In this thesis, we develop a novel aerial manipulator system with an omni-directional workspace. The system comprises of a quadrotor platform equipped with a rotating five-bar linkage and serves the purpose of demonstrating the ability to perform contour tracing tasks on complex shapes, whilst airborne. In order to remove the dependency on additional force sensors and keep the design lightweight, an onboard force estimation scheme is implemented based on the generalized momentum of the system, using the torque feedback from the manipulator's motors. The computed force estimate feeds in a position-based impedance controller with the purpose of maintaining continuous contact through the manipulator's end-effector as the system traces contours of unknown curved geometry. Results demonstrate the estimator's ability to track the applied forces, while the impedance controller shows adequate contour following. The preliminary results obtained on both stationery and flight experiments validate this approach and show potential for aerial contact inspections of more complex structures.