This paper presents a novel method for determining rank and mobility of single loop kinematic chains which is totally different from the methods based on screw theory and based on displacement subgroup. The rank of single loop kinematic chains can be determined via the position and orientation characteristic (in short, POC) equation and its symbolic operation of serial mechanism presented by authors. The symbolic operation of the POC equation is simpler and has clear geometrical meaning. The method for determining the rank of single loop kinematic chains can be used for calculating DOF of parallel mechanisms.

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