This paper discusses modeling approaches for mechanical systems which may be driven from more than one source of power and which include unidirectional coupling elements. These systems arise in various settings, including heavy-lift helicopters and hybrid automobiles. In this paper, two kinds of mathematical model are examined for the free-wheeling clutch, a key element in these systems. It is shown that it is not possible to define transition rules between coupled and decoupled states using only relative speed or only torque if idealized models are used. A model involving a mixed torque-velocity transition rule is shown to capture the essential switching behavior. By using the bond graph formalism, the inclusion of realistic continuous effects such as inertia and friction becomes simple by modular cascading. A simplified two-driver hybrid dynamical model is constructed and characterized using the mixed model and the concept of clutch line is introduced to characterize the dynamic behavior. This work serves as a basis for subsequent controllability studies and selection of feedback control strategies.

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