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Abstract According to the fractionation concept and whether containing a multiple-joint, planar kinematic chains (KCs) are primarily categorized as non-fractionated simple-joint kinematic chains (NFS-KCs), fractionated simple-joint kinematic chains (FS-KCs), non-fractionated multiple-joint kinematic chains (NFM-KCs), and fractionated multiple-joint kinematic chains (FM-KCs). Currently, there is a noticeable research gap on the enumeration of FM-KCs, whereas comprehensive investigations have been conducted on the enumeration of the other three types of KCs. Aiming at addressing this research gap, the present study develops a heuristic approach for enumerating all planar 2-DOF FM-KCs. To this end, the composition of 2-DOF FM-KCs is initially analyzed to acquire their two basic classifications. Then, utilizing the characteristic graph generation methods for NFM-KCs and NFS-KCs, the combined characteristic graph and its corresponding combined characteristic number string of a 2-DOF FM-KC are created for solving the isomorphic problem in enumeration procedure. Finally, all non-isomorphic 2-DOF FM-KCs with 9, 11, 13, 15, and 17 links are enumerated, and the corresponding database is established.
Huang et al. (Mon,) studied this question.