Abstract
Since the classical kinematics model of parallel manipulators cannot accurately reflect the angular velocity and angular acceleration of the limbs, an improved kinematics model is proposed and an inverse dynamic model of the general parallel manipulator is derived based on the improved kinematics model. This paper proves that the shortcoming of the classical kinematics model is that a single model cannot accurately describe the movement of several types of branches in a parallel manipulator. Combined with the principle of angular velocity superposition and vector chain method, the improved kinematic models of the general parallel manipulator’s several typical limbs are derived. Then, an explicit inverse dynamic model of a general parallel robot is established based on the principle of virtual work. Finally, to describe the effectiveness of the improved model, we analyzed a new type of UP+SPR+SPU parallel manipulator. The improved models had higher accuracy than the classical models through the comparison.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Dasgupta and T. S. Mruthyunjaya, The Stewart platform manipulator: a review, Mechanism and Machine Theory, 35(1) (2000) 15–40.
J. J. Yu et al., Numeration and type synthesis of 3-DOF orthogonal translational parallel manipulators, Progress in Natural Science, 18(5) (2008) 563–574.
D. Kim and S. H. Hwang, Kinematic Implementation of 3-DOF 2-link type vehicle simulator: Kinematic analysis and motion control method for 3-DOF 2-link type vehicle simulator, 2020 International Conference on Control, Automation and Diagnosis (ICCAD), IEEE (2020) 1–6.
R. Aidan, J. Padayachee and G. Bright, Research and development of a 5-axis hybrid kinematic C.N.C. machine, 2017 24th International Conference on Mechatronics and Machine Vision in Practice (M2VIP), IEEE (2017) 1–6.
H. A. G. C. Premachandra et al., Genetic algorithm based pick and place sequence optimization for a color and size sorting delta robot, 2020 6th International Conference on Control, Automation and Robotics (ICCAR), IEEE (2020) 209–213.
Y. L. Xie et al., Design and analysis of a novel compact XYZ parallel precision positioning stage, Microsystem Technologies, 27(5) (2021) 1925–1932.
S. Wang et al., Type synthesis of rehabilitation mechanism of variable axis bio-fusion knee joint, J. of Mechanism Engineering, 56(11) (2020) 72–79.
J. Y. Niu et al., Kinematic analysis of a serial-parallel hybrid mechanism and its application to a wheel-legged robot, IEEE Access, 8 (2020) 111931–111944.
B. Hu et al., Reachable workspace determination for a spatial hyper-redundant manipulator formed by several parallel manipulators, Journal of Mechanical Science and Technology, 33(2) (2019) 869–877.
X. Wu and S. Bai, Analytical determination of shape singularities for three types of parallel manipulators, Mechanism and Machine Theory, 149 (2020) 103812.
B. Hu and J. J. Yu, Unified solving inverse dynamics of 6-DOF serial-parallel manipulators, Applied Mathematical Modelling, 39(16) (2015) 4715–4732.
Y. Rong, X. C. Zhang and M. K. Qu, Unified inverse dynamics for a novel class of metamorphic parallel mechanisms, Applied Mathematical Modelling, 74 (2019) 280–300.
X. Wang, J. Wu and Y. Wang, Dynamics evaluation of 2UPU/S.P. parallel mechanism for a 5-DOF hybrid robot considering gravity, Robotics and Autonomous Systems, 135 (2021) 103675.
Y. Rong et al., Dynamics modeling and drive parameter prediction of a 5-DOF wheel grinding manipulator arm, China Mechanical Engineering, 29(4) (2018) 449–456.
Y. Rong and Z. L. Jin, Dynamic modeling of 3-DOF parallel mechanical leg and peak prediction of servo motor, Optics and Precision Engineering, 20(9) (2012) 1974–1983.
Y. Q. Li et al., Dynamics parameter identification and control of a spherical 2-DOF redundant driven parallel robot system, China Mechanical Engineering, 30(16) (2019) 1967–1975.
B. Dasgupta and T. S. Mruthyunjaya, A newton-euler formulation for the inverse dynamics of the stewart platform manipulator, Mechanism and Machine Theory, 33(8) (1998) 1135–1152.
J. Wang and C. M. Gosselin, A new approach for the dynamic analysis of parallel manipulators, Multibody System Dynamics, 2(3) (1998) 317–334.
G. Cheng and X. L. Shan, Dynamics analysis of a parallel hip joint simulator with four degree of freedoms (3R1T), Nonlinear Dynamics, 70(4) (2012) 2475–2486.
E. F. Fichter, Stewart platform-based manipulator: general theory and practical construction, International J. of Robotics Research, 5(2) (1986) 157–182.
L. W. Tsai, Solving the inverse dynamics of a Stewart-Gough manipulator by the principle of virtual work, ASME J. of Mechanical Design, 122(1) (2000) 3–9.
M. Li et al., Dynamic formulation and performance comparison of the 3-DOF modules of two reconfigurable P.K.M. — the tricept and the trivariant, ASME J. of Mechanical Design, 127(6) (2005) 1129–1136.
S. Briot et al., Degeneracy conditions of the dynamic model of parallel robots, Multibody System Dynamics, 37(4) (2016) 371–412.
C. C. Li et al., An improved inverse dynamics model of 6 D.O.F. motion simulator dynamic, Acta Armamentarii, 30(4) (2009) 446–450.
Z. Q. He et al., Improved newton-euler dynamic models for a Stewart platform, J. of Vibration and Shock, 37(9) (2018) 221–229.
S. Pedrammehr, M. Mahboubkhah and N. Khani, Improved dynamic equations for the generally configured stewart platform manipulator, Journal of Mechanical Science and Technology, 26(3) (2012) 711–721.
Y. Lu, N. J. Ye and Z. F. Chang, Derivation of general acceleration and hessian matrix of kinematic limbs in parallel manipulator by extended skew-symmetric matrixes, Archives of Computational Methods in Engineering, 28(4) (2021) 3035–3047.
Y. Yu et al., Kinematic analysis and testing of a 6-RRRPRR. parallel manipulator, Proceedings of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 231(13) (2017) 2515–2527.
A. Bayram, Trajectory tracking of a planer parallel manipulator by using computed force control method, Chinese J. of Mechanical Engineering, 30(2) (2017) 449–458.
M. C. Garau et al., Drying of orange skin: Drying kinetics modelling and functional properties, J. of Food Engineering, 75(2) (2006) 288–295.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (U1713219), the European Commission Marie Skodowska-Curie SMOOTH (Smart Robots for Fire-fighting) Project under Grant H2020-MSCA-RISE-2016-734875, and the Science and Technology (S&T) Program of Hebei under Grant 19211820D and E2020103001, Hebei Natural Science Foundation (E2021203018).
Author information
Authors and Affiliations
Corresponding author
Additional information
Xingchao Zhang received the M.S. in Mechanical Engineering from Hebei Normal University of Science & Technology, China, in 2019. He is currently pursuing the doctorate in Mechatronic Engineering at Yanshan University, China. His main research interests are kinematics and dynamics of parallel robots.
Hongbo Wang received his B.S. and M.S. from Institute of Northeast Heavy Machinery, Qiqihar, China, in 1982 and 1986, respectively. His Ph.D. is from Nagasaki University, Nagasaki, Japan in 1997. Since 2009, he has been with Yanshan University, Qinhuangdao, China as a Professor. His current research interests are in rehabilitation robot and assisting robot for the disabled and the elderly.
Yu Rong has a B.S. in Mechanical Engineering, M.S. and Ph.D. in Mechatronic Engineering from Yanshan University, Qinhuangdao, China, in 2005, 2008, and 2015, respectively. He is currently a lecturer with Yanshan University, China. His research interests include parallel mechanism, robotics.
Jianye Niu received his B.S. in Mechanical Engineering, M.S. and Ph.D. in Mechatronic Engineering from Yanshan University, Qinhuangdao, China, in 2005, 2008, and 2019, respectively. He is currently a postdoctoral researcher with the School of Mechanical Engineering, Hebei University of Technology, Tianjin, China. His research interests include parallel mechanism and its application, rehabilitation robot, mechanical engineering, and artificial neural network.
Junjie Tian received the M.S. in Chemical Process Equipment from Tianjin University, China, in 2018. He is currently pursuing the doctorate in Mechatronic Engineering at Yanshan University, China. His current research interests include rehabilitation robot, robotic compliance control.
Shanshan Li is currently a Ph.D. candidate in Mechanical Engineering, Yanshan University, China. She received her Master’s in Mechanical engineering in Hebei Normal University of Science & Technology, China, in 2019. Her current research interests include rehabilitation robot, mechanical engineering.
Yuansheng Ning received the M.S. in Mechanical Engineering from Taiyuan University of Science and Technology, China, in 2020. He is currently pursuing the doctorate in Mechatronic Engineering at Yanshan University, China. His current research interests include rehabilitation robot, robot motion planning and control, robotic compliance control, etc.
Rights and permissions
About this article
Cite this article
Zhang, X., Wang, H., Rong, Y. et al. Improved inverse kinematics and dynamics model research of general parallel mechanisms. J Mech Sci Technol 37, 943–954 (2023). https://doi.org/10.1007/s12206-023-0134-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-023-0134-1