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Kinematic calibration of a 5-DOF double-driven parallel mechanism with sub-closed loop on limbs

Published online by Cambridge University Press:  14 October 2024

Xuhao Wang Open the ORCID record for Xuhao Wang [Opens in a new window] ,
Shuo Sun ,
Mengli Wu Open the ORCID record for Mengli Wu [Opens in a new window] ,
Yiran Cao ,
Zhiyong Guo  and
Zefu Liu
Xuhao Wang
Affiliation:
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, China
Shuo Sun
Affiliation:
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, China
Mengli Wu*
Affiliation:
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, China
Yiran Cao
Affiliation:
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, China
Zhiyong Guo
Affiliation:
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, China
Zefu Liu
Affiliation:
College of Aeronautical Engineering, Civil Aviation University of China, Tianjin, China
*
Corresponding author: Mengli Wu; Email: wuml2004@qq.com
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Abstract

This paper proposes a kinematic calibration method of a novel 5-degree-of-freedom double-driven parallel mechanism with the sub-closed loop on limbs. At first, considering the introduction of a sub-closed loop significantly increased the complexity and difficulty of kinematic error modeling, an equivalent transformation method is proposed for the limb with a sub-closed loop. Then kinematic error model of the parallel mechanism is established based on the closed-loop vector method and parasitic motion analysis, which is verified by virtual prototype technology. Because the full kinematic error model is generally redundant, error parameter identifiability analysis is carried out by QR decomposition of the identification Jacobian matrix, and the redundant parameters are removed. Additionally, the Sequence Forward Floating Search algorithm is utilized to optimize measurement configurations to reduce the influence of measurement noise. Finally, with a laser tracker as the measuring device, numerical simulations and experiments are implemented to verify the proposed kinematic calibration method. The experiment results show that average position and orientation errors are reduced from 2.778 mm and 1.115° to 0.263 mm and 0.176°, respectively, within the prescribed workspace.

Keywords

double-driven parallel mechanismkinematic calibrationgeometric error modelparasitic motionsub-closed loop

Information

Type
Research Article
Information
Robotica , Volume 42 , Issue 11 , November 2024 , pp. 3709 - 3730
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Jiang, B., Huang, G., Zhu, S., Fang, H., Tian, X., Xie, A., Zhang, L., Zhao, P., Gu, J. and Kong, L., “Type synthesis and trajectory planning of 5-DOF redundantly actuated parallel robots with large output rotational angles for large workpieces,” Robotica 42(1), 242–264 (2024).CrossRefGoogle Scholar
Wang, C., Duan, H. and Li, L., “Design, simulation, control of a hybrid pouring robot: Enhancing automation level in the foundry industry,” Robotica 42(4), 1018–1038 (2024).Google Scholar
Peng, S., Cheng, Z., Che, L., Cui, S. and Jin, Z., “Configuration design and dimensional synthesis of an asymmetry 2R1T parallel mechanism,” Robotica 41(2), 713–734 (2023).CrossRefGoogle Scholar
Liu, J., Fan, X. and Ding, H., “Investigation of a novel 2R1T parallel mechanism and construction of its variants,” Robotica 39(10), 1834–1848 (2021).CrossRefGoogle Scholar
Laryushkin, P., Antonov, A., Fomin, A. and Essomba, T., “Velocity and singularity analysis of a 5-DOF (3T2R) parallel-serial (hybrid) manipulator,” Machines 10(4), 276 (2022).CrossRefGoogle Scholar
Antonov, A., Fomin, A., Glazunov, V., Petelin, D. and Filippov, G., “Type synthesis of 5-DOF hybrid (parallel-serial) manipulators designed from open kinematic chains,” Robotics 12(4), 98 (2023).CrossRefGoogle Scholar
Wang, X., Lin, Y., Cao, Y., Wu, M. and Sun, S., “Design and multi-objective optimization of a novel 5-DOF parallel mechanism with two double-driven chains,” Robotica 41(9), 2829–2849 (2023).CrossRefGoogle Scholar
Liu, J., Yang, D. and Li, T., “Drive layout configuration strategy and scale optimization design of multi-drive mode parallel mechanism,” J. Mech. Rob. 16, 100209 (2024).Google Scholar
Wang, L., Fang, Y., Zhang, D. and Yang, Y., “Kinematics and optimization of a novel 4-DOF two-limb gripper mechanism,” Robotica 41(12), 3649–3671 (2023).CrossRefGoogle Scholar
Laryushkin, P., Fomin, A., Glazunov, V., Brem, I. and Fomina, O., “Redundantly actuated 5-DOF delta-type parallel robot with linear drives,” Mech. Mach. Sci. 148, 820–827 (2023).CrossRefGoogle Scholar
Schreiber, L. T. and Gosselin, C., “Exploiting the kinematic redundancy of a (6 + 3) degrees-of-freedom parallel mechanism,” J. Mech. Rob. 11(2), 021005 (2019).CrossRefGoogle Scholar
Kansal, S. and Mukherjee, S., “Vision-based kinematic analysis of the Delta robot for object catching,” Robotica 40(6), 2010–2030 (2022).CrossRefGoogle Scholar
Luo, J., Chen, S., Fan, X., Xiong, C., Zheng, T., Zhang, C. and Yang, G., “Kinematic calibration of a 4PPa-2PaR parallel mechanism with subchains on limbs,” IEEE Trans. Instrum. Meas. 71, 1–11 (2022).Google Scholar
Zhang, H., Cheng, G., Shan, X. and Guo, F., “Kinematic accuracy research of 2 (3HUS+ S) parallel manipulator for simulation of hip joint motion,” Robotica 36(9), 1386–1401 (2018).CrossRefGoogle Scholar
Tian, W., Shen, Z., Lv, D. and Yin, F., “A systematic approach for accuracy design of lower-mobility parallel mechanism,” Robotica 38(12), 2173–2188 (2020).CrossRefGoogle Scholar
Luo, R., Gao, W., Huang, Q. and Zhang, Y., “An improved minimal error model for the robotic kinematic calibration based on the POE formula,” Robotica 40(5), 1607–1626 (2022).CrossRefGoogle Scholar
Ni, Y., Zhang, B. and Sun, Y., “Accuracy analysis and design of A3 parallel spindle head,” Chin. J. Mech. Eng. 29(2), 1–11 (2016).CrossRefGoogle Scholar
Tang, T., Chi, C., Fang, H. and Zhang, J., “Geometric error propagation model-based accuracy synthesis and its application to a 1T2R parallel manipulator,” J. Mech. Des. 144(7), 073304 (2022).CrossRefGoogle Scholar
Luo, Y., Gao, J., Zhang, L., Chen, D. and Chen, X., “Kinematic calibration of a symmetric parallel kinematic machine using sensitivity-based iterative planning,” Precis. Eng. 77, 164–178 (2022).CrossRefGoogle Scholar
Chen, G., Kong, L., Li, Q. and Wang, H., “A simple two-step geometric approach for the kinematic calibration of the 3-PRS parallel manipulator,” Robotica 37(5), 837–850 (2019).CrossRefGoogle Scholar
Guo, J., Wang, D., Fan, R., Chen, W. and Zhao, G., “Kinematic calibration and error compensation of a hexaglide parallel manipulator,” P. I. Mech. Eng. B-J. Eng. 233(1), 215–225 (2019).Google Scholar
Shen, H., Meng, Q., Li, J., Deng, J. and Wu, G., “Kinematic sensitivity, parameter identification and calibration of a non-fully symmetric parallel Delta robot,” Mech. Mach. Theory 161, 104311 (2021).CrossRefGoogle Scholar
Song, Y., Zhang, J., Lian, B. and Sun, T., “Kinematic calibration of a 5-DoF parallel kinematic machine,” Precis. Eng. 45, 242–261 (2016).CrossRefGoogle Scholar
Li, T., Li, F., Jiang, Y., Zhang, J. and Wang, H., “Kinematic calibration of a 3-P (Pa) S parallel-type spindle head considering the thermal error,” Mechatronics 43, 86–98 (2017).CrossRefGoogle Scholar
Yin, F., Tian, W., Liu, H., Huang, T. and Chetwynd, D., “A screw theory based approach to determining the identifiable parameters for calibration of parallel manipulators,” Mech. Mach. Theory 145, 103665 (2020).CrossRefGoogle Scholar
Chen, X., Zhang, Q. and Sun, Y., “Non-kinematic calibration of industrial robots using a rigid-flexible coupling error model and a full pose measurement method,” Rob. Comput. Integr. Manuf. 57, 46–58 (2019).CrossRefGoogle Scholar
Gao, G., Sun, G., Na, J., Guo, Y. and Wu, X., “Structural parameter identification for 6 DOF industrial robots,” Mech. Syst. Sig. Process. 113, 145–155 (2018).CrossRefGoogle Scholar
Tian, W., Mou, M., Yang, J. and Yin, F., “Kinematic calibration of a 5-DOF hybrid kinematic machine tool by considering the ill-posed identification problem using regularisation method,” Rob. Comput. Integr. Manuf. 60, 49–62 (2019).CrossRefGoogle Scholar
Wang, X., Xie, L., Jiang, M., He, K. and Chen, Y., “Kinematic calibration and feedforward control of a heavy-load manipulator using parameters optimization by an ant colony algorithm,” Robotica 42(3), 728–756 (2024).CrossRefGoogle Scholar
Han, C., Yu, Y., Xu, Z., Wang, X., Yu, P. and Zhou, X., “Complete kinematic calibration of a 6-RRRPRR parallel kinematic machine based on the optimal measurement configurations,” P. I. Mech. Eng. C-J. Mec. 234(1), 121–136 (2020).Google Scholar
Huang, C., F.Xie, X. L. and Meng, Q., “Measurement configuration optimization and kinematic calibration of a parallel robot,” J. Mech. Rob. 14(3), 031017 (2022).CrossRefGoogle Scholar
Ye, H. and Wu, J., “Residual index for measurement configuration optimization in robot kinematic calibration,,” Sci. China Technol. Sci. 66(7), 1899–1915 (2023).CrossRefGoogle Scholar
Sun, T. and Huo, X., “Type synthesis of 1T2R parallel mechanisms with parasitic motions,” Mech. Mach. Theory 128, 412–428 (2018).CrossRefGoogle Scholar
Ma, L., Bazzoli, P., Sammons, P. M., Landers, R. G. and Bristow, D. A., “Modeling and calibration of high-order joint-dependent kinematic errors for industrial robots,” Rob. Comput. Integr. Manuf. 50, 153–167 (2018).CrossRefGoogle Scholar
Sun, T., Zhai, Y., Song, Y. and Zhang, J., “Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker, Rob,” Comput. Integr. Manuf. 41, 78–91 (2016).CrossRefGoogle Scholar
Wang, X., Sun, S., Zhang, P., Wu, M., Zhao, C., Zhang, D. and Meng, X., “Model-based kinematic and non-kinematic calibration of a 7R 6-DOF robot with non-spherical wrist,” Mech. Mach. Theory 178, 105086 (2022).CrossRefGoogle Scholar
Chen, X. and Zhan, Q., “The kinematic calibration of a drilling robot with optimal measurement configurations based on an improved multi-objective PSO algorithm,” Int. J. Precis. Eng. Manuf. 22(9), 1537–1549 (2021).CrossRefGoogle Scholar
Fu, L., Liu, Z., Cai, C., Tao, M., Yang, M. and Huang, H., “Joint space-based optimal measurement configuration determination method for Stewart platform kinematics calibration,” Measurement 211, 112646 (2023).CrossRefGoogle Scholar
Zhu, L., Luo, H. and Ding, H., “Optimal design of measurement point layout for workpiece localization,” ASME J. Manuf. Sci. Eng. 131(1), 011006 (2008).CrossRefGoogle Scholar
Deng, K., Gao, D., Ma, S., Zhao, C. and Lu, Y., “Elasto-geometrical error and gravity model calibration of an industrial robot using the same optimized configuration set, Rob,” Comput. Integr. Manuf. 83, 102558 (2023).CrossRefGoogle Scholar
Li, X., Jiang, W., Luo, Z., Yang, L., Guo, B. and Hu, X., “Calibration of a manipulator with a regularized parameter identification method,” IEEE Access 10, 90535–90547 (2022).CrossRefGoogle Scholar