This article presents the design and modeling of a new aerial manipulator system, called Q-PRR, composed of three joints with a fixed base in the center of mass of the multirotor considered as a whole system. This structure has a prismatic joint as a first joint which allows to keep the center of gravity of the Q-PRR as close as possible to the center of gravity of the multirotor. This will also allow to reduce the influence of arm motion on the multirotor roll thus to ensure the stability of the system on trajectory tracking with dynamic changes in the multirotor’s center of gravity. Furthermore, the configuration of the manipulator arm for the desired position of the end-effector given by the inverse kinematics model is kept without any change in the position and attitude of the multirotor. This article develops both forward and inverse kinematics models for a nonlinear underactuated system using the Denavit–Hartenberg notation. When a new algorithm is presented for the inverse kinematics based on Levenberg–Marquardt algorithm. Then, the dynamic model in the joint spaces is developed with the Lagrangian formalism. The Q-PRR is controlled using a model-free control with a comparison of two states, a free fly and disturbance forces applied to the whole system with manipulator arm movement.