Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T09:15:51.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Forward kinematics modeling of spatial parallel linkage mechanisms based on constraint equations and the numerical solving method

Published online by Cambridge University Press:  19 June 2015

Liyang Gao  and
Weiguo Wu
Liyang Gao
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Heilongjiang, Harbin, P. R. China
Weiguo Wu*
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Heilongjiang, Harbin, P. R. China
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In order to solve general kinematics modeling problems and numerical stability problems of numerical methods for spatial parallel linkage mechanisms, a general modeling method and its numerical solving algorithm is proposed. According to the need for avoiding direct singular configurations, valid joint variable space and valid forward kinematics solutions (VKSs) are defined. Taking numerical convergence near singular points into account, the pseudo-arc length homotopy continuation algorithm is given to solve the kinematics model. Finally as an example, the joint variable space of the general Stewart platform mechanism is analyzed, which is proved to be divided into subspaces by direct singular surfaces. And then, forward kinematics solutions of 200 testing points are solved separately using the pseudo-arc length homotopy continuation algorithm, the Newton homotopy continuation algorithm and the Newton–Raphson algorithm (NRA). Comparison of the results shows that the proposed method is convergent to the same solution branch with the initial configuration on all the testing points, while the other two algorithms skip to other solution branches on some near singular testing points.

Keywords

Spatial parallel linkage mechanismForward kinematicsNumerical solutionsDirect singularityHomotopy continuation method
Type
Articles
Information
Robotica , Volume 35 , Issue 2 , February 2017 , pp. 293 - 309
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Gan, D., Liao, Q., Dai, J. S. et al., “Forward displacement analysis of the general 6–6 Stewart mechanism using Gröbner bases,” Mech. Mach. Theory, 44 (9), 1640–1647 (2009).Google Scholar
2. Huang, X. G., “A Study on some Issues for Kinematics of Mechanism and their Algebraic Methods [D],” (Beijing University of Posts and Telecommunications, Beijing, 2008).Google Scholar
3. Tsai, M. S., Shiau, T. N., Tsai, Y. J. et al., “Direct kinematic analysis of a 3-PRS parallel mechanism,” Mech. Mach. Theory, 38 (1), 71–83 (2003).CrossRefGoogle Scholar
4. Gan, D. and Wei, S., “Forward Kinematics Analysis of the New 3-CCC Parallel Mechanism,” IEEE, International Conference on Mechatronics and Automation, (2007) pp. 905–910.Google Scholar
5. Lu, Y., Wang, P., Zhao, S., Hu, B., Han, J. and Sui, C., “Kinematics and statics analysis of a novel 5-DoF parallel manipulator with two composite rotational/linear active legs,” Robot. Comput.-Integr. Manuf. 30 (1), 25–33 (2014).CrossRefGoogle Scholar
6. Gao, H., “Research on Application and Theory of Mechanism for 6–3–3 Parallel Mechanism [D],” (Hefei University of Technology, Hefei, 2007).Google Scholar
7. Yang, C., Huang, Q., Ogbobe, P. O. et al., “Forward Kinematics Analysis of Parallel Robots using Global Newton–Raphson Method,” IEEE, Intelligent Computation Technology and Automation, (2009), vol. 3, pp. 407–410.Google Scholar
8. Liu, F., Zhang, X., Wei, Y. and Wu, H., “The Forward Kinematics Analysis of 6-UPS Parallel Mechanism based on Newton Iteration,” Machinery Design & Manufacture, (2013) (5), pp. 173–176.Google Scholar
9. Dehghani, M., Ahmadi, M., Khayatian, A. et al., “Neural Network Solution for Forward Kinematics Problem of HEXA Parallel Robot,” IEEE, American Control Conference, (2008) pp. 4214–4219.Google Scholar
10. Parikh, P. J. and Lam, S. S. Y., “A hybrid strategy to solve the forward kinematics problem in parallel manipulators,” IEEE Trans. Robot. 21 (1), 18–25 (2005).Google Scholar
11. Jamwal, P. K., Xie, S. Q., Tsoi, Y. H. and Aw, K. C., “Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference,” Mech. Mach. Theory, 45 (11), 1537–1554 (2010).Google Scholar
12. Morell, A., Tarokh, M. and Acosta, L., “Solving the forward kinematics problem in parallel robots using support vector regression,” Eng. Appl. Artif. Intell. 26 (7), 1698–1706 (2013).Google Scholar
13. Wang, L. C. T. and Chen, C. C., “On the numerical kinematic analysis of general parallel robotic manipulators,” IEEE Trans. Robot. Autom. 9 (3), 272–285 (1993).Google Scholar
14. Raghavan, M., “The Stewart Platform of General Geometry has 40 Configurations,” ASME Design and Automation Conference, Chicago, IL, (1991), vol. 32 (2), pp. 397–402.Google Scholar
15. Sreenivasan, S. V. and Nanua, P., “Solution of the Direct Position Kinematics Problem of the General Stewart Platform using Advanced Polynomial Continuation,” 22nd Biennial Mechanisms Conference, Scottsdale, AZ, (1992) pp. 99–106.Google Scholar
16. Varedi, S. M., Daniali, H. M. and Ganji, D. D., “Kinematics of an offset 3-UPU translational parallel manipulator by the homotopy continuation method,” Nonlinear Anal.: Real World Appl. 10 (3), 1767–1774 (2009).Google Scholar
17. de Jalón, J. G., Serna, M. A. and Avilés, R., “Computer method for kinematic analysis of lower-pair mechanisms––II position problems,” Mech. Mach. Theory, 16 (5), 557–566 (1981), ISSN 0094-114X.Google Scholar
18. Sugiyama, H., Escalona, J. L. and Shabana, A. A., “Formulation of three-dimensional joint constraints using the absolute nodal coordinates,” Nonlinear Dyn. 21 (2), 167–195 (2003), ISSN 0924-090X.Google Scholar
19. Masarati, P., “A formulation of kinematic constraints imposed by kinematic pairs using relative pose in vector form,” Multibody Syst. Dyn. 29 (2), 119–137 (2013), ISSN .Google Scholar
20. Ma, O. and Angeles, J., “Architecture singularities of platform manipulators,” IEEE, International Conference on Robotics and Automation, (1991) pp. 1542–1547.Google Scholar
21. Ma, O. and Angeles, J., “Architecture singularities of parallel manipulators,” Int. J. Robot. Autom. 7 (1), 23–29 (1992).Google Scholar
22. Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).Google Scholar
23. Tsai, L. W., “Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley & Sons, Hoboken, New Jersey, USA, 1999).Google Scholar
24. Macho, E., Altuzarra, O., Petuya, V. and Hernndez, A., “Workspace enlargement merging assembly modes. Application to the 3-RRR planar platform,” Int. J. Mech. Control, 10 (1), 13–20 (2009).Google Scholar
25. Macho, E., Petuya, V., Altuzarra, O. and Hernandez, A., “Planning nonsingular transitions between solutions of the direct kinematic problem from the joint space,” J. Mech. Robot. 4 (4), 041005–1–041005–9 (2012); doi:10.1115/1.4007306.Google Scholar
26. Bamberger, H., Wolf, A. and Shoham, M., “Assembly mode changing in parallel mechanisms,” IEEE Trans. Robot. 24 (4), 765–772 (2008). doi: 10.1109/TRO.2008.926863.Google Scholar
27. Keller, H. B., “Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems,” Applications of Bifurcation Theory, (1977), pp. 359–384.Google Scholar
28. Keller, H. B., “Constructive Methods for Bifurcation and Nonlinear Eigenvalue Problems,” Computing Methods in Applied Sciences and Engineering, I. (Berlin Heidelberg, Springer, 1979) pp. 241–251.Google Scholar