This paper deals with the bending shape of space manipulator with a rotating flexible link in order to determine the position of the ends of the space manipulator. Using Taylor expansion, the mathematical model of link deformation is obtained considering the effect of link deformation on moment as well as the square of its first derivative in moment and curvature expressions. Based on the mathematical model, an analytical formulation of first derivative on link deformation is obtained by order reduction method. The shape function of link is therefore obtained by numerical integration of the analytical formulation. Moreover, a method to search the maximal abscissa of bending link in fixed coordinate frame using dichotomy is put forward in this paper. It is also validated against simulation results that this method is feasible to determine the position of the ends for space manipulator.