On the number synthesis of kinematic chains

•Literature review of number synthesis of kinematic chains is reviewed.•Different kinds of kinematic chains are introduced.•The numbers of kinematic chains with up to 15 links are listed.

Number synthesis of kinematic chains is one of the major steps in the structural synthesis or conceptual design of mechanisms. The work presents a comprehensive literature review on the number synthesis of kinematic chains of mechanisms. The terminology and definitions regarding kinematic chains in literature are introduced first. Then, various methods for the number synthesis of kinematic chains are presented and discussed. Finally, the numbers of kinematic chains with up to 15 links and 7 degrees of freedom are listed.