Dynamic balance generalized problem and the promising areas of its application

Abstract

The paper considers the generalized problem of the machines and mechanisms dynamic balance in terms of ensuring the given laws of altering reactions in the selected links. Representation of equations of the mechanical systems dynamics in the form of differential algebraic equations was used making it possible to obtain mathematical models of the nonlinear mechanical systems dynamics with the arbitrary structure of kinematic and force connections. With this approach, the constraint reactions are determined by algebraic equations from the system coordinates. The problem solution is based on changing the bonds selected reactions due to the impact on reactions in the other selected bonds by adding non-stationary terms to the selected bonds equation. Conditions for rigorous solution of the optimal control problem for a mechanical system are shown for the integral quality criterion not explicitly containing the control functions. The method is aimed at numerical models of the mechanical systems widely used in the programs for dynamic analysis of the coupled systems of bodies. Test examples are provided for manipulator, anthropomorphic robot and controlled suspension of a transport vehicle. The method was realized in the software package for simulating the controlled motion dynamics of the coupled systems of bodies.