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A transmission system model for Ford Motor Company's automatic transmission (AOD) system used in the Lincoln Town Car has been developed using the free-body diagram method (Newtonian approach). This model is sophisticated enough to represent the dynamic behavior of the transmission system, yet simple enough to use as a real time computer simulation tool, and as an embedded model within a dynamic observer. The transmission system and torque converter models presented in this paper are part of a larger powertrain system model at the Powertrain Control Research Laboratory, University of Wisconsin-Madison.