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This paper analyzes the dynamic character of a planar multi-degree-of-freedom industrial machine using an industrial robot as a reference model. A nonlinear dynamics model of a multi-body structure including the end effector, base and the manipulator is established using the Lagrange's principle. The validity was verified by ADAMS simulation with the established dynamic model. Focusing on the low-frequency region, the influence of the robot assembly parameters on the vertical vibration response of the body is discussed. Based on the data summary, some optimization recommendations are made. The results of this paper may contribute to the design of vibration isolation for such robotic arm structures. • Considered the nonlinear multi-body dynamics of an industrial machine. • Established a seven-degree-of-freedom nonlinear dynamics model and verified by ADAMS. • Multiple super-harmonic resonance peaks and complex soft nonlinear phenomena were observed. [ABSTRACT FROM AUTHOR]