It is always a difficult point in the manufacturing field to realize the surface rolling of complex surface workpieces with both positive and negative curvature and taper by using robot technology. This working condition requires the working manipulator to carry the roller. In the process of advancing along the roller path, the feed direction of the roller always coincides with the normal line at the current point to ensure that the roller pressure is adjustable and controllable. Therefore, the manipulator needs to meet the performance characteristics of high stiffness, large workspace and flexible pose transformation. According to the analysis of the complex curved surface workpiece, we conclude that the manipulator configuration to realize the working action should have the 5-degree-of-freedom motion ability of 3R2T. After analyzing the work of the serial manipulator, we find that the attitude change will cause the joint angle of the manipulator to change suddenly, which will cause the potential risk of interference between the manipulator and the workpiece. Therefore, it can be determined that the manipulator with a series-parallel hybrid (SPH) configuration is more suitable for solving such problems. The first-level parallel mechanism is assigned to realize the position adjustment function and the second-level parallel mechanism is used to realize the attitude transformation. The configuration evolution is carried out by using the displacement manifold theory, and finally the SPH configuration is obtained. In the analysis of the workspace, a new solution method is proposed. Compared with the traditional solution method that requires a fixed attitude or position, the new method can obtain the full-attitude workspace while greatly reducing the amount of calculation. Finally, we prove that the designed configuration can realize the surface rolling task of complex curved workpieces through workspace analysis. The SPH manipulator configuration scheme proposed in this study can completely change the current production status of manual ways for such engineering problems. The proposed new method of workspace solution can be used as a tool to provide a more efficient solution path for mechanism workspace analysis.