The importance of system design in the field of mechanical engineering has been increasingly recognized recently. But suitable and useful methods for machine design are not yet established. So we must derive easy and useful designing methods for each machine element. We derived a new designing method by linear graph theory and analyzed the results of the dynamic behaviour of a power transmission mechanism as an example. And we understand that the mechanisms which are subject to restrictions of high accuracy and high performance must be designed by considering the characteristic of each machine element. This report deals with a more general power transmission mechanism containing a motor, bearing, support an so on, and analyzes the results of dynamic behaviour. Provided that the analytical model and system graph as in this report are prepared for the mechanism, the performance of the mechanism is easily grasped by this method.