There are 32 ways in which the two RR constraints are added to the 6R loop to form 1DOF eightbar linkage. First, the solution curve was obtained based on expanding burmester curve theory. Then the eightbar linkage can be synthesized by adding two RR constraints on the solution curves. Each point on the solution curve can be viewed as the added RR constraint, so infinitely many solutions can be got. The solution curve can be converted into the solution plane which presents infinitely many solutions. The solution plane was called solution region. The solution region was divided into two categories according to whether the two added RR constraints were related. The linkages were classified by the method of Assur group. The motion of eightbar linkage was analyzed by the iterative position analysis method which relegated the fourbar Assur groups or sixbar Assur groups to several twobar Assur groups. Whether a linkage could be defected depends on if it can sequently move through the four positions of 6R loop. After the defect linkages were removed, the feasible solution region can be got. In the solution region, the feasible linkage can be classified into two types, the crank and the noncrank, according to the rotatable angle range of the driving link. The solution region synthesis theory makes designers choose the feasible linkage directly and accurately, so the design efficiency was improved. In addition, eightbar linkage can achieve more movement function compared with sixbar linkage and fourbar linkage. The synthesis of eightbar linkage for 6R loop through four positions makes the solution region synthesis theory more perfectly, provides more choices for designer and lays the foundation for the application of eightbar linkage in practice. Finally, an example of eightbar linkage specifies the four positions synthesis.