Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-24T13:26:26.927Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinematic analysis of a novel 2(3-RUS) parallel manipulator

Published online by Cambridge University Press:  20 January 2015

Róger E. Sánchez-Alonso ,
José-Joel González-Barbosa ,
Eduardo Castillo-Castaneda  and
Jaime Gallardo-Alvarado
Róger E. Sánchez-Alonso*
Affiliation:
Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Instituto Politécnico Nacional. Cerro Blanco, No. 141, Colinas del Cimatario, Querétaro, QRO, México
José-Joel González-Barbosa
Affiliation:
Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Instituto Politécnico Nacional. Cerro Blanco, No. 141, Colinas del Cimatario, Querétaro, QRO, México
Eduardo Castillo-Castaneda
Affiliation:
Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada, Instituto Politécnico Nacional. Cerro Blanco, No. 141, Colinas del Cimatario, Querétaro, QRO, México
Jaime Gallardo-Alvarado
Affiliation:
Departamento de Ingeniería Mecánica, Instituto Tecnológico de Celaya. Av. Tecnológico y Av. García Cubas, No. 38010, Celaya, GTO, México
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper introduces a novel 6-DOF parallel manipulator, which is composed of two 3-RUS parallel manipulators that share a common three-dimensional moving platform. Semi-analytical form solutions are easily obtained to solve the forward displacement analysis of the robot using the non-planar geometry of the moving platform, whereas the velocity, acceleration, and singularity analyses are performed using screw theory. A case study is included to show the application of the kinematic model, which is verified with the aid of a commercially available software. Simple kinematic analysis and reduced singular regions are the main benefits of the proposed parallel manipulator.

Keywords

Parallel manipulatorsHexapodsKinematic analysisSemi-analytical form solutionScrew theory
Type
Articles
Information
Robotica , Volume 34 , Issue 10 , October 2016 , pp. 2241 - 2256
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. Gough, V. E, “Contribution to Discussion to Papers on Research in Automobile Stability and Control and in Type Performance,” Proceedings of the Automation Division Institution of Mechanical Engineers, UK (1957) pp. 392–365.Google Scholar
2. Gough, V. E. and Whitehall, S. G., “Universal Tyre Testing Machine,” Proceedings of the FISITA Ninth International Technical Congress, IMechE 1, London, UK (1962) pp. 117–137.Google Scholar
3. Stewart, D., “A Platform with Six Degrees of Freedom,” Proceedings of the Institution of Mechanical Engineers, I (180), UK (1965) pp. 371–386.Google Scholar
4. Clavel, R., “Delta, a Fast Robot with Parallel Geometry,” Proceedings of the 18th International Symposium of Industrial Robots, Lausanne (1988) pp. 91–100.Google Scholar
5. Clavel, R., “Device for the movement and positioning of an element in space,” US Patent No. 4976582A, (Dec. 11, 1990).Google Scholar
6. Neumann, K.-E., “Robot,” US Patent No. 4732525A, (Mar. 22, 1988).Google Scholar
7. Siciliano, B., “The Tricept robot: Inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm,” Robotica 17, 437–445 (1999).CrossRefGoogle Scholar
8. Ronga, F. and Vust, T., “Stewart Platforms without Computer?,” Proceedings of the Internnational Conference of Real, Analytic and Algebraic Geometry, Trento (1992) pp. 197–212.Google Scholar
9. Mourrain, B., “The 40 Generic Positions of a Parallel Robot,” Proceedings of ISSAC'93, Kiev (1993) pp. 173–182.Google Scholar
10. Lazard, D., “On the representation of rigid-body motions and its application to generalized platform manipulators,” J. Comput. Kinematics 1 (1), 175–182 (1993).Google Scholar
11. Raghavan, M., “The Stewart platform of general geometry has 40 configurations,” ASME J. Mech. Des. 115 (2), 277–282 (1993).Google Scholar
12. Wampler, C. W., “Forward displacement analysis of general six-in-parallel sps (Stewart) platform manipulators using soma coordinates,” Mech. Mach. Theory 31 (3), 331–337 (1996).CrossRefGoogle Scholar
13. Husty, M., “An algorithm for solving the direct kinematic of Stewart-Gough type platforms,” Mech. Mach. Theory 31 (4), 365–379 (1996).Google Scholar
14. Innocenti, C., “Forward kinematics in polynomial form of the general Stewart platform,” ASME J. Mech. Des. 123 (2), 254–260 (2001).Google Scholar
15. Lee, T.-Y. and Shim, J.-K., “Forward kinematics of the general 6–6 Stewart platform using algebraic elimination,” Mech. Mach. Theory 36 (9), 1073–1085 (2001).Google Scholar
16. Lee, T.-Y. and Shim, J.-K., “Improved dialytic elimination algorithm for the forward kinematics of the general Stewart-Gough platform,” Mech. Mach. Theory 38 (6), 563–577 (2003).CrossRefGoogle Scholar
17. Liu, A.-X. and Yang, T.-L., “Configuration Analysis of a Class of Parallel Structures using Improved Continuation,” 9th World Congress on the Theory of Machines and Mechanisms, Milan, Italy (1995) pp. 155–158.Google Scholar
18. Mu, Z. and Kazerounian, K., “A real parameter continuation method for complete solution of forward position analysis of the general Stewart,” J. Mech. Des. 124 (2), 236–44 (2002).Google Scholar
19. Rolland, L., “Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator,” Adv. Robot. 19 (9), 995–1025 (2005).Google Scholar
20. Gan, D., Liao, Q., Dai, J. S., Wei, S. and Seneviratne, L. D., “Forward displacement analysis of the general 6–6 Stewart mechanism using Gröbner bases,” Mech. Mach. Theory 44 (9), 1640–1647 (2009).Google Scholar
21. Merlet, J.-P., “Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis,” Int. J. Robot. Res. 23 (3), 221–235 (2004).Google Scholar
22. Shen, H. and Wu, X., “Numerical solution of direct kinematic problems for parallel manipulators based on interval dividing search algorithms,” Mech. Sci. Technol. 23, 185–188 (2004).Google Scholar
23. Liu, S., Li, W., Du, Y. and Fang, L., “Forward on Kinematics of the Stewart Platform using Hybrid Immune Genetic Algorithm,” Proceedings of the IEEE Conference on Mechatronics and Automation, Luoyang (2006) pp. 2330–2335.Google Scholar
24. Omran, A., El-Bayiumi, G., Bayoumi, M. and Kassem, A., “Genetic algorithm based optimal control for a 6-dof non redundant stewart manipulator,” In. J. Mech. Syst. Sci. Eng. 2 (2), 73–79 (2008).Google Scholar
25. Rolland, L. and Chandra, R., “On Solving the Forward Kinematics of the 6–6 General Parallel Manipulator with an Efficient Evolutionary Algorithm,” ROMANSY 18 Robot Design, Dynamics and Control: Proceedings of The Eighteenth CISM-IFToMM Symposium, Springer Vienna, (2010) pp. 117–124.CrossRefGoogle Scholar
26. Parikh, P. J. and Lam, S. S., “A hybrid strategy to solve the forward kinematics problem in parallel manipulators,” IEEE Trans. Robot. 21 (1), 18–25 (2005).Google Scholar
27. Yurt, S. N., Anli, E. and Ozkol, I., “Forward kinematics analysis of the 6–3 SPM by using neural networks,” Meccanica 42 (2), 187–96 (2007).Google Scholar
28. Merlet, J.-P., “Closed Form Resolution of the Direct Kinematics of Parallel Manipulators Using Extra Sensors Data,” Proceedings of the 1993 IEEE International Conference on Robotics and Automation, Atlanta (1993) pp. 200–204.Google Scholar
29. Baron, L. and Angeles, J., “Kinematic decoupling of parallel manipulators using joint-sensor data,” IEEE Trans. Robot. Autom. 16 (6), 644–651 (2000).Google Scholar
30. Zubizarreta, A., Cabanes, I., Marcos, M. and Pinto, Ch., “Dynamic modeling of planar parallel robots considering passive joint sensor data,” Robotica 28 (5), 649–661 (2010).CrossRefGoogle Scholar
31. Chen, S.-L. and You, I.-T., “Kinematic and singularity analyses of a six-DOF 6–3–3 parallel link machine tool,” Int. J. Adv. Manuf. Technol. 16 (11), 835–842 (2000).CrossRefGoogle Scholar
32. Chen, S.-L. and Liu, Y.-C., “Post-processor development for a six degrees-of-freedom parallel-link machine tool,” Int. J. Adv. Manuf. Technol. 18 (4), 254–265 (2001).Google Scholar
33. Zhang, M. and Zhuo, B., “Workspace Analysis and Parameter Optimization of a Six-DOF 6–3–3 Parallel Link Machine Tool,” Intelligent Robotics and Applications, Lecture Notes in Computer Science, 5928, (2009) pp. 706–712.Google Scholar
34. Gao, H., Xiao, P. and Zhang, H., “Configuration Optimization of Physical Prototype for 6–3–3 Parallel Mechanism,” Proceedings of 2011 International Conference on Electrical and Control Engineering (ICECE), Yichang, China (2011) pp. 2937–2939.Google Scholar
35. Gallardo-Alvarado, J., García-Murillo, M. and Castillo-Castaneda, E., “A 2(3-RRPS) parallel manipulator inspired by Gough-Stewart platform,” Robotica 31 (3), 381–388 (2013).Google Scholar
36. García-Murillo, M., Castillo-Castaneda, E. and Gallardo-Alvarado, J., “Dynamics of a 2(3-RRPS) Parallel Manipulator,” Proceedings of the 9th International Workshop on Robot Motion and Control, Poland, (2013) pp. 270–275.Google Scholar
37. Mayer, B. and Gosselin, C., “Singularity analysis and representation of the general Gough-Stewart platform,” Int. J. Robot. Res. 19 (3), 271–288 (2000).Google Scholar
38. Huang, Z. and Cao, Y., “Property identification of the singularity loci of a class of Gough–Stewart manipulators,” Int. J. Robot. Res. 24 (8), 675–685 (2005).Google Scholar
39. Bandyopadhyay, S. and Ghosal, A., “Geometric characterization and parametric representation of the singularity manifold of a 6–6 Stewart platform manipulator,” Mech. Mach. Theory 41 (11), 1377–1400 (2006).Google Scholar
40. Jiang, Q. and Gosselin, C., “Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform,” Mech. Mach. Theory 44 (6), 1281–1293 (2009).CrossRefGoogle Scholar
41. Dasgupta, B. and Mruthyunjaya, T. S., “Singularity-free path planning for the Stewart platform manipulator,” Mech. Mach. Theory 33 (6), 711–725 (1998).Google Scholar
42. Sen, S., Dasgupta, B. and Mallik, A., “Variational approach for singularity-free path-planning of parallel manipulators,” Mech. Mach. Theory 38 (11), 1165–1183 (2003).CrossRefGoogle Scholar
43. Bohigas, O., Manubens, M. and Ros, L., “Planning Singularity-Free Force-Feasible Paths on the Stewart Platform,” Latest Advances in Robot Kinematics, Springer Netherlands, (2012) pp. 245–252.Google Scholar
44. Pierrot, F., Uchiyama, M., Dauchez, P. and Fournier, A., “A new design of a 6-DOF parallel robot,” J. Robot. Mechatronics 2 (4), 308–315 (1990).Google Scholar
45. Nielsen, J. and Roth, B., “Formulation and Solution for the Direct and Inverse Kinematics Problems for Mechanisms and Mechatronic Systems,” Computational Methods in Mechanical Systems: Mechanism Aanalysis, Synthesis, and Optimization, NATO ASI Series, Springer Berlin Heidelberg, vol. 161, (1998) pp. 33–52.CrossRefGoogle Scholar
46. Gallardo-Alvarado, J., Aguilar-Nájera, C., Casique-Rosas, L., González, L. Pérez and Rico-Martinez, J., “Solving the kinematics and dynamics of a modular spatial hyper-redundant manipulator by means of screw theory,” Multibody Syst. Dyn. 20, 307–325 (2008).Google Scholar
47. Rico, J. M. and Duffy, J., “An application of screw algebra to the acceleration analysis of serial chains,” Mech. Mach. Theory 31 (5), 445–457 (1996).Google Scholar
48. Rico, J. M. and Duffy, J., “Forward and inverse acceleration analyses of in-parallel manipulators,” ASME J. Mech. Des. 122 (3), 299–303 (2000).Google Scholar
49. Gallardo-Alvarado, J., Orozco-Mendoza, H. and Rodriguez-Castro, R., “Finding the jerk properties of multibody systems using helicoidal vector fields,” IMechE Part C, J. Mech. Eng. Sci. 222 (11), 2217–2229 (2008).Google Scholar
50. Lung-Wen, T., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley & sons, INC., USA, 1999).Google Scholar
51. Gallardo-Alvarado, J., Rico, J. M and Alici, G., “Kinematics and singularity analyses of a 4-dof parallel manipulator using screw theory,” Mech. Mach. Theory 41 (9), 1048–1061 (2006).Google Scholar
52. Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).Google Scholar
53. Bonev, I., Zlatanov, D. and Gosselin, C., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” J. Mech. Des. 125 (3), 573–581 (2003).Google Scholar
54. Gross, E., Petrovic, S. and Verschelde, J., “Interfacing with PHCpack,” J. Softw. Algebra Geom. 5, 20–25 (2013).Google Scholar