Degree-Of-Freedom(DOF) for most power transmission system varies according to the operation status which consists of friction elements to change the power flow or to adjust the speed ratio such as clutches, brakes or one-way clutches. To simulate the dynamic characteristics of automatic power transmission system which is a typical example of such a variable DOF systems, many sets of governing equations and complicated phase decision routines are necessary. In this paper dynamic constraint theorem is derived explaining the torque transmission characteristics during the clutch engagement process and a robust stable algorithm is developed describing this phase transition phenomenon effectively by introducing the concept of direct torque and virtual damping. Finally, applying this algorithm to a passenger car automatic transmission gear consisting of several friction elements, an efficient simulation methods for such a complex system will be suggested that is very simple and systematic.