A formulation is introduced for the dynamic modeling of multibody robotic mechanisms to incorporate closed chains, higher pair joints, friction (including stiction, Coulomb, rolling and viscous friction), and unactuated and unsensed joints. Although this formulation was developed for the dynamic modeling of Uranus, and omnidirectional wheeled mobile robot, the methodology is directly applicable to a spectrum of multibody robotic mechanisms. The methodology is based on Newtonian dynamics, kinematics, and the concepts of force/torque propagation and frictional coupling at a joint introduced in this work. The extensible matrix-vector dynamics formulation allows the application of classical methodologies for the solution of systems of linear algebraic equations. To illustrate the procedure, the dynamics formulation is applied to a planar double pendulum and a biped in the frontal plane.