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Recently quite a few applications of an omnidirectional mobile robot have been reported. However, understanding some fundamental issues still remains as further study. One of the issues is the exact dynamic model. Previous studies very often ignore the wheel dynamics of the mobile robot and suffer from algorithmic singularity. Thus, actuator sizing or control algorithms based on the incomplete plant model does not guarantee the control performance of the system. This paper deals with the singularity-free, exact dynamic modeling and analysis of an omnidirectional mobile robot with three caster wheels. Initially, the exact dynamic model of the mobile robot including the wheel dynamics is introduced. A natural orthogonal complement approach is also introduced. The joint-space and operational-space dynamic models are derived as analytical forms. Through simulation, the discrepancy of the incomplete dynamic model is shown by comparison with the exact dynamic model. Furthermore, the useful aspect of operational dynamics in terms of impact geometry is also discussed.