Mobile robots for automatically transporting products in factories and warehouses contribute to an increase in efficiency. Omnidirectional mobile robots can move immediately in an arbitrary direction and overcome the disadvantages of lack of mobility in conventional mobile robots. However, the omnidirectional mobile robots proposed in the past have not been as reliable as the conventional mobile robots such as AGVs due to their complicated wheel mechanisms. This research proposes a novel omnidirectional mobile robot named SWOM (slidable-wheeled omnidirectional mobile robot), which has three wheels that connect to the robot body by three passive sliding joints. The relative movements of the sliding joints allow SWOM to use conventional wheels. Thus, SWOM realizes both omnidirectional mobility and structural reliability. In this paper, we discuss the kinematic conditions for omnidirectional mobile robots and prove theoretically that SWOM can achieve omnidirectional movement. We present a kinematic analysis, a reachable region evaluation considering the limited movable range of the sliding joints, and trajectory generation that enables SWOM to move unlimitedly. We develop a prototype of SWOM and conduct experiments that show SWOM actually moves according to the theory. From the above, we verify the effectiveness of SWOM as an omnidirectional mobile robot.