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Position and orientation characteristics(POC) of parallel mechanism describes the relative motion properties between arbitrary two links of parallel mechanism. POC has close relationship with topological characteristics of parallel mechanism. Whereas, POC of general parallel mechanism cannot be obtained easily sometimes. So it is important for topological structural analysis or design to program the POC calculation. Some important concepts were analyzed systematically such as the topological polynomial expression, the orientation group and POC, etc. The aligning structures of limbs and pairs of parallel mechanism were expressed by the topological polynomial expression. The orientation group provides the orientation relationships shared by axes of all pairs and limbs of parallel mechanism. With the motion characteristics of movable platform of parallel mechanism considered, a conception of motion characteristic space was proposed. Based on the correlation among motion characteristic spaces, two elimination principles were constructed: serial elimination and parallel one. These elimination principles build the quotient relationships between topological polynomial expression and orientation group, supporting for iteration calculations with the POC of parallel mechanism and returned as the result. Based on the string description, POCs of some parallel mechanism were derived with symbolic fashion and the results validated the proposed method. The results of this paper lay some necessary theory and methodology foundations for the computer aided analysis of topological structural characteristics and prototype synthesis of parallel mechanism.