Omnidirectional mobile robots offer interesting features for industrial and service applications, in particular, when operating in tight spaces. Compared to car-like nonholonomic vehicles, they provide a higher degree of maneuverability, and often require less complex path planning and control schemes. Three different types of holonomic wheels that enable omnidirectional motion have been proposed in literature: universal, Mecanum, and ball wheel mechanisms. A problem commonly associated with the first two wheel types is that they induce vibrations in the system due to the discontinuous contact points. In this article, a ball wheel mechanism with superior features including slip measurement, free-wheel modus and attrition sensing is presented. The first prototype was built using additive manufacturing. The requirements for the design and possible improvements for future versions are discussed. Based on the presented ball wheel drive, a design for an omnidirectional mobile robot platform driven by three redundant ball wheel units is proposed. The velocity kinematic model of this mobile base is also addressed. Moreover, motion planning for an individual ball drive is demonstrated by means of an online trajectory generation scheme. The pseudocode of the trajectory planning algorithm implemented in LabVIEW is then presented. Finally, the motion characteristics of the ball drive mechanism are tested and its functionality is evaluated in detail. Measurements obtained from these tests show that the slip between the ball wheel and the ground can be estimated quite accurately. Hence, it is expected that these improved dead-reckoning estimates will result in a higher positioning accuracy of the final base.