Addition method with 2 links and 3 pairs of type synthesis to planar closed kinematic chains

Based on the graph theory, a method called addition method with 2 links and 3 pairs is presented for type synthesis of planar closed kinematic chains. The NK-link FP-DOF (degree of freedom) NP-pair kinematic chains (KCS) can be got by adding 2 links and 3 pairs to the (NK-2)-link FP-DOF (NP-3)-pair KCS. Three arithmetic operators: adding operators, replacing operators and dismantling operators are defined. And three operations: basic operation (OB), supplementary operation (OA) and replacing operation (OR) are carried out for convenience to type synthesis. Then based on the contracted link adjacency matrix, basic link sequence and so on, sequence code method is presented for the classification of KCS. And sequence-similarity method is developed for isomorphic identification. And a method to identification of basic rigid chains based on loop method is investigated. Finally based on isomorphic identification and identification of basic rigid chains, the addition method with 2 links and 3 pairs is applied to synthesize all KCS with up to 12 links and some KCS with 13 links or 14 links.