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Some geometric, kinematic, and dynamic considerations on Stewart-Gough platforms with singularity analysis

Published online by Cambridge University Press:  13 December 2013

A. Saide Sarıgül*
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering, Dokuz Eylül University, İzmir, Turkey
Burcu Güneri
Affiliation:
İzmir Refinery, Turkish Petroleum Refineries Co., İzmir, Turkey
*
*Corresponding author. E-mail: saide.sarigul@deu.edu.tr

Summary

In this study, some geometric, kinematic, and dynamic aspects of the design of a Stewart-Gough platform are examined. The focus of the analyses is on a particular Stewart-Gough platform that we have constructed. The analysis begins with workspace simulations for different moving platform orientations. The computations extend to a parametric study of some geometric and kinematic constraints: Joint angle, rotation angle, and limb length. Actuator force is another parameter considered; and the triple relationship between workspace, joint angle, and actuator force is discussed. Parametric analyses are culminated with a brief discussion of the real design parameters.

Type
Articles
Copyright
Copyright © Cambridge University Press 2013 

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References

1. Fichter, E. F., “A Stewart platform based manipulator: General theory and practical considerations,” Int. J. Robot. Res. 5 (2), 157182 (1986).Google Scholar
2. Ceccarelli, M., “A formulation for the workspace boundary of general N-revolute manipulators,” Mech. Mach. Theor. 31 (5), 637646 (1996).CrossRefGoogle Scholar
3. Chirikjian, G. S. and Ebert-Uphoff, I., “Numerical convolution on the Euclidean group with applications to workspace generation,” IEEE Trans. Robot. Autom. 14 (1), 123136 (1998).CrossRefGoogle Scholar
4. Asada, H. and Youcef-Toumi, K., “Analysis and design of a direct-drive arm with a five-bar-link parallel drive mechanism,” ASME J. Dyn. Syst. Meas. Control 106 (3), 225230 (1984).CrossRefGoogle Scholar
5. Yang, D. C. H. and Lee, T. W., “Feasibility study of a platform type of robot manipulators from a kinematic viewpoint,” ASME J. Mech. Transmissions Autom. Des. 106, 191198 (1984).Google Scholar
6. Bajpai, A. and Roth, B., “Workspace and mobility of a closed-loop manipulator,” Int. J. Robot. Res. 5 (2), 131142 (1986).CrossRefGoogle Scholar
7. Lee, K. M. and Shah, D. K., “Kinematic analysis of a three-degree-of-freedom in-parallel actuated manipulator,” IEEE J. Robot. Autom. 14 (3), 354360 (1988).Google Scholar
8. Nguyen, C. C. and Pooran, F. J., Kinematic Analysis and Workspace Determination of a 6 Dof CKCM Robot End-Effector (Elsevier, Amsterdam, 1989).CrossRefGoogle Scholar
9. Gosselin, C., “Determination of a workspace of 6-DOF parallel manipulators,” ASME J. Mech. Des. 112, 331336 (1990).Google Scholar
10. Kumar, V., “Characterization of workspaces of parallel manipulators,” ASME J. Mech. Des. 114, 368375 (1992).Google Scholar
11. Merlet, J. P., “Determination of the workspace of a parallel manipulator for a fixed orientation,” Mech. Mach. Theor. 29 (8), 10991110 (1994).Google Scholar
12. Merlet, J. P., “Trajectory verification in the workspace for parallel manipulators,” Int. J. Robot. Res. 13 (4), 326333 (1994).Google Scholar
13. Ji, Z., “Workspace analysis of Stewart platforms via vertex space,” J. Robotic Syst. 11 (7), 631639 (1994).CrossRefGoogle Scholar
14. Luh, C., Adkins, F., Haung, E. and Qiu, C., “Working capability analysis of Stewart platforms,” ASME J. Mech. Des. 118, 220227 (1996).Google Scholar
15. Merlet, J. P., “Designing a parallel manipulator for a specific workspace,” Int. J. Robot. Res. 16 (4), 545556 (1997).Google Scholar
16. Conti, J., Clinton, C., Zhang, G. and Wavering, A., Workspace Variation of a Hexapod Machine Tool, NISTIR 6135 (National Institute of Standards and Technology, Gaithersburg, MD, 1998).Google Scholar
17. Merlet, J. P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theor. 33 (1/2), 720 (1998).CrossRefGoogle Scholar
18. Wang, Z., Wang, Z., Liu, W. and Lei, Y., “A study on workspace, boundary workspace analysis and work piece positioning for parallel machine tools,” Mech. Mach. Theor. 36, 605622 (2001).Google Scholar
19. Xi, F., “A comparison study on hexapods with fixed-length legs,” Int. J. Mach. Tools Manu. 41, 17351748 (2001).Google Scholar
20. Badescu, M. and Mavroidis, C., “Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints,” ASME J. Mech. Des. 126, 291300 (2004).Google Scholar
21. Ferraresi, C., Paoloni, M. and Pescarmona, F., “A new methodology for the determination of the workspace of six-DOF redundant parallel structures actuated by nine wires,” Robotica 25, 113120 (2007).CrossRefGoogle Scholar
22. Pond, G. and Carretero, J. A., “Quantitative dexterous workspace comparison of parallel manipulators,” Mech. Mach. Theor. 42, 13881400 (2007).CrossRefGoogle Scholar
23. Lu, Y. and Hu, B., “Analyzing kinematics and solving active/constrained forces of a 3 SPU+UPR parallel manipulator,” Mech. Mach. Theor. 42, 12981313 (2007).Google Scholar
24. Alp, H. and Özkol, İ., “Extending the workspace of parallel working mechanisms,” J. Mech. Eng. Sci. 22, 13051313 (2008).Google Scholar
25. Glozman, D. and Shoham, M., “Novel 6-dof parallel manipulator with large workspace,” Robotica 27, 891895 (2009).Google Scholar
26. Wang, Z., Ji, S., Li, Y. and Wan, Y., “A unified algorithm to determine the reachable and dexterous workspace of parallel manipulators,” Robot. Comput. Integr. Manuf. 26, 454460 (2010).Google Scholar
27. Dasgupta, B. and Mruthyunjaya, T. S., “Singularity-free path planning for the Stewart platform manipulator,” Mech. Mach. Theor. 33 (6), 711725 (1998).Google Scholar
28. Merlet, J. P., “A generic trajectory verifier for the motion planning of parallel robots,” ASME J. Mech. Des. 123, 510515 (2001).CrossRefGoogle Scholar
29. Macho, E., Altuzarro, O., Amezua, E. and Hernandez, A., “Obtaining configuration space and singularity maps for parallel manipulators,” Mech. Mach. Theor. 44, 21102125 (2009).CrossRefGoogle Scholar
30. Tsai, K. Y. and Lee, T. K., “6-DOF parallel manipulators with better dexterity, rotatibility or singularity-free workspace,” Robotica 27, 599606 (2008).CrossRefGoogle Scholar
31. Jiang, Q. and Gosselin, C. M., “The maximal singularity-free workspace of the Gough-Stewart platform for a given orientation,” ASME J. Mech. Des. 130 (11), 112304112304 (2008).Google Scholar
32. Jiang, Q. and Gosselin, C. M., “Determination of the maximal singularity-free orientation workspace for the Gough-Stewart platform,” Mech. Mach. Theor. 44, 12811293 (2009).Google Scholar
33. Enferadi, J. and Tootoonchi, A. A., “A novel spherical parallel manipulator: Forward position problem, singularity analysis, and isotropy design,” Robotica 27, 663676 (2009).Google Scholar
34. Cao, Y., Zhou, H., Zhang, Q. J. and Ji, W. X., “Research on the orientation-singularity and orientation-workspace of a class of Stewart-Gough parallel manipulators,” J. Multi-body Dynamics 224 (K1), 1932 (2010).Google Scholar
35. Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a planar three-degree-of freedom parallel manipulator,” ASME J. Mech. Transmissions Autom. Des. 110 (1), 3541 (1988).Google Scholar
36. Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a spherical three-degree-of freedom parallel manipulator,” ASME J. Mech. Transmissions Autom. Des. 111 (2), 202207 (1989).Google Scholar
37. Tsai, L. W. and Joshi, S., “Kinematics and optimization of a spatial 3-UPU parallel manipulator,” ASME J. Mech. Des. 122 (4), 439446 (2000).Google Scholar
38. Hwang, Y. K., Yoon, J. W. and Ryu, J. H., “The optimum design of a 6-dof parallel manipulator with large orientation workspace,” IEEE Int. Conf. Robot. Autom. 163–168, (2007).Google Scholar
39. Ruggiu, M., “Position analysis, workspace and optimization of a 3-PPS spatial manipulator,” ASME J. Mech. Des. 131, 051010/19 (2009).Google Scholar
40. Wang, Y., Wu, C. and Liu, X. J., “Performance evaluation of parallel manipulators: Motion/force transmissibility and its index,” Mech. Mach. Theor. 45, 14621476 (2010).Google Scholar
41. Garg, V., Nokleby, S. B. and Carretero, J. A., “Determining the force and moment workspaces of redundantly-actuated spatial parallel manipulators,” ASME Int. Des. Eng. Tech. Conf. Comp. Inf. Eng. Conf. 8, 10631070 (2008).Google Scholar
42. Güneri, B., A Complete Dynamic Analysis of Stewart Platform Including Singularity Detection, M.Sc. Thesis (İzmir, Turkey: Graduate School of Natural and Applied Sciences, Dokuz Eylül University, 2007).Google Scholar
43. Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley, New York, 1999).Google Scholar
44. Masory, O. and Wang, J., “Workspace evaluation of Stewart platforms,” Adv. Rob. 9 (4), 443461 (1995).Google Scholar
45. Sen, S., Dasgupta, B. and Mallik, A. K., “Variational approach for singularity-free path-planning of parallel manipulators,” Mech. Mach. Theor. 38, 11651183 (2003).Google Scholar