The family of planar kinematic chains with two multiple joints

• The whole family of planar non-fractionated kinematic chains with two multiple joints and up to 15 links is synthesized.
• Kinematic chains with two multiple joints are synthesized directly from kinematic chains with one multiple joint.
• An improved algorithm is developed to enhance the efficiency of isomorphism identification.
• All valid kinematic chains with two multiple joints and more than 10 links are generated for the first time.

This paper proposes an automatic method to synthesize planar non-fractionated kinematic chains with two multiple joints, which are generated from kinematic chains with one multiple joint by transforming a multiple link to a multiple joint. First, the interconversion relationship between kinematic chains with different numbers of multiple joints is revealed. Then, an improved algorithm is developed to obtain the characteristic number string of topological graphs with two multiple joints to enhance the efficiency of isomorphism identification. Finally, based on the atlas database of kinematic chains with one multiple joint, a systematic method is proposed to automatically synthesize kinematic chains with two multiple joints. As a result, the whole family of planar non-fractionated kinematic chains with two multiple joints and up to 15 links is acquired for the first time, and the contrastive analysis with existing research results is also conducted.