The appearance of algebraic constraints among energy variables in models of physical systems leads to sets of (possibly nonlinear) implicit state equations, which usually complicate the treatment of the problems to be solved on the model. Building up on the Bond Graph model of a Planar Mobile Robotic Manipulator, this paper discusses some techniques to handle this kind of situations, determined here by the coupling of rigid bodies. Two alternatives to break the constraints are presented, consisting in the insertion between the coupled elements of: a) parasitic components –mostly spring-dampers, which is standard practice– or b) residual sinks – which is equivalent to the practice of adding constraint forces. Modifying the Bond Graph through the introduction of storage fields is the third method presented. Further, the extraction of constraint-free Euler-Lagrange and Hamiltonian descriptions from the Bond Graph are addressed. Finally, the suitability of all of these five alternatives for the purposes of simulation, analysis and control system design are discussed, and illustrated with simulation results.