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Singularity Analysis of a 3DOF Parallel Manipulator Using Infinite Constraint Plane Method

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Abstract

In this article a novel geometrical method is presented to obtain singular points of a parallel manipulator. First, the constrained plain method (CPM) and some of its application in parallel mechanism is introduced. Given the definition of constraint plane (CP) and infinite constraint plane (ICP) the dependency conditions of constraints is achieved with the use of a new theorem based on the Ceva geometrical theorem. Another theorem is used to achieve the direction of angular velocity of a body having three ICPs. Finally, as an example, using these two theorems, singularities of the 3UPS_PU mechanism are obtained. This method is completely geometrical, involving no complex or massive calculations and yields the answer quickly. In the previous methods based on the Grassmann geometry, the mechanism needs to be statically analyzed at first, so that the Inverse Jacobian matrix is achieved, and then the Plucker-vector is derived. It usually needs exhaustive search of the workspace using an accurate analytical model of the mechanism kinematics and may lead to plenty of conditions remained to be pondered in order to obtain the singularity conditions.

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References

  1. Gosselin, C., Angeles, J.: Singularity analysis of closed-loop kinematic chains. IEEE J. Robot. Autom. 6(3), 281–290 (1990)

    Article  Google Scholar 

  2. Zlatanov, D., Fenton, R.G., Benhabib, B.: A unifying framework for classification and interpretation of mechanism singularities. J. Mech. Des. 117(4), 566–572 (1995)

    Article  Google Scholar 

  3. Sefrioui, J., Gosselin, C.: Singularity analysis and representation of planar parallel manipulator. Robot. Auton. Syst. 10(4), 209–224 (1993)

    Article  Google Scholar 

  4. Sefrioui, J., Gosselin, C.M.: On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators. Mech. Mach. Theory 30(4), 533–551 (1995)

    Article  Google Scholar 

  5. Park, F.C., Kim, J.W.: Singularity analysis of closed kinematic chains. ASME J. Mech. Des. 121(1), 32–38 (1999)

    Article  Google Scholar 

  6. Gosselin, C., Wang, J.: Singularity loci of planar parallel manipulators with revolute actuators. Robot. Auton. Syst. 21, 377–398 (1997)

    Article  Google Scholar 

  7. Sefrioui, J., Gosselin, C.M.: Singularity analysis and representation of planar parallel manipulators. Robot. Auton. Syst. 10, 209–224 (1993)

    Article  Google Scholar 

  8. Takeda, Y., Funabashi, H.: Kinematic and static characteristics of in-parallel actuated manipulators at singular points and in their neighborhood. JSME Int. J. Ser. C 39(1), 85–93 (1996)

    Google Scholar 

  9. Bandyopadhay, S., Ghosal, A.: Analysis of configuration space singularities of closed-loop mechanisms and parallel mechanisms. Mech. Mach. Theory 39, 519–554 (2004)

    Article  MathSciNet  Google Scholar 

  10. Agrawal, S.K., Roth, B.: Statics of in-parallel manipulator systems. ASME J. Mech. Des. 114, 564–568 (1992)

    Article  Google Scholar 

  11. Dasgupta, B., Mruthyunjaya, T.S.: Force redundancy in parallel manipulators: theoretical and practical issues. Mech. Mach. Theory 33(6), 727–742 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Merlet, J.P.: Singularity configurations of parallel manipulators and Grassman geometry. Int. J. Rob. Res. 10(2), 123–134 (1991)

    Article  Google Scholar 

  13. Merlet, J.P.: Parallel manipulators, part 2: singular configurations and Grassman geometry. INRIA Report no. 791 (1988)

  14. Basu, D., Ghosal, A.: Singularity analysis of platform-type multi-loop spatial mechanisms. Mech. Mach. Theory 32(3), 375–389 (1997)

    Article  Google Scholar 

  15. Ghosal, A., Ravani, B.: Differential geometric analysis of singularities of point trajectories of serial and parallel manipulators. ASME J. Mech. Des. 123, 80–89 (2001)

    Article  Google Scholar 

  16. Huang, Z., Zhao, Y.S., Wang, J., Yu, J.J.: Kinematics principle and geometrical condition of general-linear-complex special configuration of parallel manipulators. Mech. Mach. Theory 34(8), 1171–1186 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  17. O’Brien, J., Wen, J.T.: Singularities in three-legged platform-type parallel mechanisms. IEEE Trans. Robot. Autom. 19(4), 720–725 (2003) Aug

    Article  Google Scholar 

  18. Liu, X.-J., Wang, J., Pritschow, G.: Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms. Mech. Mach. Theory 41(2), 145–169 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pendar, H., Mahnama, M., Zohhor, H.: A novel method on singularity analysis in parallel manipulators. Submitted to the 8th biennial ASME Conference on Engineering Systems Design and Analysis, ESDA (2006)

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Authors and Affiliations

  1. Tehran, Islamic Republic of Iran

    Hodjat Pendar, Hajir Roozbehani, Hoda Sadeghian & Hassan Zohoor

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  1. Hodjat Pendar
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  2. Hajir Roozbehani
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  3. Hoda Sadeghian
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  4. Hassan Zohoor
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Correspondence to Hodjat Pendar.

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Pendar, H., Roozbehani, H., Sadeghian, H. et al. Singularity Analysis of a 3DOF Parallel Manipulator Using Infinite Constraint Plane Method. J Intell Robot Syst 53, 21–34 (2008). https://doi.org/10.1007/s10846-008-9216-7

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  • DOI: https://doi.org/10.1007/s10846-008-9216-7

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