In this paper, a new design is presented for shape morphing using parameterized curves. Inspired by minimal actuation effort, a multiloop linkage is designed with a single input, allowing a morphing curve to take on three distinct shapes. The underlying design is based on a network of four-bar linkages connected together to form a multiloop linkage, referred to as the curve adaptive linkage array (CALA). A three-step method is developed and presented here to find the geometric dimensions of the CALA. The proposed solution is based on the simultaneous recursive solving of the traditional single-loop dyad equations for multiple loops. The key in obtaining a feasible solution is through parameterization of the curves that the linkage is required to morph. To show the effectiveness of the method, an airfoil morphing application is presented, solved using the proposed method, and validated by a prototype. The presented synthesis method provides an effective means for designing a multiloop linkage with a single input.