Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- Forward kinematic singularity avoiding design of a Schönflies motion generator by asymmetric attachment of subchains
International Journal of Control, Automation and Systems
Volume 11, Issue 1 , pp 116-126
- Cover Date
- Print ISSN
- Online ISSN
- Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers
- Additional Links
- Forward kinematic singularity
- kinematic design
- mobility analysis
- parallel mechanism
- Schönflies motion
- singularity analysis
- Industry Sectors