Elastodynamic modeling and parameter sensitivity analysis of a parallel manipulator with articulated traveling plate

  • Binbin LianEmail author
  • Lihui Wang
  • Xi Vincent Wang
Open Access


This paper deals with the elastodynamic modeling and parameter sensitivity analysis of a parallel manipulator with articulated traveling plate (PM-ATP) for assembling large components in aviation and aerospace. In the elastodynamic modeling, the PM-ATP is divided into four levels, i.e., element, part, substructure, and the whole mechanism. Herein, three substructures, including translation, bar, and ATP, are categorized according to the composition of the PM-ATP. Based on the kineto-elastodynamic (KED) method, differential motion equations of lower levels are formulated and assembled to build the elastodynamic model of the upper level. Degrees of freedom (DoFs) at connecting nodes of parts and deformation compatibility conditions of substructures are considered in the assembling. The proposed layer-by-layer method makes the modeling process more explicit, especially for the ATP having complex structures and multiple joints. Simulations by finite element software and experiments by dynamic testing system are carried out to verify the natural frequencies of the PM-ATP, which show consistency with the results from the analytical model. In the parameter sensitivity analysis, response surface method (RSM) is applied to formulate the surrogate model between the elastic dynamic performances and parameters. On this basis, differentiation of performance reliability to the parameter mean value and standard variance are adopted as the sensitivity indices, from which the main parameters that greatly affect the elastic dynamic performances can be selected as the design variables. The present works are necessary preparations for future optimal design. They can also provide reference for the analysis and evaluation of other PM-ATPs.


Parallel manipulator Articulated traveling plate Elastodynamic modeling Parameter sensitivity 


  1. 1.
    Morozov A, Angeles J (2007) The mechanical design of a novel Schönflies-motion generator. Robot Com-Int Manuf 23(1):82–93CrossRefGoogle Scholar
  2. 2.
    Altuzarra O, Sandru B, Pinto C, Pentuya V (2011) A symmetric parallel Schönflies-motion manipulator for pick-and-place operations. Robotica 29:853–862CrossRefGoogle Scholar
  3. 3.
    Sun T, Song Y, Gao H, Yang Q (2015) Topology synthesis of a 1T3R parallel manipulator with an articulated traveling plate. J Mech Robot 7(3):310151–310159CrossRefGoogle Scholar
  4. 4.
    Nabat V, Rodriguez MO, Company O, Krut S (2005) Par4: very high speed parallel robot for pick-and-place. Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS’05), Alberta, Canada, 1202–1207Google Scholar
  5. 5.
    Krut S, Company O, Benoit M, Ota H, Pirrot F (2003) I4: a new parallel mechanism for SCARA motions. Proceedings of IEEE International Conference on Robotics and Automation (ICRA’03), Taipei, Taiwan, 1875–1880Google Scholar
  6. 6.
    Xie F, Liu X (2016) Analysis of the kinematic characteristics of a high-speed parallel robot with Schönflies motion: mobility, kinematics, and singularity. Front Mech Eng 11(2):135–143CrossRefGoogle Scholar
  7. 7.
    Qi Y, Sun T, Song Y, Jin Y (2015) Topology synthesis of three-legged spherical parallel manipulators employing lie group theory. P IMech Eng C-J Mech Eng Sci 229(10):1873–1886CrossRefGoogle Scholar
  8. 8.
    Huo X, Sun T, Song Y, Qi Y, Wang P (2017) An analytical approach to determine motions/constraints of serial kinematic chains based on Clifford algebra. P IMech Eng C-J Mech Eng Sci 231(7):1324–1338CrossRefGoogle Scholar
  9. 9.
    Zhang D, Wang L, Lang SY (2004) Parallel kinematic machines: design, analysis and simulation in an integrated virtual environment. J Mech Des 127(4):580–588CrossRefGoogle Scholar
  10. 10.
    Qi Y, Sun T, Song Y (2018) Multi-objective optimization of parallel tracking mechanism considering parameter uncertainty. J Mech Robot 10(4):0410061–04100612CrossRefGoogle Scholar
  11. 11.
    Wu J, Chen X, Wang L (2016) Design and dynamics of a novel solar tracker with parallel mechanism. ASME/IEEE T Mech 21(1):88–97Google Scholar
  12. 12.
    Bi ZM, Wang L (2009) Optimal design of reconfigurable parallel machining systems. Robot Com-Int Manuf 25(6):951–961CrossRefGoogle Scholar
  13. 13.
    Gao Z, Zhang D, Ge Y (2010) Design optimization of a spatial six degree-of-freedom parallel manipulator based on artificial intelligence approaches. Robot Com-Int Manuf 26(2):180–189CrossRefGoogle Scholar
  14. 14.
    Sun T, Xiang X, Su W, Wu H, Song Y (2017) A transformable wheel-legged mobile robot: design, analysis and experiment. Robot Auton Sys 98:30–41CrossRefGoogle Scholar
  15. 15.
    Zhang D, Wang L, Gao Z, Su X (2013) On performance enhancement of parallel kinematic machine. J Intell Manuf 24(2):267–276CrossRefGoogle Scholar
  16. 16.
    Sun T, Zhai Y, Song Y, Zhang J (2016) Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker. Robot Com-Int Manuf 41:78–91CrossRefGoogle Scholar
  17. 17.
    Sun T, Liang D, Song Y (2018) Singular-perturbation-based nonlinear hybrid control of redundant parallel robot. IEEE T Ind Electron 65(4):3326–3336CrossRefGoogle Scholar
  18. 18.
    Wang L, Xi F, Zhang D (2006) A parallel robotic attachment and its remote manipulation. Robot Com-Int Manuf 22(5–6):515–525CrossRefGoogle Scholar
  19. 19.
    Song Y, Qi Y, Dong G, Sun T (2016) Type synthesis of 2-DoF rotational parallel mechanisms actuating the inter-satellite link antenna. Chin J Aeronaut 29(6):1795–1805CrossRefGoogle Scholar
  20. 20.
    Song Y, Gao H, Sun T, Dong G, Lian B, Qi Y (2014) Kinematic analysis and optimal design of a novel 1T3R parallel manipulator with an articulated travelling plate. Robot Com-Int Manuf 30(5):508–516CrossRefGoogle Scholar
  21. 21.
    Yang S, Sun T, Huang T, Li Q, Gu D (2016) A finite screw approach to type synthesis of three-DoF translational parallel mechanisms. Mech Mach Theory 104:405–419CrossRefGoogle Scholar
  22. 22.
    Qi Y, Sun T, Song Y (2017) Type synthesis of parallel tracking mechanism with varied axes by modeling its finite motions algebraically, J Mech Robot 9(5):054504–1–054504–6Google Scholar
  23. 23.
    Huo X, Sun T, Song Y (2017) A geometric algebra approach to determine motion/constraint, mobility and singularity of parallel mechanism. Mech Mach Theory 116:273–293CrossRefGoogle Scholar
  24. 24.
    Yang S, Sun T, Huang T (2017) Type synthesis of parallel mechanisms having 3T1R motion with variable rotational axis. Mech Mach Theory 109:220–230CrossRefGoogle Scholar
  25. 25.
    Sun T, Yang S, Huang T, Dai JS (2017) A way of relating instantaneous and finite screws based on the screw triangle product. Mech Mach Theory 108:75–82CrossRefGoogle Scholar
  26. 26.
    Sun T, Song Y, Li Y, Zhang J (2010) Workspace decomposition based dimensional synthesis of a novel hybrid reconfigurable robot. J Mech Robot 2(3):310091–310098CrossRefGoogle Scholar
  27. 27.
    Liang D, Song Y, Sun T, Dong G (2016) Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance. Nonlinear Dynam 83:631–658MathSciNetCrossRefGoogle Scholar
  28. 28.
    Sun T, Song Y, Li Y, Liu L (2010) Dimensional synthesis of a 3-DOF parallel manipulator based on dimensionally homogeneous Jacobian matrix. Sci China-Technol Sci 53(1):168–174CrossRefzbMATHGoogle Scholar
  29. 29.
    Cao W, Ding H (2018) A method for stiffness modeling of 3R2T overconstrained parallel robotic mechanisms based on screw theory and strain theory. Prec Eng 51:10–29CrossRefGoogle Scholar
  30. 30.
    Sun T, Song Y, Yan K (2011) Kineto-static analysis of a novel high-speed parallel manipulator with rigid-flexible coupled links. J Cent South Univ Tech 18(3):593–599CrossRefGoogle Scholar
  31. 31.
    Bi ZM, Wang L (2012) Energy modeling of machine tools for optimization of machine setup. IEEE T Aotum Sci Eng 9(3):607–613Google Scholar
  32. 32.
    Wu G, Caro S, Bai S, Kepler J (2014) Dynamic modeling and design optimization of a 3-DoF spherical parallel manipulator. Robot Auton Syst 62:1377–1386CrossRefGoogle Scholar
  33. 33.
    Liang D, Song Y, Sun T, Jin X (2018) Dynamic modeling and hierarchical compound control of a novel 2-DOF flexible parallel manipulator with multiple actuation modes. Mech Sys Sign Proc 103:413–439CrossRefGoogle Scholar
  34. 34.
    Bi ZM, Wang L (2012) Optimization of machining processes from the perspective of energy consumption: a case study. J Manuf Syst 31(4):420–428CrossRefGoogle Scholar
  35. 35.
    Krefft M, Hesselbach J (2005) Elastodynamic optimization of parallel kinematics. Proceedings of the 2005 IEEE International Conference on Automation Science and Engineering, Edmonton, Canada, 357–362Google Scholar
  36. 36.
    Liang D, Song Y, Sun T, Jin X (2017) Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes. J Sound Vib 403:129–151CrossRefGoogle Scholar
  37. 37.
    Yao J, Gu W, Feng Z, Chen L, Xu Y, Zhao Y (2017) Dynamic analysis and driving force optimization of a 5-DoF parallel manipulator with redundant actuation. Robot Com-Int Manuf 48:51–58CrossRefGoogle Scholar
  38. 38.
    Liang D, Song Y, Sun T (2017) Nonlinear dynamic modeling and performance analysis of a redundantly actuated parallel manipulator with multiple actuation modes based on FMD theory. Nonlinear Dynam 89(1):391–428CrossRefGoogle Scholar
  39. 39.
    Zhao Y, Gao F, Dong X, Zhao X (2011) Dynamics analysis and characteristics of the 8-PSS flexible redundant parallel manipulator. Robot Com-Int Manuf 27:918–928CrossRefGoogle Scholar
  40. 40.
    Alessandro C, Rosario S (2014) Elastodynamic optimization of a 3T1R parallel manipulator. Mech Mach Theory 73:184–196CrossRefGoogle Scholar
  41. 41.
    Stojanovic V, Nedic N (2016) Joint state and parameter robust estimation of stochastic nonlinear systems. Int J Rob Non Con 26(14):3058–3074MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Filipovic V, Nedic N, Stojanovic V (2011) Robust identification of pneumatic servo actuators in the real situations. Forsch Ingenieurwes 75(4):183–196CrossRefGoogle Scholar
  43. 43.
    Fan C, Zhao G, Zhao J, Zhang L, Sun L (2015) Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm. Int J Adv Manuf Technol 81(1–4):27–37CrossRefGoogle Scholar
  44. 44.
    Lian B, Sun T, Song Y (2017) Parameter sensitivity analysis of a 5-DoF parallel manipulator. Robot Com-Int Manuf 46:1–14CrossRefGoogle Scholar
  45. 45.
    Sun T, Song Y, Li Y, Xu L (2011) Separation of comprehensive geometrical errors of a 3-dof parallel manipulator based on Jacobian matrix and its sensitivity analysis with Monte-Carlo method. Chinese J Mech Eng (English Edition) 24(3):406–413CrossRefGoogle Scholar
  46. 46.
    Chen Y, Xie F, Liu X, Zhou Y (2014) Error modeling and sensitivity analysis of a parallel robot with SCARA (selective compliance assembly robot arm) motions. Chinese J Mech Eng 27(4):693–702CrossRefGoogle Scholar
  47. 47.
    Witek-Krowiak A, Chojnacka K, Podstawczyk D, Dawiec A, Pokomeda K (2014) Application of response surface methodology and artificial neural network methods in modelling and optimization of biosorption process. Bioresour Technol 160:150–160CrossRefGoogle Scholar
  48. 48.
    Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Struct Multidiscip O 23:1–13CrossRefGoogle Scholar

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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Machine DesignKTH Royal Institute of TechnologyStockholmSweden

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