On the Dynamics of Floating Four-Bar Linkages. II. Bifurcations of Relative Equilibria

Abstract

Continuing our program to understand the geometry and dynamics of floating four-bar linkages, we explore the relative equilibria of an assembly that admits symmetric configurations. We show that a symmetric configuration is a relative equilibrium. As we vary certain kinematic parameters which preserve the symmetry, a symmetric relative equilibrium is bifurcated. The type of bifurcations can be either supercritical or subcritical pitchfork. The stability of the relative equilibria at symmetric configurations is investigated. Elementary techniques of singularity theory are applied in the analysis of the bifurcations. This investigation illustrates the possible rich dynamics in multibody systems with closed loop structure even with a small number of degrees of freedom.