Advertisement

Study of Vibrations of a Robotic Arm, Using the Lagrange Equations with Respect to a Non-inertial Reference Frame

  • Andrei CraifaleanuEmail author
  • Ion Stroe
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 198)

Abstract

The paper studies the free vibrations of a robotic arm, located on a rotating platform. The robotic arm is modeled as a system with a finite number of degrees of freedom, consisting of elastically coupled rigid bodies. The differential equations of the free vibrations are obtained using the Lagrange equations formalism, in a generalized form, valid with respect to a non-inertial reference frame. The influence of the kinematic parameters of the platform motion upon the eigenfrequencies of the robotic arm is analyzed, considering two configurations of the system.

References

  1. 1.
    L.D. Landau, E.M. Lifshitz, in Mechanics (translated from Russian), 3rd edn. Volume 1 of Course of Theoretical Physics (Butterworth, Heinemann, 2000)Google Scholar
  2. 2.
    C. Gignoux, B. Silvestre-Brac, Solved Problems in Lagrangian and Hamiltonian Mechanics (Springer, Dordrecht, Heidelberg, London, New York, 2009), pp. 23, 48Google Scholar
  3. 3.
    A.I. Lurie, Analytical Mechanics (Springer, New York, 2002)Google Scholar
  4. 4.
    A. Brizard, Introduction to Lagrangian and Hamiltonian Mechanics (World Scientific Publishing Company, Singapore, 2008)Google Scholar
  5. 5.
    I. Stroe, A. Craifaleanu, Calculus of a compass robotic arm using Lagrange equations in non-inertial reference frames, in Proceedings of the International Conference of Aerospace Sciences “AEROSPATIAL 2012” pp. 137–141, Bucharest, 11–12 Oct 2012Google Scholar
  6. 6.
    I. Stroe, A. Craifaleanu, in Generalization of the Lagrange equations formalism, for motions with respect to non-inertial reference frames. Applied Mechanics and Materials, vol. 656 (Trans Tech Publications, Switzerland, 2014), pp. 171–180Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University “Politehnica” of BucharestBucharestRomania

Personalised recommendations