As ordinary dual-axis driving mechanisms in X-Y directions, for example, commercially available X-Y stages with ball screws are familiar. However, such driving mechanisms have two stages, namely both upper and lower linear actuators, the latter of which must generate sufficient thrust to carry large weights, including that of the upper actuator mechanism, which has hampered efforts to achieve suitably fast and smooth driving motion due to the inertial force effect. It is also difficult to achieve a small and slimline driving mechanism with such overlapping two-stage structure. In these ordinary two-stage driving mechanisms, the motion of the X-Y stage can be disturbed by the wires of the upper actuator. In this research, we have considered the abovementioned problems, and propose a new omnidirectional driving gear mechanism that enhances its driving area from the normal X-Y plane to convex and concave curved surfaces respectively, and even various combinations of both. The smoothness of basic omnidirectional motion and effectiveness of the driving method of this proposed omnidirectional driving gear mechanism have been confirmed with several experiments involving our setups.