An infinite number of linkages can be produced for given four angle-displacements of rotating links. It is difficult for designers to synthesize the best linkage through rapidly and precisely selecting curve points that ensure to satisfy every design condition. To solve this problem, based on mapping theory, an infinite number of mechanism solutions generated by Burmester curves were expressed as finite solution ranges. Through solution analysis, the mechanism property graphs of interest have been computed, including their types, defects, minimum transmission angles, link-length ratios, and so on. After design constraints were considered and imposed, feasible solution ranges could be calculated. To avoid aimlessness in choosing positions and mechanisms, property analysis graphs on the feasible solution ranges were displayed, along with which the optimized solution which satisfies practical design conditions can be synthesized.