Energy method for position stability analysis of critical points of robot manipulators

An energy method for the position stability analysis of critical points (equilibrium positions) of dynamical systems with an arbitrary finite number of degrees of freedom is presented. The method proposed consists in the analysis of the potential energy balance of a perturbation of an arbitrary number of generalised co-ordinates of the dynamical system in order to establish the energy stability of individual degrees of freedom and of the whole system. In the case of mechanical systems, the position stability criterion, understood as minimisation of loads of driving systems with conservative forces, is discussed. Some examples of application of the method to the position stability analysis of critical points of one- and two-degree-of-freedom systems are analysed.