An efficient method is proposed for the design of six-bar function generators with complex design tasks. Especially, the desired functions are defined for the entire motion ranges of the input variables. The design problem is defined as a nonlinear optimization problem. A concept of a weighted structural error is introduced for the definition of the objective function. Also simple branch identifiers are incorporated to eliminate the branch problems commonly encountered in a typical linkage synthesis problem. Two example problems of designing a Watt-II type double dwell mechanism and a Stephenson-III type double beat-up mechanism are demonstrated with numerical results. Constraints such as on the Grashof conditions and on the transmission angles are included for practical solutions.