Under the effect of external driving force and noise, a directed transport model for coupled particles in a two-dimensional potential is established. Here, a one-dimensional potential is taken as the periodic piecewise ratchet potential, and the other one is taken as the periodic symmetric non-ratchet potential to which the external periodic driving force and noise are applied. According to the nonequilibrium statistical theory and the nonlinear dynamics, the transport characters of the coupled system in the overdamped case are researched and discussed. Numerical results show that an obvious directed transport can appear both in the ratchet potential and in the non-ratchet potential case. But, the average velocities of the coupled system in the two potentials have completely different dependence on the system parameters. In the case of ratchet potential, the average velocity is strongly dependent on the coupling intensity, noise intensity, the driving strength, and the particle population; the average velocity can reach the maximum at appropriate coupling intensity, noise intensity, the driving strength or the particle population. Otherwise, in the case of non-ratchet potential, the average velocity is strongly dependent on the barrier height for the non-ratchet potential, but fluctuates as the coupling intensity, the driving strength, the driving initial phase difference or the particle population varies. This shows that the average velocity of the coupled system in the non-ratchet potential has weak dependence on system parameters, including the coupling intensity, the driving strength, the driving initial phase difference and the particle population.