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Highlights • A new dynamic model is developed for a flexible single-link manipulator. • The model includes an infinite number of uncoupled Duffing oscillators. • Two methods are presented for controlling the vibrations of Duffing oscillators. • Experiments validate Duffing model and the effectiveness of control methods. Abstract Unwanted vibrations caused by the commanded motions lower the positioning accuracy and degrade the control performance of flexible link manipulators. Much work has been devoted to the dynamics and control of flexible link manipulators. However, there are few studies dedicated to the flexible link manipulators having Duffing oscillator dynamics. This paper develops a new model for a flexible single-link manipulator by assuming large mechanical impedance in the drives or large inertia of the motor hub and by considering the flexibility of the single-link manipulator. The derived model includes an infinite number of uncoupled Duffing oscillators by ignoring the modal coupling effects. Two new methods are presented for controlling the vibrations of the flexible manipulator governed by Duffing oscillators. One is designed for the single-mode Duffing oscillator, and the other is for the multi-mode Duffing oscillators. A comparison of these two methods is made using the results of numerical simulations and experimental measurements. Experimental investigations are also performed on a flexible single-link manipulator to validate the dynamic behavior of Duffing oscillators and the effectiveness of the new control methods. [ABSTRACT FROM AUTHOR]

• Planar dynamic model of an underwater soft-link manipulator is derived. • Equations for estimating frequency and mode shape are proposed. • A control method is presented to control coupled vibrations. • Experiments validate effectiveness of dynamic model and control method. Underwater soft-link manipulators can be applied in offshore and marine industries. However, the soft-body link may interact with the fluid flow in this type of coupled liquid-link system. Both frequencies and mode shapes of the coupled system differ from those of uncoupled link vibrations and water flow due to the liquid-link interaction. Therefore, the dynamic model of underwater soft-body manipulators that account for liquid-link interaction is required to comprehend and control. Although significant work has been focused on the underwater manipulator and the soft manipulator, no significant dynamic modeling, control study, and experimental validation have been directed at the liquid-link interaction in underwater soft-body manipulators. A dynamic model of underwater soft-link manipulators undergoing planar motions is presented in this article. The analyses of frequencies and mode shapes for the liquid-link interaction are also described. Meanwhile, a control method is designed to mitigate coupled vibrations in underwater soft-link manipulators. Simulated and experimental results validate the utility of the dynamic model and control method. [ABSTRACT FROM AUTHOR]