Abstract: Branch (assembly mode or circuit) identification is a way to assure motion continuity among discrete linkage positions,which is the most fundamental issue among the mobility problems that may also include sub-branch (singularity-free) identification,range of motion,and order of motion.Branch analysis becomes more complex in spherical or spatial linkages.In this paper,an automated branch identification method was proposed based on discriminants of kinematic equations and the concept of joint rotation space (JRS) to analyze the branch formation of a spherical six-bar linkage.And an automated identification algorithm was presented to rectify the motion of a spherical six-bar linkage.The proposed method is general and conceptually straightforward.It can be applied for all linkage inversions.Examples were employed to illustrate the application of the proposed method.