This paper proposes an innovative and systematic approach for synthesizing mechanical structures of wheeled mobile robots. The principle and terminologies used for the proposed synthesis method are presented by adopting the concept of modular design, isomorphic and non-isomorphic, and set theory with its associated combinatorial mathematics. The modular-based innovative synthesis and design of wheeled robots were conducted at two levels. Firstly at the module level, by creative design and analysing the structures of classic wheeled robots, a wheel module set containing four types of wheel mechanisms, a suspension module set consisting of five types of suspension frames and a chassis module set composed of five types of rigid or articulated chassis were designed and generalized. Secondly at the synthesis level, two kinds of structure synthesis modes, namely the isomorphic-combination mode and the non-isomorphic combination mode were proposed to synthesize mechanical structures of wheeled robots; which led to 241 structures for wheeled mobile robots including 236 novel ones. Further, mathematical models and a software platform were developed to provide appropriate and intuitive tools for simulating and evaluating performance of the wheeled robots that were proposed in this paper. Eventually, physical prototypes of sample wheeled robots/rovers were developed and tested so as to prove and validate the principle and methodology presented in this paper.