The generalized tracta coupling R0-RERR and its variant mechanisms R0-ERRR, R0-RRER and R0-RRRE are all kinematically analyzed by a new Vector Algebraic Method. The input-output displacement equations of these mechanisms are derived as fourth order polynomials. Compared to existing methods, the new approach presented in this paper has standardized analysis steps and compact algebraic expressions. For each of the different variant mechanisms the analysis procedure is the same.

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