm is implemented to distribute the control effort among all quadrotors while guaranteeing an achievable solution satisfying the aforementioned constraints. A proof of concept is realized and allows presenting preliminary experimental results of the flying gripper.