An efficient and systematic methodology for the topological synthesis of geared robotic mechanisms is developed. The approach is based on the idea that the kinematic structure of a geared robotic mechanism can be described by an equivalent open-loop chain (EOLC) and mechanical transmission lines (MTLs) which drive the joints of the EOLC. It is shown that an MTL can be decomposed as an input unit and several transmission units connected in series. The characteristics of the input and transmission units are laid out and a systematic methodology is developed to enumerate all admissible input and transmission units from the existing atlas of nonfractionated geared kinematic chains. The atlas of admissible MTLs are then generated accordingly. Thus, all admissible geared robotic mechanisms can be enumerated efficiently with the atlas of admissible MTLs and a preferred form of the EOLC. With this new methodology, some novel structures of geared robotic mechanisms are obtained and it is believed that new areas of application can be further explored.

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