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This paper focuses on the kinematic modelling, mobility analysis and mechatronics design of a singularityless omni-directional wheeled mobile robot (OWMR). To achieve a singularityless motion, firstly, the kinematic model of a wheeled mobile robot (WMR), a platform equipped with three omni-directional wheels (ODW), is formulated. Based on this model, a smooth trajectory and control command for the 3-wheel OWMR can be obtained. The analysis on the mobility of a WMR is carried out using the functional matrix. It is shown that a WMR with three ODWs has a mobility of three. A WMR with three ODWs was designed and prototyped. Experimental results have been employed to verify the theoretical conclusions.