In order to guarantee simultaneous changes of running power and variable delivery capacity for saving resources, new mechanism solution of external gear pumps with variable delivery capacity was proposed.The new mechanism was simple. By the dynamic force balance of output oil pressure and spring force for variable delivery capacity, the dynamic effective mesh width of gear pairs was automatically determined,then the variable delivery capacity and synchronization running power of external gear pumps along with the dynamic effective mesh width was thoroughly realized. With respect to its trappedoil performance and trappedoil relief, the related deep research and analysis were operated, and the new relief groove with microcircle profile was invented. Finally, an example computation and results analysis were executed. All results show that greater relief area and relief capacity are owned by the new relief groove with microcircle profile; the smaller the effective mesh width is, the lower the trappedoil pressure peak is, and the better the trappedoil performance is; on the other hand, the poorer the trappedoil performance is, but its degree is not big, etc.