Partitioned dynamic simulation of multibody systems offers the benefit of increased modularity over direct simulation, thereby allowing for the use of softwares tailored to the needs of each physical subsystem. In this paper, the partitioned simulation of multibody systems is accomplished by deriving an explicit expression for the constraint forces acting between subsystems. These constraint forces form the basis of a coupling module that communicates results between subsystems, each of which can be simulated independently using tailored numerical solvers. We provide details of how this partitioned solution approach can be implemented in the framework of implicit and explicit time integrators. The computational efficiency of the proposed partitioned simulation approach is established, in comparison with direct simulation, by solving three suitable problems containing both rigid and deformable components.