184
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

An analytical approach for positioning error and mode shape analysis of n – legged parallel manipulator

, &
Pages 677-691 | Received 10 Nov 2016, Accepted 31 Aug 2017, Published online: 18 Sep 2017

References

  • Afzali-Far, B., P. Lidström, and K. Nilsson. 2014. “Parametric Damped Vibrations of Gough–Stewart Platforms for Symmetric Configurations.” Mechanism and Machine Theory 80: 52–69. doi:10.1016/j.mechmachtheory.2014.04.018.
  • Ahmad, A., K. Andersson, U. Sellgren, and S. Khan. 2014. “A Stiffness Modeling Methodology for Simulation-Driven Design of Haptic Devices.” Engineering with Computers 30 (1): 125–141. doi:10.1007/s00366-012-0296-4.
  • Beh-Horin, P., M. Shoham, and G. Grossman. 2000. “A Parallel Six Degrees-of-Freedom Inflatable Robot.” Proceedings of 26th Biennal Mechanism and Robotics Conference, September 2000, Baltimore, 435-442.
  • Butt, S. U., J.-F. Antoine, and P. Martin. 2013. “A Kinematic Approach for 6-DOF Part Positioning.” In Smart Product Engineering, 147–157. Springer. http://link.springer.com/chapter/10.1007/978-3-642-30817-8_15.
  • Butt, S. U., S. Ullah, J.-F. Antoine, and P. Martin. 2012. “An Analytical Model for Repositioning of 6 DOF Fixturing System.” Mechanics & Industry 13 (3): 205–217. doi:10.1051/meca/2012016.
  • Carbone, G. 2011. “Stiffness Analysis and Experimental Validation of Robotic Systems.” Frontiers of Mechanical Engineering 6 (2): 182–196.
  • Clinton, C. M., G. Zhang, and A. J. Wavering. 1997. “Stiffness Modeling of a Stewart Platform Based Milling Machine.” http://drum.lib.umd.edu/handle/1903/5859.
  • Dasgupta, B., and T. S. Mruthyunjaya. 1998a. “A Newton-Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator.” Mechanism and Machine Theory 33 (8): 1135–1152. doi:10.1016/S0094-114X(97)00118-3.
  • Dasgupta, B., and T. S. Mruthyunjaya. 1998b. “Closed-Form Dynamic Equations of the General Stewart Platform through the Newton–Euler Approach.” Mechanism and Machine Theory 33 (7): 993–1012. doi:10.1016/S0094-114X(97)00087-6.
  • Dasgupta, B., and T. S. Mruthyunjaya. 2000. “The Stewart Platform Manipulator: A Review.” Mechanism and Machine Theory 35 (1): 15–40. doi:10.1016/S0094-114X(99)00006-3.
  • Deblaise, D., X. Hernot, and P. Maurine. 2006. “A Systematic Analytical Method for PKM Stiffness Matrix Calculation.” In Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006, 4213–4219. IEEE. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1642350.
  • Dukkipati, V. R. A. O., and J. Srinivas. 2012. Textbook of Mechanical Vibrations. PHI Learning Pvt. https://books.google.com.pk/books?hl=en‎&id=JQkDEYvAGDAC&oi=fnd&pg=PR2&dq=textbook+of+mechanical+vibrations+rao+v+dukkipati+second+edition&ots=J38yUlICjm&sig=3p6ELpqeZx2qVIdM8KF2TPSgx08.
  • El-Khasawneh, B. S., and P. M. Ferreira. 1999. “Computation of Stiffness and Stiffness Bounds for Parallel Link Manipulators.” International Journal of Machine Tools and Manufacture 39 (2): 321–342. doi:10.1016/S0890-6955(98)00039-X.
  • Fichter, E. F. 1986. “A Stewart Platform-Based Manipulator: General Theory and Practical Construction.” The International Journal of Robotics Research 5 (2): 157–182. doi:10.1177/027836498600500216.
  • Gexue, R., L. Qiuhai, H. Ning, N. Rendong, and B. Peng. 2004. “On Vibration Control with Stewart Parallel Mechanism.” Mechatronics 14 (1): 1–13. doi:10.1016/S0957-4158(02)00092-2.
  • Gosselin, C. 1990. “Stiffness Mapping for Parallel Manipulators.” IEEE Transactions on Robotics and Automation 6 (3): 377–382. doi:10.1109/70.56657.
  • Gosselin, C. M., and D. Zhang. 2002. “Stiffness Analysis of Parallel Mechanisms Using a Lumped Model.” International Journal of Robotics and Automation 17 (1): 17–27.
  • Gough, V. E., and S. G. Whitehall. 1962. “Universal Tyre Test Machine.” In Proceedings of the FISITA 9th International Technical Congress, 117–137.
  • H-840 6-Axis Hexapod. 2016. Accessed March 14. http://www.physikinstrumente.com/product-detail-page/h-840-700810.html.
  • Hanieh, A. A. 2003. “Active Isolation and Damping of Vibrations via Stewart Platform.” Active Structure Laboratory, ULB, PH. D. Thesis. http://www.ulb.ac.be/scmero/documents/these/Hanieh03.pdf.
  • Hibbeler, R. C., and T. Kiang. 2015. Structural Analysis. Prentice Hall. https://www.uvic.ca/engineering/civil/assets/docs/3A_outlines_Spring_2016/CIVE350-201601.pdf.
  • Horin, B. 1999. “P., 1999,‘Analysis and Synthesis of an Inflatable Parallel Robot’.” M. Sc. Thesis, Technion, Haifa.
  • Hu, X., R. Wang, W. Fangfang, D. Jin, X. Jia, J. Zhang, F. Cai, and S. Zheng. 2007. “Finite Element Analysis of a Six-Component Force Sensor for the Trans-Femoral Prosthesis.” In Digital Human Modeling, 633–639. Springer. http://link.springer.com/chapter/10.1007/978-3-540-73321-8_72.
  • Huang, T., X. Zhao, and D. J. Whitehouse. 2002. “Stiffness Estimation of a Tripod-Based Parallel Kinematic Machine.” IEEE Transactions on Robotics and Automation 18 (1): 50–58. doi:10.1109/70.988974.
  • Klimchik, A. 2011. “Enhanced Stiffness Modeling of Serial and Parallel Manipulators for Robotic-Based Processing of High Performance Materials.” Ecole Centrale de Nantes (ECN)(ECN)(ECN)(ECN); Ecole des Mines de Nantes. https://tel.archives-ouvertes.fr/tel-00711978/.
  • Lalanne, M., P. Berthier, and J. Der Hagopian. 1986. Mécanique Des Vibrations Linéaires (Avec Exercices Corrigés et Programmes de Calcul). Masson. http://infoscience.epfl.ch/record/60508.
  • Mahboubkhah, M., M. J. Nategh, and S. Esmaeilzade Khadem. 2008. “Vibration Analysis of Machine Tool’s Hexapod Table.” The International Journal of Advanced Manufacturing Technology 38 (11–12): 1236–1243. doi:10.1007/s00170-007-1183-9.
  • Majou, F. 2004. “Kinetostatic Analysis of Translational Parallel Kinematic Machines.” Ph. D. thesis, Universite Laval, Quebec, Canada and Ecole Centrale Nantes, France.
  • Pang, H., and M. Shahinpoor. 1994. “Inverse Dynamics of a Parallel Manipulator.” Journal of Robotic Systems 11 (8): 693–702. doi:10.1002/rob.v11:8.
  • Pashkevich, A., D. Chablat, and P. Wenger. 2009. “Stiffness Analysis of Overconstrained Parallel Manipulators.” Mechanism and Machine Theory 44 (5): 966–982. doi:10.1016/j.mechmachtheory.2008.05.017.
  • Pigoski, T., M. Griffis, and J. Duffy. 1998. “Stiffness Mappings Employing Different Frames of Reference.” Mechanism and Machine Theory 33 (6): 825–838. doi:10.1016/S0094-114X(97)00083-9.
  • Piras, G. W., L. Cleghorn, and J. K. Mills. 2005. “Dynamic Finite-Element Analysis of a Planar High-Speed, High-Precision Parallel Manipulator with Flexible Links.” Mechanism and Machine Theory 40 (7): 849–862. doi:10.1016/j.mechmachtheory.2004.12.007.
  • Portman, V. T. 2000. “Stiffness and Damping in Mechanical Design.” Precision Engineering 3(24): 274–275. doi: 10.1016/s0141-6359(00)00034-9
  • Ruggiu, M. 2012. “On the Lagrangian and Cartesian Stiffness Matrices of Parallel Mechanisms with Elastic Joints.” Advanced Robotics 26 (1–2): 137–153. doi:10.1163/016918611X607680.
  • Stewart, D. 1965. “A Platform with Six Degrees of Freedom.” Proceedings of the Institution of Mechanical Engineers 180 (1): 371–386. doi:10.1243/PIME_PROC_1965_180_029_02.
  • Stoughton, R. S., and T. Arai. 1993. “A Modified Stewart Platform Manipulator with Improved Dexterity.” IEEE Transactions on Robotics and Automation 9 (2): 166–173. doi:10.1109/70.238280.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.