This paper focuses on modeling forward and inverse kinematics of a 12-DOF bipedal robot and parametrizing its body trajectory to generate different gaits on 3D terrain.The 12-DOF kinematic chain represents the lower body part of the humanoid robot. The Cartesian coordinate is assigned to each link of the biped robot using the Denavit-Hartenberg (DH) convention. One step of the bipedal walk is divided into three walk phases depending on whether one foot or both feet are in contact with the ground.Time parameterized cubic splines construct the biped robot’s mid-hip and swinging foot trajectory.The inverse kinematic determines the values of the joint angles corresponding to hip and swinging foot frame trajectory using the geometric relation between foot ankle point, knee position,and hip position. The complete one-step gait of the biped robot is represented in the form of a stick diagram.The proposed method is a geometrical approach to parameterize the gait of a biped robot for one step of the walk in terms of hip and swinging foot trajectory optimization is required to determine energy optimal balanced gait, which we envisage as our future task.