The recent studies in robotics tend to develop legged robots to perform highly dynamic movement on rough terrain. Before implementing on robots, the reference generation and control algorithms are preferably tested in simulation and animation environments. For simulation frameworks dedicated to the test of legged locomotion, the contact modeling is of pronounced signi cance. Simulation requires a correct contact model for obtaining realistic results. Penalty based contact modeling is a popular approach that de nes contact as a spring - damper combination. This approach is simple to implement. However, penetration is observed in this model. Interpenetration of simulated objects results in less than ideal realism. In contrast to penalty based method, exact contact model de nes the constraints of contact forces and solves them by using analytical methods. In this thesis, a quadruped robot is simulated with exact contact model. The motion of system is solved by the articulated body method (ABM). This algorithm has O(n) computational complexity. The ABM is employed to avoid calculation of the inverse of matrices. The contact is handled as a linear complementarity problem and solved by using the projected Gauss Seidel algorithm. Joint and contact friction terms consisting of viscous and Coulomb friction components are implemented
