The primary objective of this thesis is to propose a design method for linkages simulating the transformation of a planar curve from an initial form to a final form. First, the topologies of fundamental loops are examined using symmetry patterns. Design methodologies for the hence obtained mechanisms are formulated. The given curves are discretized initially, and the nodes are constructed. Then the side lengths of the loops are obtained in order to obtain the desired transformation between the given curves. Finally, different deployable and transformable linkage examples are presented.