In the field of the system dynamics related to the vibration characteristics, there are lots of examples introduced for the translational system, however the analysis of the torsional systems such as driveline in the automobile is rare compared with the translational system. The purpose of this study is to show the simple concepts for the torsional system analysis and explain how to adjust the mathematical methods for the geared motions, which can be applied to the driveline of the automobile. In order to do it, there are several systematical approaches described about how the sub-system motions can be understood with the mathematical descriptions. Based upon this fundamental study, several torsional system modeling methods will be suggested. Therefore, the characteristics of the torsional system and the gear motions will be explained, which can be adjusted in a further study as a next step.