Reduced Elastodynamic Modelling of Parallel Robots for the Computation of their Natural Frequencies

In this paper, it is presented an approach for computing the first natural frequencies of parallel robots. This approach, based on the Rayleigh-Ritz approximation, aims at reducing the model dimension by decreasing the size of the matrices describing the robot mass and stiffness. This allows saving computational time and avoiding inaccuracy due to ill-conditioning and thus can be used in design procedure as well as in real-time control. Simulations are carried out on a PRRRP robot modelized in 3D and comparisons with FEA software are presented. Keywords: elastodynamic modelling, model dimension reduction, natural frequencies, parallel robots. 1

[1]  Placid Mathew Ferreira,et al.  Computation of stiffness and stiffness bounds for parallel link manipulators 1 This research was sup , 1999 .

[2]  Damien Chablat,et al.  Stiffness Analysis of Overconstrained Parallel Manipulators , 2009, ArXiv.

[3]  J F Imbert,et al.  ANALYSE DES STRUCTURES PAR ELEMENTS FINIS , 1979 .

[4]  Warren P. Seering,et al.  Figure 1: Input Shaping by Convolving Desired Input with an Impulse Sequence. Comparison of Command Shaping Methods for Reducing Residual Vibration , 1995 .

[5]  Pan Zhenkuan,et al.  Dynamics of flexible multibody systems with tree topologies , 1992 .

[6]  E. Wittbrodt,et al.  Dynamics of Flexible Multibody Systems: Rigid Finite Element Method , 2006 .

[7]  Hélène Chanal,et al.  A study of the impact of machine tool structure on machining processes , 2006 .

[8]  Torgny Brogårdh,et al.  Present and future robot control development - An industrial perspective , 2007, Annu. Rev. Control..

[9]  C. D. Boor,et al.  Rayleigh-Ritz Approximation by Piecewise Cubic Polynomials , 1966 .

[10]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[11]  Neil C. Singer,et al.  Residual Vibration Reduction in Computer controlled Machines , 1989 .

[12]  Philip A. Voglewede,et al.  Overarching framework for measuring closeness to singularities of parallel manipulators , 2005, IEEE Transactions on Robotics.

[13]  E. Bautista,et al.  Input shaping reference commands for trajectory following Cartesian machines , 2005 .

[14]  Dominique Deblaise,et al.  A systematic analytical method for PKM stiffness matrix calculation , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[15]  G. Gogu,et al.  Rigidity analysis of T3R1 parallel robot with uncoupled kinematics , 2004 .

[16]  Jean-Yves Hascoët,et al.  Modeling of a High Speed Machining Center with a Multibody Approach: the Dynamic Modeling of Flexible Manipulators , 2007 .

[17]  Sébastien Briot,et al.  On the optimal design of parallel robots taking into account their deformations and natural frequencies , 2009, ArXiv.