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In order to give an insight into the work of the machine before the production and assembly and to obtain good analysis, this paper presents detailed solutions to the specific problem occured in the field of analytical mechanics. In addition to numerical procedures in the paper, a review of the theoretical foundations was made.Various types of analysis are very common in mechanical engineering, due to the possibility of an approximation of complex machines. For the proposed system, Lagrange's equations of the first kind, covariant and contravariant equations, Hamiltons equations and the generalized coordinates, as well as insight in Coulumb friction force are provided.Also, the conditions of static equilibrium are solved numerically and using intersection of the two curves. Finally, stability of motion for the disturbed and undisturbed system was investigated.

When a mobile manipulator's wheel loses contact with the ground, the manipulator may overturn, causing material damage, and in the worst case, putting human lives in danger. The overturning stability of wheeled mobile manipulators must not be overlooked at any stage of the mobile manipulator's life, starting from the design phase, continuing through the commissioning period and extending to the operational phase. The various overturning stability criteria formulated throughout the years do not explicitly consider normal wheel loads, with most of them relying on the prescribed stability margins in terms of overturning moments. These formulations commonly consider the overturning moments regarding axes connecting the adjacent manipulator's contact points with the ground and could be notably restrictive. Explicit expressions for the supporting forces of the manipulator provide the best insights into the relevant affecting terms that contribute to the overturning (in)stability. They also reduce the necessity for considering about which axis the manipulator could overturn and simultaneously enable the formulation of more intuitive stability margins and on-line overturning prevention techniques. The present study presents a general dynamics modelling approach in the Newton-Euler framework using 6D vectors and provides normal wheel load equations for a typical 4-wheeled rigid-chassis mobile manipulator traversing uneven terrain. The given expressions are expected to become the standard guidelines in considered wheeled mobile manipulators and to provide a basis for effective overturning stability criteria and overturning avoidance techniques. Based on the presented results, specific improvements of the state-of-the-art criteria are discussed.