Similar articles

Abstract: The singular points of a 6-SPS Stewart platform are distributed on the multi-dimensional singularity hypersurface in the task-space, which divides the workspace of the manipulator into several singularity-free regions. Because of the motion uncertainty at singular points, while the manipulator traverses this kind of hypersurface from one singularity-free region to another, its motion cannot be predetermined. In this paper, a detailed approach for the manipulator to traverse the singularity hypersurface with its non-persistent configuration is presented. First, the singular point transfer disturbance and the pose disturbance, which make the perturbed singular point transfer horizontally and vertically, respectively, are constructed. Through applying these disturbances into the input parameters within the maximum loss control domain, the perturbed persistent configuration is transformed into its corresponding non-persistent one. Under the action of the disturbances, the manipulator can traverse the singularity hypersurface from one singularity-free region to another with a desired configuration.

[1] Bandyopadhyay, S., Ashitava, G., 2006. Geometric characterization and parametric representation of the singularity manifold of a 6-6 Stewart platform manipulator. Mechanism and Machine Theory, 41(11):1377-1400.

[2] Bandyopadhyay, S., Ghosal, A., 2004. Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators. Mechanism and Machine Theory, 39(5):519-544.

[3] Chen, Y.S., Leung, A.Y.T., 1998. Bifurcation and Chaos in Engineering. Springer-Verlag, London, p.112-127.

[4] Choudhury, P., Ghosal, A., 2000. Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms. Mechanism and Machine Theory, 35(10):1455-1479.

[5] Dasgupta, B., Mruthyunjaya, T.S., 2000. The Stewart platform manipulator: a review. Mechanism and Machine Theory, 35(1):15-40.

[6] Dash, A.K., Chen, I.M., Yao, S.H., Yang, G.L., 2003. Singularity-free Path Planning of Parallel Manipulators Using Clustering Algorithm and Line Geometry. IEEE International Conference on Robotics and Automation, ICRA, Taipei, Taiwan, September 14-19.

[7] Di Gregorio, R., 2002. Singularity-locus expression of a class of parallel mechanisms. Robotica, 20(3):323-328.

[8] Gosselin, C., Angeles, J., 1990. Singularity analysis of closed loop kinematic chains. IEEE Transactions on Robotics and Automation, 6(3):281-290.

[9] Huang, Z., Cao, Y., 2005. Property identification of the singularity loci of a class of Gough-Stewart manipulator. International Journal of Robotics Research, 24(8):675-685.

[10] Kim, D., Chung, W., 1999. Analytic singularity equation and analysis of six-DOF parallel manipulators using local structurization method. IEEE Transactions on Robotics and Automation, 15(4):612-622.

[11] Kim, W.H., Lee, H.J., Suh, H., Yi, B.J., 2005. Comparative study and experimental verification of singular-free algorithms for a 6 DoF parallel haptic device. Mechatronics, 15(4):403-422.

[12] Li, H.D., Gosselin, C.M., Richard, M.J., St-Onge, B.M., 2006. Analytic form of the six-dimensional singularity locus of the general Gough-Stewart platform. Journal of Mechanical Design, 128(1):279-287.

[13] Li, H.D., Gosselin, C.M., Richard, M.J., 2007. Determination of the maximal singularity-free zones in the six-dimensional workspace of the general Gough-Stewart platform. Mechanism and Machine Theory, 42(4):497-511.

[14] Sen, S., Dasgupta, B., Mallik, K.A., 2003. Variational approach for singularity-free path-planning of parallel manipulators. Mechanism and Machine Theory, 38(11):1165-1183.

[15] St-Onge, B.M., Gosselin, C., 1996. Singularity analysis and representation of spatial six-DOF parallel manipulators. Recent Advances in Robot Kinematics, 2(3):389-398.

[16] St-Onge, B.M., Gosselin, C., 2000. Singularity analysis and representation of the general Gough-Stewart platform. International Journal of Robotics Research, 19(3):271-288.

[17] Wang, J., Gosselin, M.C., 2004. Kinematic analysis and design of kinematically redundant parallel mechanisms. Journal of Mechanical Design, 126(1):109-118.

[18] Wang, Y.X., Li, Y.T., 2008. Disturbed configuration bifurcation characteristics of Gough-Stewart parallel manipulators at singular points. Journal of Mechanical Design, 130(2):1-9.

[19] Wang, Y.X., Liu, X.S., 2004. Study on the configuration bifurcation characteristics of the five-bar linkage. Chinese Journal of Mechanical Engineering, 40(11):17-20.

[20] Wang, Y.X., Wang, Y.M., 2005. Configuration bifurcations analysis of six degree-of-freedom symmetrical Stewart parallel mechanisms. Journal of Mechanical Design, 127(1):70-77.

[21] Wang, Y.X., Wang, Y.M., Liu, X.S., 2003. Bifurcation property and persistence of configurations for parallel mechanisms. Science in China (Series E), 33(1):1-9.

[22] Wang, Y.X., Wang, Y.M, Chen, Y.S., Huang, Z., 2005. Research on loss of controllability of Stewart parallel mechanisms at bifurcation points. Chinese Journal of Mechanical Engineering, 41(7):40-49.

[23] Wolf, A., Shoham, M., 2003. Investigation of parallel manipulators using linear complex approximation. Journal of Mechanical Design, 125(3):564-572.

[24] Wu, W., 1993. The Expending Method for Solving Nonlinear Bifurcation Problem. Science Publish House, Beijing, p.41-56.