Dynamic stability of four-bar and slider-crank mechanisms with viscoelastic (Kelvin-Voigt model) coupler

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The effect of internal material damping on the dynamic stability of the flexible coupler of four-bar and slider-crank mechanisms is studied. The linearized partial differential equation of motion is transformed into a set of coupled, damped Hill's equations by use of Galerkin's method. Stability analysis of the first kind is considered and the problem of determining the stability boundaries is shown to coincide with the problem of determining the eigenvalues of a double-size Hill's matrix. Case studies have been presented concerning slider-crank and four-bar mechanisms and results are discussed.