Many manmade machines and mechanisms including robots function based on the concept of nature-inspired design so that they can perform their intended duties by mimicking the working mechanisms of animals and insects. Accordingly, walking machines (robots) use wheels and tracks to cross rough terrain efficiently and in a stable way than more conventional robots. Legged walking robots in particular get a discontinuous contact with the ground that provides them the capability to select tractions such that obstacles or holes are escaped. This article reports a study conducted on kinematic modelling and analysis of a walking machine (robot) leg mechanism that can operate on rough terrain. Its kinematic mechanisms is analyzed using the Denavit-Hartenberg (DH) convention approach. Symbolic computations are also implemented to parametrically optimize the motion parameters of the robot leg mechanism. The equation of motion is derived from the dynamic analysis using the Euler-Lagrange method which involves kinetic and potential energy expressions. In order to validate the performance of the robot leg mechanism and motion behaviors, kinematic motion analysis in SolidWorks and MATLAB are used. The leg mechanism used is effective for rough terrain areas because it is capable of walking on terrain with different amplitudes due to surface toughness and aerodynamics.