TGA-based solutions map method for four-position synthesis of planar 4R linkage

Abstract. In this study, the authors propose a solutions map based on a telomere genetic algorithm (TGA) to improve the efficiency of 4R-linkage synthesis. First, the points on the center curve are obtained by using projective geometry, and those of the circle curve are obtained by vector elimination. Second, the definition of the linkage type, assessment of linkage performance, and a method to identify defects in the linkage are introduced. Third, the solutions map method is proposed that can map the linkage solutions obtained by all combinations of the points on the center curve to a 3D color-coded surface to represent the distribution of solutions with different attributes of linkages in the solution domain. Fourth, we use the proposed telomere operator and pseudo-histogram method to improve the traditional genetic algorithm, and expand the domain of solutions of the solutions map by using the TGA. Finally, the linkage synthesis software BurLink is developed based on the solutions map method. The results show that the TGA-based solutions map can quickly locate the required 4R-linkage solution in the solution domain, and provides engineers with more candidate solutions than traditional methods.