Orthogonally assembled double-layered corrugated (OADLC) mechanisms are a class of foldable structures that harness origami-inspired methods to enhance the structural stiffness of resulting devices; these mechanisms have extensive applications due to their lightweight, compact nature as well as their high strength-to-weight ratio. However, the design of these mechanisms remains challenging. Here, we propose an efficient method to rapidly design OADLC mechanisms from desired behavioral specifications, i.e. in-plane stiffness and out-of-plane stiffness. Based on an equivalent plate model, we develop and validate analytical formulas for the behavioral specifications of OADLC mechanisms; the analytical formulas can be described as expressions of design parameters. On the basis of the analytical expressions, we formulate the design of OADLC mechanisms from behavioral specifications into an optimization problem that minimizes the weight with given design constraints. The 2D folding patterns of the optimized OADLC mechanisms can be generated automatically and directly delivered for fabrication. Our rapid design method is demonstrated by developing stiffness-enhanced mechanisms with a desired out-of-plane stiffness for a foldable gripper that enables a blimp to perch steadily under air disturbance and weight limit.