Bifurcation in a planar four-bar mechanism with revolute clearance joint

Generally, multi-body mechanical systems in which the impact phenomena occur exhibit chaotic and quasi-periodic behavior. Mechanisms with clearance joint are categorized in such systems due to contact between the connecting bodies. In this paper, we would investigate the nonlinear dynamic behavior of a four-bar mechanism with joint and clearance at the connection between the coupler and rocker. Motion equations are derived based on the Lagrangian approach. The nonlinear continuous contact force model proposed by Lankarani and Nikravesh is utilized to evaluate the normal contact force developed in the journal–bearing system. Furthermore, the friction effect on the clearance joint is considered using a modified Coulomb friction law. The dynamical behaviors are numerically identified in discrete state space, based on the Poincaré portraits. Numerical simulations display both periodic and chaotic motions in the system behavior. Therefore, bifurcation analysis has been performed with a change in the size of clearance corresponding to the various values of crank rotational velocities. Then, we compare some clearance ranges, in which the system response becomes stable for these cases. Fast Fourier transformation is also applied to analyze the frequency spectrum of the system response.

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