This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. The existing mechanization process is extended specifically to enable the design of morphing aircraft wings. A portion of the closed-curve morphing chain that has minimal displacement is identified as the structural ground after the segmentation process. Because of the revolute joints placed at the endpoints of the ground section, the moving links of the fixed-end morphing chain need to be repositioned relative to each of the desired wing shapes so as to minimize the error in approximating them. With the introduction of prismatic joints, a building-block approach is employed to mechanize the fixed-end morphing chain. The blocks are located in an assembly position to generate a single degree-of-freedom (DOF) mechanism. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A multi-objective genetic algorithm is employed instead to find a group of viable designs that tradeoff minimizing matching error with maximizing mechanical advantage. The procedure is demonstrated with a synthesis example of a 1-DOF mechanism approximating eight closed-curve wing profiles.