Kinematic analysis of legged robotic systems is our focus of study in this paper. The detailed forward and inverse kinematic analysis of the quadruped robots using the geometric method has been discussed in this paper. DH convention is used to assign frames to the link of a quadruped robot. The gait of the quadruped robot under study depends upon many things like type of motion, mobility constraint, terrain structure, etc. The configuration of a quadruped robot for one complete gait cycle is shown with the help of a stick diagram. Time variations of kinematic quantities like joint angles and angular velocity of the knee and hip have been studied. In the future, we have a plan to generate the optimal gait of a quadruped robot on uneven terrain.