Movement of each executive mechanism of the automatic packaging machines is complicated. The packaging machine standard executive mechanism requests coordination between the movements each other and a strict machine operating cycle period is required. The paper assimilates conventional design knowledge about periodic diagram of the automaton and gives a very comprehensive analysis of the internal relation among periodic motions of executive mechanisms of automatic packaging machines, summarizes three periods: movement-period, coordination-period and integration-period. A new way began to form in the paper. Called as three-ply analytics, of which principle is conciseness, it easy to be popularized.