Abstract
In most of the previous studies on parallel mechanisms (PMs), architectural design mainly relying on symmetric geometry was investigated without in-depth analysis of its performance. This work demonstrates that such a symmetric geometry of multiple subchains sometimes induces a forward kinematic singularity which degrades the overall kinematic performance of PMs within the desired workspace and claims that an asymmetric attachment of those subchains on a moving platform can effectively resolve such a singularity problem. A 4-Degree-of-Freedom (DOF) PM exhibiting Schönflies motions is examined as an example device. First, its mobility analysis and kinematic modeling via screw theory are conducted. Then a singularity analysis based on Grassmann line geometric conditions is carried out, and the forward kinematic singularities of the mechanism are identified and verified by simulations. Based on these analysis and simulations, a forward kinematic singularity-free design is suggested. To show the high potential of the device in practical applications, its output stiffness and dynamic motion capability are examined. Then a prototype is built and its motions capability is verified through experiments.
Article PDF
Similar content being viewed by others
References
R. S. Ball, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, 1900.
J. M. Herve, “The mathematical group structure of the set of displacements,” Mech. Mach. Theory, vol. 29, no. 1, pp. 73–81, 1994.
Y. Fang and L.-W. Tsai, “Structure synthesis of a class of 4-DOF and 5-DOF parallel manipulators with identical limb structures,” International Journal of Robotics Research, vol. 21, no. 9, pp. 799–810, September 2002.
Z. Huang and Q. Li, “Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method,” International Journal of Robotics Research, vol. 22, no. 1, pp. 59–79, January 2003.
X. Kong and C. M. Gosselin, “Type synthesis of 3T1R 4-DOF parallel manipulators based on screw theory,” IEEE Trans. on Robotics and Automation, vol. 20, no. 2, pp. 181–190, April 2004.
X. Kong and C. Gosselin, “Type synthesis of 4-DOF SP-equivalent parallel manipulators: a virtual chain approach,” Mechanism and Machine Theory, vol. 41, no. 11, pp. 1306–1319, 2006.
Q. Li, Z. Huang, and J. M. Herve, “Type synthesis of 3T2R 5-DOF parallel mechanisms using the lie group of displacements,” IEEE Trans. on Robotics and Automation, vol. 20, no. 2, pp. 173–180, 2004.
C. Gosselin, M. T. Masouleh, V. Duchaine, P. L. Richard, S. Foucault, and X. Kong. “Parallel mechanisms of the multipteron family: kinematic architectures and benchmarking,” Proc. IEEE Int. Conf. on Robot. and Auto., pp. 555–560, 2007.
R. Clavel, “Delta, a fast robot with parallel geometry,” Proc. of the 18th Int’l Symp. on Industrial Robots, Lausanne: IFS Publications, pp. 91–100, 1988.
H. B. Choi, O. Company, F. Pierrot, A. Konno, T. Shibukawa, and M. Uchiyama, “Design and control of a novel 4-DOF parallel robot H4,” Proc. IEEE Int. Conf. Robot. Auto., pp. 1185–1190, 2003.
S. Krut, O. Company, M. Benoit, H. Ota, and F. Pierrot, “I4: new parallel mechanism for Scara motions,” Proc. IEEE Int. Conf. Robot. Auto., pp. 1875–1880, 2003.
O. Company, F. Marquet, and F. Pierrot, “A new high-speed 4-DOF parallel robot synthesis and modeling issues,” IEEE Trans. on Robotics and Automation, vol. 19, no. 3, pp. 411–420, June 2003.
S. Krut, V. Nabat, O. Company, and F. Pierrot, “A high-speed parallel robot for Scara motions,” Proc. IEEE Int. Conf. Robot. Auto., pp. 4109–4115, 2004.
S. Krut and F. Pierrot, “Internal singularity analysis of a class of lower mobility parallel manipulators with articulated traveling plate,” IEEE Trans. on Robotics, vol. 22, no. 1, pp. 1–11, February 2006.
F. Pierrot, V. Nabat, O. Company, S. Krut, and P. Poignet, “Optimal design of a 4-DOF parallel manipulator: from academia to industry,” IEEE Trans. on Robotics, vol. 25, no. 2, pp. 213–224, 2009.
A. Cammarata, J. Angeles, and R. Sinatra, “Kinetostatic and Inertial Conditioning of the McGill Schönflies-Motion Generator,” Advances in Mechanical Engin., Hindawi Publishing Corporation, vol. 2010, article no. ID. 186203.
P. L. Richard, C. M. Gosselin, and X. Kong, “Kinematic analysis and prototyping of a partially decoupled 4-DOF 3T1R parallel manipulator,” ASME Journal of Mechanical Design, vol. 129, pp. 611–616, 2007.
O. Salgado, O. Altuzarra, V. Petuya, and A. Hernandez, “Synthesis and design of a novel 3T1R fully-parallel manipulator,” ASME Journal of Mechanical Design, vol. 130, no. 4, doi:10.1115/1.2839005, 2008.
S. M. Kim, W. K. Kim, and B.-J. Yi, “Kinematic analysis and optimal design of a 3T1R type parallel mechanism,” Proc. IEEE Int. Conf. on Robotics and Automation, pp. 2199–2204, 2009.
Q. C. Li and Z. Huang, “Mobility analysis of a novel 3-5R parallel mechanism family,” Trans. of the ASME Mechanical Design, vol. 126, pp. 79–82, 2004.
J. S. Dai, Z. Huang, and H. Lipkin, “Mobility of over-constrained parallel mechanisms,” Trans. of the ASME Journal of Mechanical Design, vol. 128, pp. 220–229, 2006.
C. Gosselin and J. Angeles, “Singularity analysis of closed-loop kinematics chains,” IEEE Trans. on Robotics and Automation, vol. 6, no. 3, pp. 281–290, 1991.
L. W. Tsai, Robot Analysis, John Wiley & Sons, 1999.
J. P. Merlet, Parallel Robots, Springer, 2006.
F. Hao and J. M. McCarthy, “Conditions for linebased singularities in spatial platform manipulators,” Journal of Robotic Systems, vol. 15, no. 1, pp. 43–55, 1988.
B. Monsarrat and C. M. Gosselin, “Singularity analysis of a three-leg six-degree-of-freedom parallel platform mechanism based on Grassmann line geometry,” International Journal of Robotics Research, vol. 20, no. 4, pp. 312–328, 2001.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editorial Board member Yangmin Li under the direction of Editor Hyouk Ryeol Choi.
This research was in part supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2011-0010708), and in part supported by the Converging Research Center Program funded by the Ministry of Education, Science and Technology (2012K001328). Also, this work is in part supported by GRRC program of Gyeonggi Province (GRRC HANYANG 2010-A02), and in part financially supported by the Ministry of Knowledge Economy (MKE) and Korea Institute for Advancement in Technology (KIAT) through the Workforce Development Program in Strategic Technology.
Sung Mok Kim received his M.S. degree in Control and Instrumentation Engineering from Korea University at SeoJong in 2011. He is currently a graduate student at department of Control and Instrumentation Engineering, Korea University. His research interests includes robot kinematics, singularity analysis, parallel robot design, and medical robot.
Byung-Ju Yi received his Ph.D. degree in Mechanical Engineering from The University of Texas at Austin in 1991. He is currently a professor in the Department of Electronic Systems Engineering at Hanyang University. His research interests include robot kinematics, parallel mechanism, medical robot, pipeline robot, and biomimetic robot design.
Wheekuk Kim received his Ph.D. degree in Mechanical Engineering from The University of Texas at Austin, in 1990. Since 1991, he has been working as a professor at the Department of Control and Instrumentation Engineering, Korea University at Seojong. His current research interests include parallel robot design, screw theory, singularity analysis, parallel robot synthesis, robot kinematics, medical robot, mobile robot, haptics, etc.
Rights and permissions
About this article
Cite this article
Kim, S.M., Yi, BJ. & Kim, W. Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains. Int. J. Control Autom. Syst. 11, 116–126 (2013). https://doi.org/10.1007/s12555-012-0005-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-012-0005-5