In the present work kinematics of a four link biped robot is modeled using body coordinate formulation. The kinematic analysis of the biped robot is done for both stance and flight phases. Apart from joint constraints, constraint equations are introduced on the zero moment point (ZMP) and the centroidal angular momentum of the biped robot during stance phase. While the constraint on ZMP ensures stability during stance phase, constraint on angular momentum makes the biped robot non-holonomic even during the stance phase. During flight phase (during which angular momentum is conserved, and hence the system is non-holonomic by nature), the vertical distance between the foot and the center of mass is planned such that the velocity of the foot reaches zero at the time of landing to ensure a smooth landing without impact. Simulations are done in MATLAB using RK4 method. Simulation results have been presented for both the support and flight phases for various initial configurations of the robot, which resulted in variation of the horizontal distance and vertical height covered by the biped robot.