A two-stage general optimization approach is presented for generating link mechanisms from a highly connected ground structure. The structure is modeled as a pinjointed truss, which is to be optimized so that a large displacement is generated in the specified direction at the output node. The design variables are the cross-sectional areas of the members and the nodal locations. The equilibrium path of an unstable mechanism is traced by the displacement control method. In the first step, the unnecessary members are removed by solving the optimization problem for minimizing the total structural volume under constraints on the maximum load, the displacement at the specified node, and the stiffnesses at the initial and final states. In the second step, the deviation of the displacement of the output node from the specified direction is minimized. It is shown in the numerical examples that several mechanisms can be naturally found as a result of the two-stage optimization starting from randomly selected initial solutions.