Active damping of the elastodynamic vibrations of a flexible slider-crank mechanism using an energy approach

In this paper, the problem of active damping of the elastodynamic vibrations of a flexible slider-crank mechanism is addressed. The slider-crank mechanism is such that the connecting rod is flexible and the crank link is rigid. The slider-crank mechanism system is underactuated since the connecting rod is not directly controlled. A dynamic model for the slider-crank mechanism is derived using the Hamiltonian principle. Then, a control scheme based on an energy approach is proposed. The control scheme uses the passivity of the system to eliminate the vibrations of the flexible connecting rod. Simulation results are given to illustrate the theoretical developments.

XIII.—Partial Differential Equations and the Calculus of Variations

A partial differential equation of physics may be defined as a linear second-order equation which is derivable from a Hamiltonian Principle by means of the methods of the Calculus of Variations. This principle states that the actual course of events in a physical problem is such that it gives to a certain integral a stationary value.