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Cartesian workspace optimization of Tricept parallel manipulator with machining application

Published online by Cambridge University Press:  14 May 2014

M. A. Hosseini and
H. M. Daniali
M. A. Hosseini*
Affiliation:
Department of Mechanical Engineering, University of Mazandaran, Babolsar, Iran
H. M. Daniali
Affiliation:
Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
*
*Corresponding author. E-mail: ma.hosseini@umz.ac.ir
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Summary

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In this research work, the maximum Cartesian workspace of a Tricept parallel robot with two rotational and one translational degrees of freedom was investigated. Generally, the Cartesian workspace identifies the maximum size of a work-piece, specifying its cubic x, y and z dimensions, on which the milling machine could perform operations. However, the workspace of a robot can be considered in its task space, such as ψ × θ × z for the Tricept Parallel Kinematic Mechanism (PKM). A novel homogeneous Jacobian matrix which transforms joint space velocity vector into end-effector Cartesian velocity vector has been generated named as a Cartesian Jacobian matrix. Using the indices derived from the homogeneous Cartesian Jacobian matrix, i.e. the maximum singular values and local conditioning indices, the manipulator is designed to reach the Cartesian workspace with rapid positioning rates as well as with singularity avoidance.

Keywords

Cartesian workspaceRapid positioningHomogenized Cartesian Jacobian matrixParallel robot

Information

Type
Articles
Information
Robotica , Volume 33 , Issue 9 , November 2015, pp. 1948 - 1957
Copyright
Copyright © Cambridge University Press 2014 

References

1. Merlet, J.-P., Parallel Robots (Springer, Dordrecht, 2006).Google Scholar
2. Masory, O. and Wang, J., “Workspace evaluation of Stewart platforms,” Adv. Robot. J. 9 (4), 443–461 (1995).Google Scholar
3. Carretero, J. A., Podhorodeski, R. P., Nahon, M. A. and Gosselin, C. M., “Kinematic analysis and optimization of a new three degree-of freedom spatial parallel manipulator,” J. Mech. Des. 122 (1), 17–24 (2000).Google Scholar
4. Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 3–9 (1985).Google Scholar
5. Salisbury, J. K. and Craig, J. J., “Articulated hands: Force control and kinematic issues,” Int. J. Robot. Res. 1 (4), 4–17 (1982).Google Scholar
6. Gosselin, C. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” ASME Trans. J. Mech. Des. 113 (3), 220–226 (1991).Google Scholar
7. Chen, H., Chen, W. and Liu, J., “Optimal design of Stewart platform safety mechanism,” Chin. J. Aeronautice 20 (4), 370–377 (2007).Google Scholar
8. Ryuand, J. and Cha, J., “Volumetric error analysis and architecture optimization for accuracy of HexaSlide type parallel manipulators,” Mech. Mach. Theory 38 (3), 227–240 (2003).Google Scholar
9. LI, Y. and XU, Q., “Optimal Kinematic Design for a General 3-PRS Spatial Parallel Manipulator Based on Dexterity and Workspace,” The 11th International Conference on Machine Design and Production, Antalya, Turkey (Oct. 13–15, 2004) pp. 571–584.Google Scholar
10. Hosseini, M. A., Daniali, H. R. M. and Taghirad, H. D., “Dexterous workspace optimization of a tricept parallel manipulator,” Adv. Robot. 25, 1697–1712 (2011).Google Scholar
11. Hosseini, M. A. and Daniali, H. R. M., “Dexterous workspace shape and size optimization of a tricept parallel manipulator,” Int. J. Robot. 2 (1), 18–26 (2011).Google Scholar
12. Ranjbaran, F., Angeles, J., Gonzalez-Palacios, M. A. and Patel, R. V., “The mechanical design of a seven-axes manipulator with kinematic isotropy,” J. Intell. Robot. Syst. 14, 21–41 (1995).Google Scholar
13. Ma, O. and Angeles, J., “Optimum Architecture Design of Platform Manipulators,” Proceedings of the IEEE International Conference on Advanced Robotics, Montreal, Quebec, Canada, vol. 2 (Jun. 19–22, 1991) pp. 1130–1135.Google Scholar
14. Chablat, D., Wenger, Ph., Caro, S. and Angeles, J., “The ISO-Conditioning Loci of Planar Three DOF Parallel Manipulators,” Proceedings of DETC'2002, ASME Design Engineering Technical Conferences, Montreal, Quebec, Canada, vol. 1 (Oct. 22, 2002) pp. 129–138.Google Scholar
15. Gosselin, C. M., “The optimum design of robotic manipulators using dexterity indices,” J. Robot. Auton. Syst. 9 (4), 213–226 (1992).Google Scholar
16. Kim, S.-G. and Ryu, J., “New dimensionally homogeneous Jacobean matrix formulation by three end-effector points for optimal design of parallel manipulators,” IEEE Trans. Robot. Autom. 19 (4), 731–737 (2003).Google Scholar
17. Pond, G. and Carretero, J. A., “Quantitative dexterous workspace comparison of parallel manipulators,” Mech. Mach. Theory 42 (10), 1388–1400 (2007).Google Scholar
18. Angeles, J., “Is there a characteristic length of a rigid-body displacement?” Mech. Mach. Theory 41, 884–896 (2006).Google Scholar
19. Mansouri, I. and Ouali, M., “A new homogeneous manipulability measure of robot manipulators based on power concept,” J. Mechatronics 19, 927–944 (2009).Google Scholar
20. Hosseini, M. A. and Daniali, H. M., “Weighted local conditioning index of a positioning and orienting parallel manipulator,” Sientica Iranica B 18 (1), 115–120 (2011).Google Scholar
21. Neumann, K.-E., US patent 4, 732,525 (Mar. 22, 1988).Google Scholar
22. Siciliano, B., “The Tricept robot: Inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm,” Robotica 17 (4), 437–445 (1999).Google Scholar
23. Zhang, D. and Gosselin, C. M., “Kinetostatic analysis and design optimization of the tricept machine tool family,” J. Manuf. Sci. Eng. 124 (3), 725–733 (2002).Google Scholar
24. Lu, Y., Shi, Y. and Hu, B., “Solving Reachable Workspace of Some Parallel Manipulators by CAD Variation Geometry,” Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 222 (9), 1773–1781 (2008).Google Scholar
25. Lu, Y., Hu, B. and Sun, T., “Analyses of velocity, acceleration, statics, and workspace of a 2(3-SPR) serial-parallel manipulator,” Robotica 27 (4), 529–538 (2009).Google Scholar