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Kinematic accuracy research of 2(3HUS+S) parallel manipulator for simulation of hip joint motion

  • Huizhen Zhang (a1), Gang Cheng (a1), Xianlei Shan (a1) and Feng Guo (a1)

In this paper, the kinematic accuracy problem caused by geometric errors of a 2(3HUS+S) parallel manipulator is described. The kinematic equation of the manipulator is obtained by establishing a D–H (Denavit–Hartenberg) coordinate system. A D–H transformation matrix is used as the error-modeling tool, and the kinematic error model of the manipulator integrating manufacturing and assembly errors is established based on the perturbation theory. The iterative Levenberg–Marquardt algorithm is used to identify the geometric errors in the error model. According to the experimentally measured attitudes, the kinematic calibration process is simulated using MATLAB software. The simulation and experiment results show that the attitude errors of the moving platforms after calibration are reduced compared with before the calibration, and the kinematic accuracy of the manipulator is significantly improved. The correctness and effectiveness of the error model and the kinematic calibration method of the 2(3HUS+S) parallel manipulator for simulation of hip joint motion are verified.

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1. Winiarski, S., Aleksandrowicz, K., Jarzab, S., Pozowski, A. and Rutkowska-Kucharska, A., “Assessment of gait after bilateral hip replacement. Case study,” Ortopedia Traumatologia Rehabilitacja 16 (2), 197208 (2014).
2. Puccio, F. D. and Mattei, L., “Biotribology of artificial hip joints,” World J. Orthopedics 6 (1), 7794 (2015).
3. Affatato, S., Spinelli, A., Zavalloni, M., Mazzega-Fabbro, C. and Viceconti, A., “Tribology and total hip joint replacement: Current concepts in mechanical simulation,” Med. Eng. Phys. 30 (10), 13051317 (2008).
4. Cheng, G., Li, Y., Feng, L. L., Shan, X. L. and Yang, J. H., “Configuration bifurcation and self-motion analysis of 3SPS+1PS bionic parallel test platform for hip joint simulator,” Mech. Mach. Theory 86, 6272 (2015).
5. Zhao, Y. J., “Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot,” Robotica 31 (31), 193202 (2013).
6. Ruiz, A., Campa, F. J., Roldan-Paraponiaris, C., Altuzarra, O. and Pinto, C., “Experimental validation of the kinematic design of 3-PRS compliant parallel mechanisms,” Mechatronics 39, 7788 (2016).
7. Sanchez-Alonso, R. E., Gonzalez-Barbosa, J. J., Castillo-Castaneda, E. and Gallardo-Alvarado, J., “Kinematic analysis of a novel 2(3-RUS) parallel manipulator,” Robotica 34 (10), 22412256 (2016).
8. Lu, Y., Wang, P., Zhao, S. H., Hu, B., Han, J. D. and Sui, C. P., “Kinematics and statics analysis of a novel 5-DoF parallel manipulator with two composite rotational/linear active legs,” Robot. Comput. Integr. Manuf. 30 (1), 2533 (2014).
9. Briot, S. and Bonev, I. A., “Accuracy analysis of 3-DOF planar parallel robots,” Mech. Mech. Theory 43 (4), 445458 (2008).
10. Cui, G. H., Zhang, H. Q., Zhang, D. and Xu, F., “Analysis of the kinematic accuracy reliability of a 3-DOF parallel robot manipulator,” Int. J. Adv. Robot. Syst. 12, 15 (2015).
11. Fu, J. X., Gao, F., Chen, W. X., Pan, Y. and Lin, R. F., “Kinematic accuracy research of a novel six-degree-of-freedom parallel robot with three legs,” Mech. Mach. Theory 102, 86102 (2016).
12. Chen, Y. Z., Xie, F. G., Liu, X. J. and Zhou, Y. H., “Error modeling and sensitivity analysis of a parallel robot with SCARA (selective compliance assembly robot arm) motions,” Chin. J. Mech. Eng. 27 (4), 693702 (2014).
13. Dumlu, A. and Erenturk, K., “Modeling and trajectory tracking control of 6-DOF RSS type parallel manipulator,” Robotica 32 (4), 643657 (2014).
14. Bai, P. J., Mei, J. P., Huang, T. and Chetwynd, D. J., “Kinematic calibration of Delta robot using distance measurements,” Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 230 (3), 414424 (2016).
15. Chanal, H., Duc, E., Hascoet, J. Y. and Ray, P., “Reduction of a parallel kinematics machine tool inverse kinematic model with regard to machining behavior,” Mech. Mach. Theory 44 (7), 13711385 (2009).
16. Chebbi, A. H., Affi, Z. and Romdhane, L., “Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot,” Mech. Mach. Theory 44 (9), 17681783 (2009).
17. Sun, T., Zhai, Y. P., Song, Y. M. and Zhang, J.T., “Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker,” Robot. Comput.-Integr. Manuf. 41, 7891 (2016).
18. Fan, C., Zhao, G. L., Zhao, J., Zhang, L. and Sun, L. N., “Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm,” Int. J. Adv. Manuf. Technol. 81 (1–4), 2737 (2015).
19. Tian, W. J., Yin, F. W., Liu, H. T., Li, J. H., Li, Q., Huang, T. and Chetwynd, D. G., “Kinematic calibration of a 3-DOF spindle head using a double ball bar,” Mech. Mach. Theory 102, 167178 (2016).
20. Wang, L. P., Xie, F. G., Liu, X. J. and Wang, J. S., “Kinematic calibration of the 3-dof parallel module of a 5-axis hybrid milling machine,” Robotica 29 (4), 535546 (2011).
21. Chiu, Y. J. and Perng, M. H., “Self-calibration of a general hexapod manipulator with enhanced precision in 5-DOF motions,” Mech. Mach. Theory 39 (1), 123 (2004).
22. Ren, X. D., Feng, Z. R. and Su, C. P., “A new calibration method for parallel kinematics machine tools using orientation constraint,” Int. J. Mach. Tools Manuf. 49 (9), 708721 (2009).
23. Bai, Y., Zhuang, H. Q. and Wang, D. L., “Apply fuzzy interpolation method to calibrate parallel machine tools,” Int. J. Adv. Manuf. Technol. 60 (5–8), 553560 (2012).
24. Zhang, D. and Gao, Z., “Optimal kinematic calibration of parallel manipulators with pseudoerror theory and cooperative coevolutionary network,” IEEE Trans. Ind. Electron. 59 (8), 32213231 (2012).
25. Shan, X. L., Cheng, G. and Liu, X. Z., “Note: Application of a novel 2(3HUS+S) parallel manipulator for simulation of hip joint motion,” Rev. Sci. Instrum. 87 (7), 149151 (2016).
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  • ISSN: 0263-5747
  • EISSN: 1469-8668
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