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Traditional coordinated motion planning schemes for mobile robot manipulators are primarily designed at the velocity level, which limits their applicability to acceleration-oriented systems. To address this limitation, this paper proposes, for the first time, a kinematic model and a trajectory tracking scheme for a two-wheeled mobile robot manipulator (TWMRM) at the acceleration level. This innovation enables the TWMRM system to achieve improved precision and stability under complex dynamic conditions. Compared to velocity-level approaches, the proposed acceleration-level scheme is applicable to both acceleration-oriented and velocity-oriented mobile robot manipulators, offering a broader range of applications. To verify the proposed approach, trajectory-tracking simulations show that the TWMRM’s end-effector closely follows the desired trajectory, with position errors on the order of ${10}^{-7}$ and no divergence issue. Additionally, practical experiments confirm the feasibility of the acceleration-level kinematic model and trajectory tracking scheme for real-world applications.