New analytical formalisms used in finite element analysis of robots with elastic elements

ABSTRACT Obtaining the equations of motion for an element in finite element analysis (FEA) model in the analysis of a multi-body system (MBS) having component elastic elements represents an important (maybe the main) step to build a soft able to solve such a problem numerically. In use FEA in the study of a MBS with elastic elements, the method of Lagrange's equations is especially used at present. This method presents the advantages of a homogeneous writing and the possibility to follow the operations easier. However, there are also equivalent formulations, developed by analytical mechanics, for approaching such a mechanical system. The earning of these alternative forms will be presented, by comparison.

[1]  D. Lu,et al.  Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir waves , 2019, Pramana.

[2]  Aly R. Seadawy,et al.  Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev-Petviashvili modified equal width dynamical equation , 2019, Comput. Math. Appl..

[3]  Roger Ohayon,et al.  Dynamic responses of flexible-link mechanisms with passive/active damping treatment , 2008 .

[4]  T. Liu,et al.  THE MODELLING AND VIBRATION CONTROL OF BEAMS WITH ACTIVE CONSTRAINED LAYER DAMPING , 2001 .

[5]  Xianmin Zhang,et al.  Dynamic responses of flexible linkage mechanisms with viscoelastic constrained layer damping treatment , 2001 .

[6]  B. Bahgat,et al.  Finite element vibrational analysis of planar mechanisms , 1976 .

[7]  H. R. Shafei,et al.  A systematic method for the hybrid dynamic modeling of open kinematic chains confined in a closed environment , 2016 .

[8]  Dianchen Lu,et al.  Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods , 2018, Modern Physics Letters A.

[9]  Iuliu Negrean,et al.  Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems , 2019, Symmetry.

[10]  Iuliu Negrean,et al.  Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element , 2020, Symmetry.

[11]  Xian-min Zhang,et al.  Dynamic analysis of flexible linkage mechanisms under uniform temperature change , 2009 .

[12]  D. Lu,et al.  Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications , 2018, Results in Physics.

[13]  Moharam Habibnejad Korayem,et al.  Motion equations of cooperative multi flexible mobile manipulator via recursive Gibbs–Appell formulation , 2019 .

[14]  Sorin Vlase,et al.  Elimination of lagrangian multipliers , 1987 .

[15]  D. Lu,et al.  Dispersive solitary wave solutions of nonlinear further modified Korteweg–de Vries dynamical equation in an unmagnetized dusty plasma , 2018, Modern Physics Letters A.

[16]  THE EXPLICIT GIBBS-APPELL EQUATIONS of MOTION for RIGID-BODY CONSTRAINED MECHANICAL SYSTEM , 2018, 2018 6th RSI International Conference on Robotics and Mechatronics (IcRoM).

[17]  W. Cleghorn,et al.  Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with flexible links , 2005 .

[18]  Moharam Habibnejad Korayem,et al.  Derivation of dynamic equation of viscoelastic manipulator with revolute–prismatic joint using recursive Gibbs–Appell formulation , 2017 .

[19]  R. G. Fenton,et al.  Finite element analysis of high-speed flexible mechanisms , 1981 .

[20]  S. Vlase.  DYNAMICAL RESPONSE OF A MULTIBODY SYSTEM WITH FLEXIBLE ELEMENTS WITH A GENERAL THREE-DIMENSIONAL MOTION , 2012 .

[21]  A. Seadawy,et al.  A third-order nonlinear Schrödinger equation: the exact solutions, group-invariant solutions and conservation laws , 2020, Journal of Taibah University for Science.

[22]  Jorge Ambrósio,et al.  Composite materials in flexible multibody systems , 2006 .

[23]  D. Lu,et al.  Propagation of long-wave with dissipation and dispersion in nonlinear media via generalized Kadomtsive–Petviashvili modified equal width-Burgers equation , 2020, Indian Journal of Physics.

[24]  D. Lu,et al.  Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions , 2019, Modern Physics Letters B.

[25]  M. I. A. Othman,et al.  A domain of influence in the Moore–Gibson–Thompson theory of dipolar bodies , 2020, Journal of Taibah University for Science.

[26]  Sorin Vlase,et al.  Motion equation for a flexible one-dimensional element used in the dynamical analysis of a multibody system , 2018, Continuum Mechanics and Thermodynamics.

[27]  Phatiphat Thounthong,et al.  Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations , 2020, Journal of Taibah University for Science.

[28]  D. Lu,et al.  Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations , 2018, Open Physics.

[29]  J. Gibbs.  On the Fundamental Formulae of Dynamics , 1879 .

[30]  Iuliu Negrean,et al.  A New Approach in Analytical Dynamics of Mechanical Systems , 2020, Symmetry.