Abstract:By applying the notion of link units to the gear trains, the link units, especially the Jacobian units, the gear and planet carrier was gotten. The closed loops about gear train also were analyzed, and three kinds of basic closed loop were summed up. By using the effect factors and according to the basic closed loops, the units could be easily combined together to build Jacobian matrix, that was a linear equations, of whole gear train. After solved the linear equations, the angular velocities of each gears and planet carriers were yielded. It did not need to divide the compound planetary train into basic epicylic and fixed axis gear trains and also did not need to draw the arrows to determine the rotations of each links in the planar trains. It was easy to model the equations with manual hands or automatically model with computer for its modular property. The method could be used for any complex planar gear trains.