Planetary　gear　trains　have　the　advantage　of　compactness,　light　weight,　high　speed　reduction　and　capability　of　differential　drive,　so　they　are　often　used　in　transmission　systems.　The　purpose　of　this　paper　is　to　propose　a　systematic　methodology　for　the　analysis　of　the　mechanical　efficiency　of　a　planetary-gear-train　type　automatic　transmission.　Based　on　the　Graph　theory,　a　canonical　graph　representation　of　the　kinematic　structure　of　planetary-gear-train　type　automatic　transmission　is　presented.　Then,　the　equations　of　the　mechanical　efficiency　of　the　planetary-gear-train　type　automatic　transmission　have　been　constructed.　The　design　of　an　automatic　transmission　for　the　automobile　is　used　as　an　example　to　illustrate　the　proposed　methodology.　The　results　of　the　paper　provide　a　powerful　tool　for　the　design　of　the　planetary-gear-train　type　automatic　transmissions.　©　2015　Taylor　&　Francis　Group,　London.