Robots are designed in a variety of types and shapes for performing different tasks. Mostly, they are designed by looking at nature and imitating its principles (e.g. snake-like robot). Author argues that snake-like robots offer very good capability for surveillance, inspection, exploration and search & rescue operations, especially in tight & hard-to-reach areas. But they find it difficult to climb vertically flat-surfaced obstacles (e.g. flat-surfaced wall or barrier) with higher heights than their own maximum free-climbing height. Initially, the author attempted to address this deficiency by developing a planar snake-like climber robot, however, speed of locomotion under the employed rectilinear gait was very low. In this context, the research was aimed to explore the possibility of increasing the climbing speed of planar snake-like climber robots (undergoing the rectilinear gait) on vertical or near-vertical flat surfaces with higher heights than the robots’ own free-climbing height through implementation of wheeling gait. The successful development of this robot, called “Marak II" is presented herein. It should be noted that the approach for designing such a robot is not to fully copy or imitate the biological aspects. Instead, the approach is to bypass some of the limitations in nature and some of the limitations that the nature poses against the design. The next task that was carried out, was the development of a unified mathematical formula for the parallel robots that could cover some deficiencies of available inverse dynamics formulations. A novel approach is presented herein which follows the Euler-Lagrange technique and is also able to handle inverse dynamics formulation under any type of passive, and/or active joints. Experiments were repeated multiple times to validate both introduced hypotheses and the results were found to be in close proximity of each other. The experiments on “Marak II" with both gaits (under similar conditions) revealed that the wheeling gait is approximately 10 times faster than the rectilinear gait. Moreover, the novel mathematical formula (based on Euler-Lagrange approach) was successfully validated through extensive simulations and experimentation under different settings.