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A new topological manifolds method was proposed to solve the inverse kinematics problem of the redundant fiber placement manipulator. It improved the calculation precision compared with the optimized projected gradient method. A structure of smooth topological manifolds was presented by the inverse kinematics solution of redundant fiber placement manipulator, the simulation topological manifolds were obtained when the position sub-manifolds and posture sub-manifolds had a different simulation analysis for the redundant fiber placement manipulator model, it was like the function mapping in the mathematics from the manipulator joints space to the working space of the end effector. The tangent vector described velocity vector for each point on the topological manifolds, the gather of all these tangent vectors were defined as the tangent vector space on the point. The kinematics problems of the redundant fiber placement manipulator were abstracted to mathematically curved surface topological manifolds problem in the new method, it provided a new theoretical basis for manifolds analysis of the redundant fiber placement manipulator. Thus the subsequent optimization of inverse kinematics solutions manifolds problems were obtained by using self-motion curved surface manifolds theory in the mathematics, it provided a new method for improving the subsequent optimization self-motion control of the redundant fiber placement manipulator. The whole operating performance of the redundant fiber placement manipulator was improved greatly, and it would play a great role in promoting the quantity in the working fiber placement. The new method was verified by simulation of plane S shaped inlet.