Formulation of Equations of Motion for a Chain of Flexible Links Using Hamilton’s Principle

Abstract

The dynamic equations of a chain of flexible links are determined by means of Hamilton’s principle. First a continuous model is adopted and the boundary conditions are determined, along with the partial differential equations of motion. Then a model with a finite number of degrees of freedom is set up. The configuration of each link is described through the line which joins the end points and the relative deformation is described in terms of appropriate trial functions. The boundary conditions are incorporated into a set of basic trial functions. The time-dependent coefficients of the remaining shape functions play the role of Lagrangian coordinates. The dynamic equations are then derived and the procedure is contrasted with other methods for reduction of a system of links to a system with a finite number of degrees of freedom.