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On the kinematics of a new parallel mechanism with Schoenflies motion

Published online by Cambridge University Press:  13 January 2015

Po-Chih Lee
Affiliation:
Department of Mechanical Engineering, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan ROC.
Jyh-Jone Lee*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan ROC.
*
*Corresponding author. E-mail: [email protected]

Summary

This paper investigates the kinematics of one new isoconstrained parallel manipulator with Schoenflies motion. This new manipulator has four degrees of freedom and two identical limbs, each having the topology of Cylindrical–Revolute–Prismatic–Helical (C–R–P–H). The kinematic equations are derived in closed-form using matrix algebra. The Jacobian matrix is then established and the singularities of the robot are investigated. The reachable workspaces and condition number of the manipulator are further studied. From the kinematic analysis, it can be shown that the manipulator is simple not only for its construction but also for its control. It is hoped that the results of the evaluation of the two-limb parallel mechanism can be useful for possible applications in industry where a pick-and-place motion is required.

Type
Articles
Copyright
Copyright © Cambridge University Press 2015 

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References

1. Stewart, D., “A platform with 6 degrees of freedom,” Proceedings of Institution of Mechanical Engineers part 1, 180 (15), 371386 (1965).Google Scholar
2. Clavel, R., “Delta, A Fast Robot with Parallel Geometry,” 18 th International Symposium on Industrial Robotics, Lausanne: IFS Publications (1988) pp. 91100.Google Scholar
3. Clavel, R., Device for the movement and positioning of an element in space, US Patent 4976582 (1990).Google Scholar
4. Angeles, J., “The qualitative synthesis of parallel manipulators,” ASME J. Mech. Des. 126 (4), 617674 (2004).Google Scholar
5. Angeles, J., Morozov, A. and Navarro, O., “A Novel Manipulator Architecture for the Production of the SCARA Motions,” Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, California (2000) pp. 2370–2375.Google Scholar
6. Pierrot, F. and Company, O., “H4: A New Family of 4-DoF Parallel Robots,” Proceedings of IEEE/ASME International Conference Advances Intelligent Mechatronics, Atlanta, GA (1999) pp. 508–513.Google Scholar
7. Krut, S. Company, O., Benoit, M., Ota, H. and Pierrot, F., “I4: A New Parallel Mechanism for SCARA Motions,” Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sep. 14–19, 2003).Google Scholar
8. Company, O. and Pierrot, F., “A New 3T-1R Parallel Robot,” Proceedings of the 9th International Conference on Advanced Robotics, Tokyo, Japan (Oct. 25–27, 1999) pp. 557–562.Google Scholar
9. Company, O., Pierrot, F., Nabat, V. and Rodriguez, M., “Schoenflies Motion Generator: A New Non Redundant Parallel Manipulator with Unlimited Rotation Capability,” Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 3250–3255.Google Scholar
10. Marquet, F., Company, O., Krut, S., Gascuel, O. and Pierrot, F., “Control of a 3-DoF Over-Actuated Parallel Mechanism,” Proceedings of ASME International Design Engineering Technical Conferences – Computers and Information in Engineering Conference, Montreal, Canada (2002) DETC2002/MECH-34343.Google Scholar
11. Richard, P. L., Gosselin, C. M. and Kong, X. W., “Kinematic analysis and prototyping of a partially decoupled 4-DOF 3T1R parallel manipulator,” ASME J. Mech. Des. 129 (12), 611616 (2007).CrossRefGoogle Scholar
12. Kong, X. W. and Gosselin, C. M., “Type synthesis of 3T1R 4-DoF parallel manipulators based on screw theory,” IEEE Trans. Robot. Autom. 20 (2), 181190 (2004).Google Scholar
13. Pierrot, F., Nabat, V., Company, O., Krut, S. and Poignet, P.Optimal design of a 4-DOF parallel manipulator: From academia to industry,” IEEE Trans. Robot. 25 (2), 213224 (2009).CrossRefGoogle Scholar
14. Company, O., Krut, S. and Pierrot, F., “Internal singularity analysis of a class of lower mobility parallel manipulators with articulated traveling plate,” IEEE Trans. Robot. 22 (1), 111 (2006).CrossRefGoogle Scholar
15. Lee, C.-C. and Hervé, J. M., “Isoconstrained parallel generators of Schoenflies motion,” ASME J. Mech. Robot. 3 (2), 021006 (2011).Google Scholar
16. Lee, C.-C. and Lee, P.-C. “Isoconstrained Mechanisms for Fast Pick-and-Place Manipulation,” Proceeding of the 1st International Symposium Geometric Methods in Robotics and Mechanism Research, Hong Kong (Dec. 15–16, 2009).Google Scholar
17. Lee, P.-C., Lee, J.-J. and Lee, C.-C., “Four Novel Pick-and-Place Isoconstrained Manipulators and Their Inverse Kinematics,” Proceedings of ASME International Design Engineering Technical Conferences – Computers and Information in Engineering Conference, Montreal, Quebec, Canada (Aug. 15–18, 2010) DETC2010-28426.Google Scholar
18. Lee, P.-C. and Lee, J.-J., “Forward Kinematics and Numerical Verification of Four Novel Parallel Manipulators with Schoenflies motion,” The 1st IFToMM Asian Conference Mechanism and Machine Science, Taipei, Taiwan (Oct. 21–25, 2010).Google Scholar
19. Hartenberg, R. S. and Denavit, J., Kinematic Synthesis of Linkages (McGraw-Hill, New York, 1964).Google Scholar
20. Tsai, L. W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley & Sons, New York, 1999).Google Scholar
21. Craig, J. J., Introduction to Robotics: Mechanics and Control, 3rd ed. (Pearson Prentice Hall, Upper Saddle River, 2005).Google Scholar
22. Opl, M., Holub, M., Pavlik, J., Bradac, F., Blecha, P., Kozubik, J. and Coufal, J., “DELTA- Robot with Parallel Kinematics,” In: Mechatronics: Recent Technological and Scientific Advances (Springer, Berlin, 2012) pp. 445452.Google Scholar
23. Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 39 (1985).Google Scholar
24. Merlet, J. P., Parallel Robots, 2nd ed. (Springer, Dordrecht, 2006).Google Scholar
25. Salisbury, J. K. and Craig, J. J., “Articulated hands: Force control and kinematic issues,” Int. J. Robot. Res. 1 (1), 417 (1982).Google Scholar
26. Zanganeh, K. E. and Angeles, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res. 16 (2), 185197 (1997).CrossRefGoogle Scholar
27. Stan, S., Manic, M., Szep, C. and Balan, R., “Performance Analysis of 3 DOF Delta Parallel Robot,” IEEE 4th International Conference on Human System Interactions, Yokohama, Japan (May 19–21, 2011).Google Scholar
28. Stamper, R. E., Tsai, L. W. and Walsh, G. C., “Optimization of a Three DOF Translational Platform for Well-Conditioned Workspace,” Proceedings of IEEE International Conference on Robotics and Automation, Albuquerque, New Mexico (1997) pp. 3250–3255.Google Scholar