Formulations in robotics based on variational principles

On the basis of new formulations, within of this paper, a few important notions, theorems, as well as differential and variational principles from analytical mechanics will be applied about complex mechanical systems, in which the robots are integrated. It is known that, the moving differential equations for any mechanical system can be obtained by means of the Newton-Euler (D´Alembert principle) or D´Alembert-Lagrange principle considered as fundamental equation in the mechanical system dynamics with links. Using the last principle, the Lagrange-Euler-type equations, written in the generalized form, have been obtained. The same equations can be also determined by means of the variational principles from analytical mechanics. One of this is known as Hamilton´s principle. As a result, in this paper a few formulations regarding this principle will be developed and further applied for exemplify on a mechanical robot structure.