In the live-line fixed automatic operation of the “insulator-conductor” system, the application of the flying manipulator can significantly save human resources and, in the scenario of live-line operation, maximally ensure the life safety of construction workers. However, for various live-line defect elimination operations of fastening insulators and conductors, it is necessary to comprehensively carry out the design and development of the intelligent end-effector control system according to the shape parameters of the insulators, their installation positions on the cross-arm, and the environmental conditions of the distribution network. This undoubtedly imposes more stringent requirements on the control performance of the flying manipulator. This paper takes a flying manipulator with two degrees of freedom as the research object. Fully considering the influence of the gravitational force factor, a dynamic analysis is carried out, and the Udwadia-Kalaba (UK) equation is used for system modeling. At the same time, combined with the constraint following motion control method, the motion equations of the restricted flying manipulator system are derived. In addition, the fuzzy control method is adopted to describe the uncertainties in the mechanical system. Through simulations and experiments, the effectiveness of the proposed control algorithm is verified.