Automatic generation of the complete set of planar kinematic chains with up to six independent loops and up to 19 links

• The complete set of planar kinematic chains with up to six independent loops is obtained.
• The simplified characteristic code is acquired to enhance the efficiency of isomorphism identification.
• All kinematic chains are classified by the planar and non-planar characteristics of their topological graphs.
• Several contradictions found in the literature are solved and numerous original results are acquired.

The synthesis of all feasible topological (kinematic) structures of kinematic chains still has broad research spaces although various methods have been developed in the past fifty years. In this paper, a systematic method is proposed to automatically synthesize the complete set of planar non-fractionated kinematic chains with up to six independent loops. First, the contracted graphs of kinematic chains are synthesized and classified by their planar and non-planar characteristics. Then, the set of constraint equations is derived from the contracted graphs and used to synthesize topological graphs of kinematic chains. And an improved algorithm is developed to obtain the simplified characteristic codes of topological graphs to increase the efficiency of isomorphism identification. Finally, a systematic synthesis method is proposed and the complete set of planar non-fractionated kinematic chains with up to six independent loops and up to 19 links is achieved for the first time. In addition, a comparative analysis between our synthesis results and the ones in the literature is conducted, illustrating the validity and efficiency of the method.