The theoretical part of an investigation of the elastic-dynamic behavior of a counterweighted four-bar linkage rocker link, which in addition carries an overhanging mass, is given. The linearized equations of motion are derived by way of Hamilton’s integral, a novel elastic mechanism constraint equation, and the method of Kantorovich. The normal modes of the free vibration of the complex link provide the space portions of the solution, while the time portions are furnished by the resulting Hill’s equations. Floquet theory is adapted for stability considerations and a method for obtaining steady-state solutions is given. Part II applies the solution techniques to a specific mechanism and reports on confirming experimentation.

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