| Summary: | Most studies on path synthesis problems are to trace simple or smooth trajectories. In this work, an optimum synthesis for several special trajectories generated by a geared five-bar mechanism is studied using the one-phase synthesis method. The synthesis problem for the special trajectories, which is originally studied using the two-phase synthesis method discussed in the literature, is a real challenge due to very few dimensionally proportioned mechanisms that can generate the special trajectories. The challenging special trajectories with up to 41 discrete points include a self-overlapping curve, nonsmooth curves with straight segments and vertices, and sophisticated shapes. The error function of the square deviation of positions is used as the objective function and the GA-DE evolutionary algorithm is used to solve the optimization problems. Findings show that the proposed method can obtain approximately matched trajectories at the cost of a tremendous number of evaluations of the objective function. Therefore, the challenging problems may serve as the benchmark problems to test the effectiveness and efficiency of synthesis methods and/or optimization algorithms. All the synthesized solutions have been validated using the animation of the SolidWorks assembly so that the obtained mechanisms are sound and usable.
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