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Arabian Journal for Science and Engineering

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10-01-2022 | Research Article-Mechanical Engineering

An Interval Discretization Method for Workspace Determination of Parallel Mechanisms

Authors: Pengda Ye, Jingjing You, Fengfeng Xi, Jieyu Wang, Yu Ru

Published in: Arabian Journal for Science and Engineering | Issue 7/2022

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Abstract

An interval discretization method (IDM) is proposed for the workspace determination of parallel mechanisms to address the fundamental problems of unreliable prediction and missing-points existing in the traditional point discretization method (PDM). The IDM involves two parts: the workspace prediction using interval analytical forward kinematics (AFK) and the workspace correction using interval analytical inverse kinematics (AIK). Three typical parallel mechanisms are adopted as illustrative examples, i.e., the planar four-bar mechanism, the spatial 9–3 and 12–6 parallel mechanisms. Firstly, the AFK and AIK of the mechanisms are derived and extended into interval-valued form. Then, the position and orientation workspaces are predicted and corrected in sequence. Finally, numerical behaviors of the proposed and traditional methods are compared. The numerical simulations in Matlab show that: (i) IDM is about 5.34 times faster than PDM; (ii) IDM is about 45.50 times more accurate than PDM; (iii) IDM is about 1.01 times more stable than PDM; and (iv) IDM can realize the prediction of position and orientation workspaces and has no missing-points, thereby demonstrating the effectiveness of the proposed method.

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Stewart, D.: A platform with six degrees of freedom. Proc. Inst. Mech. Eng. 180(15), 371–386 (1965). https://doi.org/10.1243/PIME_PROC_1965_180_029_02CrossRef

You, J.J.; Xi, F.F.; Shen, H.P.; Wang, J.Y.; Yang, X.L.: A novel Stewart-type parallel mechanism with topological reconfiguration: design, kinematics and stiffness evaluation. Mech. Mach. Theory 162, 104329 (2021). https://doi.org/10.1016/j.mechmachtheory.2021.104329CrossRef

Luces, M.; Mills, J.K.; Benhabib, B.: A review of redundant parallel kinematic mechanisms. J. Intell. Rob. Syst. 86, 175–198 (2017). https://doi.org/10.1007/s10846-016-0430-4CrossRef

Nabavi, S.N.; Akbarzadeh, A.; Enferadi, J.: A study on kinematics and workspace determination of a general 6-PUS robot. J. Intell. Rob. Syst. 91, 351–362 (2018). https://doi.org/10.1007/s10846-017-0704-5CrossRef

Xie, F.G.; Liu, X.J.; Wang, J.S.; Wabner, M.: Kinematic optimization of a five degree-of-freedom spatial parallel mechanism with large orientational workspace. ASME J. Mech. Robot. 9(5), 051005 (2017). https://doi.org/10.1115/1.4037254CrossRef

Ye, P.D.; You, J.J.; Qiu, X.; Wang, L.K.; Li, C.G.; Ru, Y.: Status and development trend of motion performance in parallel robot. J. Nanjing Univ. of Aeron Astron 52(3), 363–377 (2020). https://doi.org/10.16356/j.1005-2615.2020.03.003CrossRef

Gosselin, C.: Determination of the workspace of 6-DOF parallel manipulators. ASME J. Mech. Des. 112(3), 331–336 (1990). https://doi.org/10.1115/1.2912612CrossRef

Kuzeci, Z.E.; Omurlu, V.E.; Alp, H.; Ozkol, I.: Workspace analysis of parallel mechanisms through neural networks and genetic algorithms. In: The 12th IEEE International Workshop on Advanced Motion Control, pp. 1–6. IEEE (2012). https://doi.org/10.1109/AMC.2012.6197147

Masory, O.; Wang, J.: Workspace evaluation of Stewart platforms. Adv. Robot. 9(4), 443–461 (1994). https://doi.org/10.1163/156855395X00508CrossRef

10.

Cao, Y.G.; Zhang, Y.R.; Ma, Y.Z.: Workspace analysis and parameter optimization of 6-RSS parallel mechanism. Chin. J. Mech. Eng. 44(1), 19–24 (2008). https://doi.org/10.3321/j.issn:0577-6686.2008.01.004CrossRef

11.

Yin, X.Q.; Zhao, G.H.; Ma, L.Z.: Workspace analysis of the end-effectors of Chinese massage robot. Chin. J. Eng. Des. 19(4), 302–306 (2012). https://doi.org/10.3785/j.issn.1006-754X.2012.04.012CrossRef

12.

Liu, Z.Z.; Liu, H.Y.; Luo, Z.; Zhang, X.H.: Improvement on Monte Carlo method for robot workspace determination. Trans. Chin. Soc. Agric. Mach. 44(1), 230–235 (2013). https://doi.org/10.6041/j.issn.1000-1298.2013.01.043CrossRef

13.

Merlet, J.P.: An improved design algorithm based on interval analysis for spatial parallel manipulator with specified workspace. In: Proceedings of the 2001 IEEE International Conference on Robotics & Automation, pp. 1289–1294. IEEE (2001). https://doi.org/10.1109/ROBOT.2001.932788

14.

Chablat, D.; Wenger, P.; Majou, F.; Merlet, J.P.: An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machines. Int. J. Robot. Res. 23(6), 615–624 (2004). https://doi.org/10.1177/0278364904044079CrossRef

15.

Oetomo, D.; Daney, D.; Shirinzadeh, B.; Merlet, J.P.: An interval-based method for workspace analysis of planar flexure-jointed mechanism. ASME J. Mech. Des. 131(1), 011014 (2009). https://doi.org/10.1115/1.3042151CrossRef

16.

Viegas, C.; Daney, D.; Tavakoli, M.; Almeida, A.T.: Performance analysis and design of parallel kinematic machines using interval analysis. Mech. Mach. Theory 115, 218–236 (2017). https://doi.org/10.1016/j.mechmachtheory.2017.05.003CrossRef

17.

FarzanehKaloorazi, M.H.; Masouleh, M.T.; Caro, S.: Collision-free workspace of parallel mechanisms based on an interval analysis approach. Robotica 35(8), 1747–1760 (2017). https://doi.org/10.1017/S0263574716000497CrossRef

18.

Cao, Y.; Lu, K.; Li, X.J.; Zang, Y.: Accurate numerical methods for computing 2D and 3D robot workspace. Int. J. Adv. Rob. Syst. 8(6), 1–13 (2011). https://doi.org/10.5772/45686CrossRef

19.

Zhao, Z.Y.; Xu, Z.B.; He, J.P.; He, S.; Xu, C.: Configuration optimization of nine degree of freedom super-redundant serial manipulator based on workspace analysis. J. Mech. Eng. 55(21), 51–63 (2019). https://doi.org/10.3901/JME.2019.21.051CrossRef

20.

Ye, P.D.; You, J.J.; Qiu, X.; Xu, S.; Wang, L.K.; Ru, Y.: Workspace analysis of Stewart derivative parallel robot. Machine Design and Research 36 (4), 47–51+61 (2020). https://doi.org/10.13952/j.cnki.jofmdr.2020.0145. (in Chinese)

21.

Chaudhury, A.N.; Ghosal, A.: Optimum design of multi-degree-of-freedom closed-loop mechanisms and parallel manipulators for a prescribed workspace using Monte Carlo method. Mech. Mach. Theory 118, 115–138 (2017). https://doi.org/10.1016/j.mechmachtheory.2017.07.021CrossRef

22.

Li, C.G.; Wu, H.T.; You, J.J.: Redundant parallel six-axis accelerometer and measuring method. China. Patent CN101949954A

23.

You, J.J.; Zuo, F.Y.; Yan, F.; Wang, J.; Wang, L.J.; Yan, P.F.: In-parallel platform and solution method of forward kinematics. China. Patent CN106142051A

24.

Shen, H.P.; Li, J.; Wang, Z.; Meng, Q.M.; Dai, L.F.: Topology structure optimization and performance improvement for parallel mechanisms based on structure coupling-reducing and motion decoupling. J. Mech. Eng. 53(19), 176–186 (2017). https://doi.org/10.3901/JME.2017.19.176CrossRef

25.

Merlet, J.P.: Interval analysis and robotics. Robot. Res. 66, 147–156 (2010). https://doi.org/10.1007/978-3-642-14743-2_13CrossRef

26.

Moore, R.E.: Interval analysis. Prentice-Hall, Englewood Cliffs, N. J., USA. (1966). http://www.researchgate.net/publication/273129945_Interval_Analysis

27.

Tannous, M.; Caro, S.; Goldsztejn, A.: Sensitivity analysis of parallel manipulators using an interval linearization method. Mech. Mach. Theory 71, 93–114 (2014). https://doi.org/10.1016/j.mechmachtheory.2013.09.004CrossRef

28.

You, J.J.; Wang, L.K.; Xi, F.F.; Shen, J.J.: Decoupling algorithm and maximum operation frequency of a novel parallel type six-axis accelerometer. IEEE Sens. J. 20(21), 12637–12651 (2020). https://doi.org/10.1109/JSEN.2020.3001250CrossRef

29.

Huang, L.; Li, Z.C.; Xie, F.; Feng, K.: Strapdown sculling velocity algorithms using novel input combinations. Math. Probl. Eng. 2018, 1–9 (2018). https://doi.org/10.1155/2018/9823138CrossRef

30.

Merlet, J.P.: Parallel robots. Springer Netherlands, Berlin, Germany. (2006). http://link.springer.com/book/10.1007%2F978-94-010-9587-7

Title: An Interval Discretization Method for Workspace Determination of Parallel Mechanisms
Authors: Pengda Ye
Jingjing You
Fengfeng Xi
Jieyu Wang
Yu Ru
Publication date: 10-01-2022
Publisher: Springer Berlin Heidelberg
Published in: Arabian Journal for Science and Engineering / Issue 7/2022
Print ISSN: 2193-567X
Electronic ISSN: 2191-4281
DOI: https://doi.org/10.1007/s13369-021-06310-2

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