This paper describes a new simulation method of multidegree-of-motion-freedom mechanical systems with the time-dependent contact and the Coulomb friction, such as a legged robot interacting with the ground and a satellite-mounted manipulator catching an object. The proposed approach is the extension of the open link manipulator simulation method and the contact simulation method of rigid body mechanics. The proposed simulation model can be said to be mathematically exact, thus this approach enables the essential investigation for control algorithms of the mechanical systems. The method is tested on a biped robot system and some results are shown.