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Approximate Stiffness Modelling and Stiffness Defect Identification for a Heavy-load Parallel Manipulator

Published online by Cambridge University Press:  18 February 2019

Shuai Fan  and
Shouwen Fan
Shuai Fan
Affiliation:
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, People’s Republic of China. E-mail: fansuai12345@163.com
Shouwen Fan*
Affiliation:
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, People’s Republic of China. E-mail: fansuai12345@163.com
*
*Corresponding author. E-mail: shouwenfan@263.net
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Summary

When using parallel manipulators as machine tools, their stiffness is an important factor in the quality of the produced products. This paper presents an overall approximate stiffness model for a heavy-load parallel manipulator, which considers the effects of actuator stiffness, joint clearance, joint contact deformation, and limb deformation. Based on the principle of virtual work and the introduced modified parameters, the proposed overall compliance matrix successfully takes four factors into a unified expression. To obtain the overall compliance matrix, the approximate stiffness models of the joint clearance, joint contact deformation, and limb deformation are given. In addition, by combining the statistical simulation including the random uncertainties and the proposed approximate stiffness models as the basis of the magnitudes for each random variable, an approach based on the expected trajectory and external load is also proposed for stiffness defect identification such that the estimation is more accurate and reliable. Finally, a numerical example of the 1PU+3UPS parallel manipulator and a discussion are presented to demonstrate the practicability of the proposed stiffness model and defect identification approach. After modifying the structure parameters of the defective components, the prototype experiences a significant stiffness improvement.

Keywords

Stiffness modelOverall compliance matrixDefect identificationParallel manipulatorStatistical simulation
Type
Articles
Information
Robotica , Volume 37 , Issue 6 , June 2019 , pp. 1120 - 1142
Copyright
Copyright © Cambridge University Press 2019 

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References

Merlet, J. P., Parallel Robots, Second Edition (Springer, Netherlands, 2006).Google Scholar
Shneor, Y. and Portman, V. T., “Stiffness of 5-axis machines with serial, parallel, and hybrid kinematics: Evaluation and comparison,” Annals-Manuf. Techn. 59(1), 409–412 (2010).CrossRefGoogle Scholar
Huang, Z., Li, Q. C. and Ding, H. F., Theory of Parallel Mechanisms (Springer, Netherlands, 2013).CrossRefGoogle Scholar
El-Khasawneh, B. S. and Ferreira, P. M., “Computation of stiffness and stiffness bounds for parallel link manipulators,” Int. J. Mach. Tools. Manuf. 39(2), 321–342 (1999).CrossRefGoogle Scholar
Huang, G. Y., Guo, S., Zhang, D., Qu, H. B. and Tang, H. Y., “Kinematic analysis and multi-objective optimization of a new reconfigurable parallel mechanism with high stiffness,” Robotica 36(2), 187–203 (2018).CrossRefGoogle Scholar
Piras, G., Cleghorn, W. L. and Mills, J. K., “Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with flexible links,” Mech. Mach. Theory 40(7), 849–862 (2005).CrossRefGoogle Scholar
Yang, C., Li, Q. C., Chen, Q. H. and Xu, L. M., “Elastostatic stiffness modeling of overconstrained parallel manipulators,” Mech. Mach. Theory 122, 58–74 (2018).CrossRefGoogle Scholar
Hu, B., Lu, Y., Tan, Q., Yu, J. P. and Han, J. D., “Analysis of stiffness and elastic deformation of a 2(SP+SPR+SPU) serial-parallel manipulator,” Robot Comput. Integr. Manuf. 27(2), 418–425 (2011).CrossRefGoogle Scholar
Gallant, M. and Gosselin, C., “Singularities of a planar 3-RPR parallel manipulator with joint clearance,” Robotica 36(7), 1098–1109 (2018).CrossRefGoogle Scholar
Venanzi, S. and Parenti-Castelli, V., “A new technique for clearance influence analysis in spatial mechanisms,” J Mech. Design 127(3), 446–455 (2005).CrossRefGoogle Scholar
Farajitabar, M., Daniali, H. M. and Varedi, S. M., “Pick and place trajectory planning of planar 3RPR parallel manipulator in the presence of joint clearance,” Robotica 35(2), 241–253 (2017).CrossRefGoogle Scholar
Flores, P., Ambrósio, J., Claro, J. C. P., Lankarani, H. M. and Koshy, C. S., “A study on dynamics of mechanical systems including joints with clearance and lubrication,” Mech. Mach. Theory 41(3), 247–261 (2006).CrossRefGoogle Scholar
Shiau, T. N., Tsai, Y. J. and Tsai, M. S., “Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects,” Mech. Mach. Theory 43(4), 491–505 (2008).CrossRefGoogle Scholar
Varedi-Koulaei, S. M., Daniali, H. M. and Farajtabar, M., “The effects of joint clearance on the dynamics of the 3RRR planar parallel manipulator,” Robotica 35(6), 1223–1242 (2017).CrossRefGoogle Scholar
Xu, L. X. and Li, Y. G., “Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator,” Robot Comput. Integr. Manuf. 30(1), 62–73 (2014).Google Scholar
Lian, B. B., Sun, T., Song, Y. M., Yan, J. and Mark, P., “Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects,” Int. J. Mach. Tools. Manuf. 95, 82–96 (2015).CrossRefGoogle Scholar
Pashkevich, A., Chablat, D. and Wenger, P., “Stiffness analysis of overconstrained parallel manipulators,” Mech. Mach. Theory 44(5), 966–982 (2009).CrossRefGoogle Scholar
Li, Y. and Xu, Q., “Stiffness analysis for a 3-PUU parallel kinematic machine,” Mech. Mach. Theory 43(2), 186–200 (2008).CrossRefGoogle Scholar
Lim, S. R., Kang, K., Park, S., Choi, W. C., Song, J. B., Hong, D. and Shim, J. K., “Error analysis of a parallel mechanism considering link stiffness and joint clearances,” Keme. Int. J. 16(6), 799–809 (2002).Google Scholar
Hafezipour, M. and Khodaygan, S., “An uncertainty analysis method for error reduction in end-effector of spatial robots with joint clearances and link dimension deviations,” Int. J. Comput. Integ. M. 30(6), 653–663 (2017).CrossRefGoogle Scholar
Aginaga, J., Altuzarra, O., Macho, E. and Iriarte, X., “Assessing position error due to clearances and deformations of links in parallel manipulators,” J. Mech. Design 135(4), 1–8 (2013).CrossRefGoogle Scholar
Flores, P., Ambrosio, J., Claro, J. C. P. and Lankarani, H. M., “Dynamics of multibody systems with spherical clearance joints,” J. Comput. Nonlin. Dyn. 1(3), 240–247 (2006).CrossRefGoogle Scholar
Wang, G. X. and Liu, H. Z., “Dynamics model of 4-SPS/CU parallel mechanism with spherical clearance joint and flexible moving platform,” J. Tribol-T. ASME 140(2), 1–10 (2018).CrossRefGoogle Scholar
Tian, Q., Flores, P. and Lankarani, H. M., “A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints,” Mech. Mach. Theory 122, 1–57 (2018).CrossRefGoogle Scholar
Meng, J., Zhang, D. J. and Li, Z. X., “Accuracy analysis of parallel manipulators with joint clearance,” J. Mech. Design 131(1), 1–9 (2009).CrossRefGoogle Scholar
Frisoli, A., Solazzi, M., Pellegrinetti, D. and Bergamasco, M., “A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances,” Mech. Mach. Theory 46(12), 1929–1949 (2011).CrossRefGoogle Scholar
Cammarata, A., “A novel method to determine position and orientation errors in clearance-affected overconstrained mechanisms,” Mech. Mach. Theory 118, 247–264 (2017).CrossRefGoogle Scholar
Wang, H., Zhang, L. S., Chen, G. L. and Huang, S. Z., “Parameter optimization of heavy-load parallel manipulator by introducing stiffness distribution evaluation index,” Mech. Mach. Theory 108, 244–259 (2017).CrossRefGoogle Scholar
Wang, Y. Y., Liu, H. T, Huang, T. and Chetwynd, D. G., “Stiffness modeling of the Tricept robot using the overall Jacobian matrix,” J. Mech. Rob. 1(2), 1–8 (2009).Google Scholar
Liu, H. T., Huang, T. and Chetwynd, D. G., “A general approach for geometric error modeling of lower mobility parallel manipulators,” J. Mech. Rob. 3(2), 1–13 (2011).Google Scholar
Wu, W. D. and Rao, S. S., “Interval approach for the modeling of tolerances and clearances in mechanism analysis,” J. Mech. Design 126(4), 581–592 (2004).CrossRefGoogle Scholar
Tannous, M., Caro, S. and Goldsztejn, A., “Sensitivity analysis of parallel manipulators using an interval linearization method,” Mech. Mach. Theory 71, 93–114 (2014).CrossRefGoogle Scholar
Merlet, J. P., “Interval analysis for certified numerical solution of problems in robotics,” Int. J. Ap. Mat.Com-Pol. 19(3), 399–412 (2009).Google Scholar
Luo, K. and Du, X. P., “Probabilistic mechanism analysis with bounded random dimension variables,” Mech. Mach. Theory 60, 112–121 (2013).CrossRefGoogle Scholar
Rao, S. S. and Bhatti, P. K., “Probabilistic approach to manipulator kinematics and dynamics,” Reliab. Eng. Syst. Safe 72(1), 47–58 (2001).CrossRefGoogle Scholar
Du, X. P., Venigella, P. K. and Liu, D. S., “Robust mechanism synthesis with random and interval variables,” Mech. Mach. Theory 44(7), 1321–1337 (2009).CrossRefGoogle Scholar
Fan, S. and Fan, S. W., “An improved approach to the inverse dynamic analysis of parallel manipulators by a given virtual screw,” Adv. Rob. 32(16), 887–902 (2018).CrossRefGoogle Scholar
Popov, V. L., Contact Mechanics and Friction Physical Principles and Applications (Springer, Berlin-Heidelberg, 2010).CrossRefGoogle Scholar
Ross, S. M., Simulation (Fifth Edition). (Elsevier, Netherlands, 2013).Google ScholarPubMed