A unified dynamic modelling approach of closed and/or open kinematic chain mechanisms is established. It is based on the use of the Newton-Euler formalism and the explicit formulation of kinematic holonomic constraints for the closed loop mechanisms. The approach is then applied to derive the dynamic modelling of a four-legged robot adopting a walking gait. The different movement sequences of the gait are analysed in order to calculate the all necessary terms in the dynamic equations of the quadruped robot.