MoodyMarine is a weakly nonlinear potential flow model for wave-body and mooring simulations with a graphical user interface. In this work we present the extension of the model to deal with constrained multi-body dynamics. By combining different translation and rotation constraints most joints can be modelled. As the constraints are imposed through springs and dampers in the explicit time-stepping algorithm, a slight manual tuning is required to make sure the bodies are constrained properly. Nevertheless, this tuning is shown not to influence the final results. In the paper we compare to existing test cases in literature as well as against experimental data. In all test cases there is a good agreement between the target solutions and MoodyMarine.