In this paper, adaptive fuzzy-based motion generation and control are investigated for nonholonomic mobile manipulators with an under-actuated dyanmics model, in the presence of parametric and functional uncertainties. It is well known that the constraints of this kind of system consist of kinematic constraints for the mobile platform and dynamic constraints for the under-actuated manipulator with a passive joint. Through using dynamic coupling property of nonholonomic mobile manipulators, we can decouple the dynamics into a fully actuated subsystem and an unactuated subsystem. Then adaptive control is employed for the fully actuated subsystem using fuzzy logic approximation. Since the non-actuated subsystem cannot be directly manipulated by torque inputs but can be indirectly affected by the motion of the actuated subsystem, the reference trajectory of the actuated subsystem is planned by the fuzzy logic system based motion generator. Rigorous theoretic analysis has been established to show that the proposed trajectory generation and control are able to achieve dynamic stability, motion tracking and optimized dynamics. Simulation studies have further validated the efficiency of the developed scheme.