On uneven ground, legged robots have the potential to be a walking machine. Theo Jansen's mechanism, which consists of eleven bar linkages, reproduces a smooth walking pattern known as gait. Parallel motions are commonly used in heavy machinery and have recently been highlighted in a biological motion model. Due to the singularity problem, the close-loop connection just gives a designed end- effector's trajectory, which is believed to be less changeable. The singularity on the modified Theo Jansen mechanism was addressed in this study by introducing the parametric orbit as a new freedom point at the joint center, and multi body dynamics were used to examine its kinematics and dynamics (MBD). In the numerical simulation, the mechanism's extensibility in terms of gait trajectory flexibility was clearly established, resulting in novel functional gait trajectories controlled by two control parameters that modify the form of the parametric oval in the joint center.