A continuous mass model for predicting the elastodynamic behaviour of rocker in a planar four-bar crank-rocker mechanism having elastic coupler and rocker

Abstract

In this paper an attempt has been made to present a procedure to predict the elastodynamic behaviour of physically damped, unbalanced planar four-bar linkage with both coupler and rocker being elastic. The basic formulation is carried out by Euler-Bernoulli theory of beams to obtain the differential equations of motion and boundary conditions for the elastodynamic behavior of the rocker with and without the endweights on the coupler and the rocker. Hamilton's integral and the method of Kantorovich are used to obtain the decoupled Hill's equation. The solution of the resulting Mathieu-Hill equation has been attempted by Runge-Kutta-Merson method. The assumed modes technique is used to model the deflection of the rocker link. The counterweight/endweight effects can then be easily included in this analysis. This aspect is important for high speed balancing of the linkage.