Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Morozov A, Angeles J (2007) The mechanical design of a novel Schönflies-motion generator. Robot Com-Int Manuf 23(1):82–93
Altuzarra O, Sandru B, Pinto C, Pentuya V (2011) A symmetric parallel Schönflies-motion manipulator for pick-and-place operations. Robotica 29:853–862
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):310151–310159
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, 1202–1207
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, 1875–1880
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):135–143
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):1873–1886
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):1324–1338
Zhang D, Wang L, Lang SY (2004) Parallel kinematic machines: design, analysis and simulation in an integrated virtual environment. J Mech Des 127(4):580–588
Qi Y, Sun T, Song Y (2018) Multi-objective optimization of parallel tracking mechanism considering parameter uncertainty. J Mech Robot 10(4):0410061–04100612
Wu J, Chen X, Wang L (2016) Design and dynamics of a novel solar tracker with parallel mechanism. ASME/IEEE T Mech 21(1):88–97
Bi ZM, Wang L (2009) Optimal design of reconfigurable parallel machining systems. Robot Com-Int Manuf 25(6):951–961
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):180–189
Sun T, Xiang X, Su W, Wu H, Song Y (2017) A transformable wheel-legged mobile robot: design, analysis and experiment. Robot Auton Sys 98:30–41
Zhang D, Wang L, Gao Z, Su X (2013) On performance enhancement of parallel kinematic machine. J Intell Manuf 24(2):267–276
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 41:78–91
Sun T, Liang D, Song Y (2018) Singular-perturbation-based nonlinear hybrid control of redundant parallel robot. IEEE T Ind Electron 65(4):3326–3336
Wang L, Xi F, Zhang D (2006) A parallel robotic attachment and its remote manipulation. Robot Com-Int Manuf 22(5–6):515–525
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):1795–1805
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):508–516
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 104:405–419
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):054504–1–054504–6
Huo X, Sun T, Song Y (2017) A geometric algebra approach to determine motion/constraint, mobility and singularity of parallel mechanism. Mech Mach Theory 116:273–293
Yang S, Sun T, Huang T (2017) Type synthesis of parallel mechanisms having 3T1R motion with variable rotational axis. Mech Mach Theory 109:220–230
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 108:75–82
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):310091–310098
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 83:631–658
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):168–174
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 51:10–29
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):593–599
Bi ZM, Wang L (2012) Energy modeling of machine tools for optimization of machine setup. IEEE T Aotum Sci Eng 9(3):607–613
Wu G, Caro S, Bai S, Kepler J (2014) Dynamic modeling and design optimization of a 3-DoF spherical parallel manipulator. Robot Auton Syst 62:1377–1386
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 103:413–439
Bi ZM, Wang L (2012) Optimization of machining processes from the perspective of energy consumption: a case study. J Manuf Syst 31(4):420–428
Krefft M, Hesselbach J (2005) Elastodynamic optimization of parallel kinematics. Proceedings of the 2005 IEEE International Conference on Automation Science and Engineering, Edmonton, Canada, 357–362
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 403:129–151
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 48:51–58
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):391–428
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 27:918–928
Alessandro C, Rosario S (2014) Elastodynamic optimization of a 3T1R parallel manipulator. Mech Mach Theory 73:184–196
Stojanovic V, Nedic N (2016) Joint state and parameter robust estimation of stochastic nonlinear systems. Int J Rob Non Con 26(14):3058–3074
Filipovic V, Nedic N, Stojanovic V (2011) Robust identification of pneumatic servo actuators in the real situations. Forsch Ingenieurwes 75(4):183–196
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):27–37
Lian B, Sun T, Song Y (2017) Parameter sensitivity analysis of a 5-DoF parallel manipulator. Robot Com-Int Manuf 46:1–14
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):406–413
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):693–702
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 160:150–160
Jin R, Chen W, Simpson TW (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Struct Multidiscip O 23:1–13
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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.
About this article
Cite this article
Lian, B., Wang, L. & Wang, X.V. Elastodynamic modeling and parameter sensitivity analysis of a parallel manipulator with articulated traveling plate. Int J Adv Manuf Technol 102, 1583–1599 (2019). https://doi.org/10.1007/s00170-018-03257-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-018-03257-x