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Nonlinear response of a flexible Cartesian manipulator with payload and pulsating axial force

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Abstract

In this present work, the nonlinear response of a single-link flexible Cartesian manipulator with payload subjected to a pulsating axial load is determined. The nonlinear temporal equation of motion is derived using D’Alembert’s principle and generalised Galerkin’s method. Due to large transverse deflection of the manipulator, the equation of motion contains cubic geometric and inertial types of nonlinearities along with linear and nonlinear parametric and forced excitation terms. Method of normal forms is used to determine the approximate solution and to study the dynamic stability and bifurcations of the system. These results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion. Influences of amplitude of the base excitation, mass ratio, and amplitude of static and dynamic axial load on the steady state responses of the system are investigated for three different resonance conditions. For some specific conditions, the results obtained in this work are found to be in good agreement with the previously published experimental work. The results obtained in this work will find applications in the design of flexible Cartesian manipulators with payload.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    Barun Pratiher & Santosha Kumar Dwivedy

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  1. Barun Pratiher
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  2. Santosha Kumar Dwivedy
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Correspondence to Santosha Kumar Dwivedy.

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Pratiher, B., Dwivedy, S.K. Nonlinear response of a flexible Cartesian manipulator with payload and pulsating axial force. Nonlinear Dyn 57, 177–195 (2009). https://doi.org/10.1007/s11071-008-9431-6

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  • DOI: https://doi.org/10.1007/s11071-008-9431-6

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