“Stiffness Analysis and Optimization of a Co-axial Spherical Parallel Manipulator”

Authors: Guanglei Wu,
Affiliation: Aalborg University
Reference: 2014, Vol 35, No 1, pp. 21-30.

Keywords: Spherical parallel manipulator, virtual spring, Cartesian stiffness matrix, singular value decomposition, stiffness optimization

Abstract: This paper investigates the stiffness characteristics of spherical parallel manipulators. By virtue of singular value decomposition, the 6x6 dimensionally inhomogeneous Cartesian stiffness matrix is transformed into two homogeneous ones, i.e., the rotational and translational stiffness matrices. The decomposed singular values and the corresponding vectors indicate the directions of high/weak stiffness and the stiffness isotropy for the manipulator at a given configuration. Two indices, one for rotation and the other for translation, are introduced to optimize the manipulator stiffness and to map the stiffness isocontours over the workspace to show an image of the overall stiffness.

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[3] Gang Xiong, Ye Ding and LiMin Zhu (2019), doi:10.1016/j.rcim.2018.07.001
[4] Henrique Simas and Raffaele Di Gregorio (2018), doi:10.1017/S0263574718000899
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[1] Angeles, J. (2010). On the nature of the Cartesian stiffness matrix, Ingenieria Mecanica. 3(5):163--170.
[2] Asada, H. and Granito, J. (1985). Kinematic and static characterization of wrist joints and their optimal design, In IEEE International Conference on Robotics and Automation, volume2. pages 244--250. doi:10.1109/ROBOT.1985.1087324
[3] Bai, S. (2010). Optimum design of spherical parallel manipulators for a prescribed workspace, Mechanism and Machine Theory. 45(2):200--211. doi:10.1016/j.mechmachtheory.2009.06.007
[4] Bai, S., Hansen, M.R., and Andersen, T.O. (2009). Modelling of a special class of spherical parallel manipulators with Euler parameters, Robotica. 27(2):161--170. doi:10.1017/S0263574708004402
[5] Bonev, I. (2008). Direct kinematics of zero-torsion parallel mechanisms, In IEEE International Conference on Robotics and Automation. Pasadena, California, USA, pages 3851--3856. doi:10.1109/ROBOT.2008.4543802
[6] Bonev, I.A., Chablat, D., and Wenger, P. (2006). Working and assembly modes of the Agile Eye, In International Conference on Robotics and Automation. pages 2317--2322. doi:10.1109/ROBOT.2006.1642048
[7] Bonev, I.A. and Gosselin, C.M. (2005). Singularity loci of spherical parallel mechanisms, In IEEE International Conference on Robotics and Automation. pages 2957--2962. doi:10.1109/ROBOT.2005.1570563
[8] Bulca, F., Angeles, J., and Zsombor-Murray, P.J. (1999). On the workspace determination of spherical serial and platform mechanisms, Mechanism and Machine Theory. 34(3):497--512. doi:10.1016/S0094-114X(98)00019-6
[9] Ciblak, N. and Lipkin, H. (1999). Synthesis of Cartesian stiffness for robotic applications, In IEEE International Conference on Robotics and Automation, volume3. pages 2147--2152. doi:10.1109/ROBOT.1999.770424
[10] Dai, J. and Ding, X. (2006). Compliance analysis of a three-legged rigidly-connected platform device, Journal of Mechanical Design. 128. doi:10.1115/1.2202141
[11] Ding, X. and Selig, J.M. (2004). On the compliance of coiled springs, International Journal of Mechanical Sciences. 46(5):703--727. doi:10.1016/j.ijmecsci.2004.05.009
[12] El-Khasawneh, B.S. and Ferreira, P.M. (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
[13] Enferadi, J. and Tootoonchi, A.A. (2011). Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator, Robotica. 29:193--209. doi:10.1017/S0263574710000032
[14] Gosselin, C. (1990). Stiffness mapping for parallel manipulators, IEEE Transactions on Robotics and Automation. 6(3):377--382. doi:10.1109/70.56657
[15] Gosselin, C.M. and Lavoie, E. (1993). On the kinematic design of spherical three-degree-of-freedom parallel manipulators, The International Journal of Robotics Research. 12(4):394--402. doi:10.1177/027836499301200406
[16] Kong, X. and Gosselin, C.M. (2004). Type synthesis of three-degree-of-freedom spherical parallel manipulators, The International Journal of Robotics Research. 23(3):237--245. doi:10.1177/0278364904041562
[17] Koevecses, J. and Ebrahimi, S. (2009). Parameter analysis and normalization for the dynamics and design of multibody systems, Journal of Computational and Nonlinear Dynamics. 4(3):031008(1--10). doi:10.1115/1.2202141
[18] Liu, X.J., Jin, Z.L., and Gao, F. (2000). Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices, Mechanism and Machine Theory. 35(9):1257--1267. doi:10.1016/S0094-114X(99)00072-5
[19] Pashkevich, A., Chablat, D., and Wenger, P. (2009). Stiffness analysis of overconstrained parallel manipulators, Mechanism and Machine Theory. 44(5):966--982. doi:10.1016/j.mechmachtheory.2008.05.017
[20] Taghvaeipour, A., Angeles, J., and Lessard, L. (2012). On the elastostatic analysis of mechanical systems, Mechanism and Machine Theory. 58:202--216. doi:10.1016/j.mechmachtheory.2012.07.011
[21] Wu, G. (2012). Multiobjective optimum design of a 3-RRR spherical parallel manipulator with kinematic and dynamic dexterities, Modeling, Identification and Control. 33(3):111--122. doi:10.4173/mic.2012.3.3
[22] Wu, G., Bai, S., and Kepler, J. (2014). Mobile platform center shift in spherical parallel manipulators with flexible limbs, Mechanism and Machine Theory. 75:12--26. doi:10.1016/j.mechmachtheory.2014.01.001

  title={{Stiffness Analysis and Optimization of a Co-axial Spherical Parallel Manipulator}},
  author={Wu, Guanglei},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}