Research on parameter plane of dynamic stability analysis

In this paper a new parameter plane for determining the instability and stability regions of fourbar mechanisms subjected to parametric excitations is proposed. The linearized partial differential equation of motion is derived, and reduced to a set of coupled Hill's equations by using Galerkin's method. Fourier series methods are then applied to obtain the stability boundaries based on Floquent theory. According to derived formulations, parametric excitations depend on the ratio of the length of the rigid link to the length of the flexible coupler which determines the kinematical characteristics of the considered mechanism and is proved to be the incentive parameter in the parameter plane unlike the incentive parameter assumed to be independent in literature.