This dissertation demonstrates the synthesis of planar four-bar mechanisms that will exhibit approximate straight line motion while being pushed at the coupler point by a linear actuator. The deviation of transmission angles from 90∘ are minimized as well as the mechanism's departure from a linear path. Prescribed timing of the linkage's driven member, the crank, is included to ensure no less than 180∘ of angular output. Additionally, equations of static equilibrium and virtual work expressions are implemented to ensure a consistent sense of output torque on the linkages driven member; this assures that the direction of motion of the mechanism does not change before acquiring 180∘ of angular displacement. The methods used to achieve the optimization include a gradient method, the generalized reduced gradient method, and two evolutionary programming models that use combinatorial optimization, simulated annealing and genetic algorithms. Hybridization of these methodologies also produce optimal mechanisms. Numerous examples are included that demonstrate the efficacy of the various methods.