Omnidirectional mobility is required for the efficient movement of transport vehicles in factories and warehouses. To meet this requirement, the active omni wheel with barrel-shaped rollers (AOWBR) was previously proposed. The barrel-shaped rollers are arranged around the outer circumference of the main wheel of the AOWBR. This structure is expected to be effective in suppressing vibration during vehicle movement. The transmission roller drives the outer roller via a friction drive, which actively moves the AOWBR in the lateral direction. However, the friction drive may cause slippage between the transmission roller and the outer roller. To solve this problem, this study investigates the effects of the design parameters for an AOWBR on vibration and wheel slippage. The kinetic models of the wheel main body, transmission roller, and outer roller are established. Then, simulations are carried out using the kinetic models for various structural parameter values. The simulation results show that a softer rubber block installed in the support mechanism of the outer roller contributes to reduce wheel slippage but cause larger vibration, and that a larger setting angle between the transmission and outer rollers contributes to reduce slippage and vibration. Finally, comparison experiments are conducted on two types of prototype to verify the simulation results.