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Advances in Reconfigurable Mechanisms and Robots I pp 355–369Cite as

A Study of the Instantaneous Kinematics of the 5-RSP Parallel Mechanism Using Screw Theory

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Abstract

This paper presents a detailed study of the instantaneous kinematics of the 5-R SP parallel mechanism with centralized motion. The study uses screw theory to investigate the mobility and the singular configurations of the mechanism. The constraint-screw set of the platform is obtained from an analysis of the motion-screw sets comprised by each kinematic chain. The analysis shows that the platform has a screw motion, that is, a one degree-of-freedom motion consisting of a rotation and a translation about an invariant axis. The motion-screw sets are also used to obtain the Jacobian matrix of the mechanism which provides closed-form solutions for the inverse and forward instantaneous kinematic problems. This matrix also provides insight into the singular configurations by investigating the constraint-screws and the motion-screws of the platform in these configurations. Finally, two numerical examples and a motion simulation of the mechanism are presented to illustrate the significance of the analytical results.

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References

  1. Ball RS (1900) A treatise on the theory of screws. Cambridge University Press, Cambridge

    Google Scholar 

  2. Von Mises R (1924) Motor calculus—a new theoretical device for mechanics. In Baker EJ, Wohlhart K (eds) University of Technology Graz, Austria

    Google Scholar 

  3. Brand L (1957) Vector and tensor analysis, sixth printing. Wiley, New York

    Google Scholar 

  4. Dimentberg FM (1965) The Screw Calculus and its Application in Mechanics. Izdat, Nauka, Moscow

    Google Scholar 

  5. Hunt KH (1978) Kinematic geometry of mechanisms. Oxford University Press, New York

    MATH  Google Scholar 

  6. Mohamed MG, Duffy J (1985) A direct determination of the instantaneous kinematics of fully parallel robot manipulators. J Mech Transm-T ASME 107(2):226–229

    Article  Google Scholar 

  7. Joshi SA, Tsai LW (2002) Jacobian analysis of limited-DOF parallel manipulators. J Mech Des-T ASME 124(2):254–258

    Article  Google Scholar 

  8. Tsai LW (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley, New York

    Google Scholar 

  9. Davidson JK, Hunt KH (2004) Robots and screw theory: applications of kinematics and statics to robotics. Oxford University Press Inc., New York

    MATH  Google Scholar 

  10. Shai O, Pennock GR (2006) A study of the duality between planar kinematics and statics. J Mech Des-T ASME 128(3):587–598

    Article  Google Scholar 

  11. Shai O, Pennock GR (2006) Extension of graph theory to the duality between static systems and mechanisms. J Mech Des-T ASME 128(1):179–191

    Article  Google Scholar 

  12. Huang Z, Li QC (2002) General methodology for type synthesis of lower mobility symmetrical parallel manipulators and several novel manipulators. Int J Robot Res 21(2):131–146

    Article  Google Scholar 

  13. Dai JS, Huang Z, Lipkin H (2006) Mobility of overconstrained parallel mechanisms. J Mech Des-T ASME 128(1):220–229

    Article  Google Scholar 

  14. Huang Z, Wang J, Fang YF (2002) Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators. Mech Mach Theory 37(2):229–240

    Article  MATH  Google Scholar 

  15. Gosselin CM, Angeles J (1990) Singularity analysis of closed-loop kinematic chains. IEEE T Robotic Autom 6(3):281–290

    Article  Google Scholar 

  16. Zhao JS, Feng ZJ, Khou K, Dong JX (2005) Analysis of the singularity of spatial parallel manipulator with terminal constraints. Mech Mach Theory 40(3):275–284

    Article  MathSciNet  MATH  Google Scholar 

  17. Rodriguez Leal E, Dai JS, Pennock GR (2011) Kinematic analysis of a 5-R SP parallel mechanism with centralized motion. Meccanica 46(1):221–237

    Google Scholar 

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Acknowledgments

This work was supported by the Grants of the Mexican Science and Technology Council (CONACYT) for a PhD degree program at King’s College London, University of London, England.

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Authors and Affiliations

  1. Tecnológico de Monterrey, 2501, Garza Sada, Mexico

    Ernesto Rodriguez-Leal

  2. King’s College London, Strand, London, WC2R2LS, UK

    Jian S. Dai

  3. Purdue University, West Lafayette, IN, 47907, USA

    Gordon R. Pennock

Authors
  1. Ernesto Rodriguez-Leal
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  2. Jian S. Dai
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  3. Gordon R. Pennock
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Corresponding author

Correspondence to Ernesto Rodriguez-Leal .

Editor information

Editors and Affiliations

  1. King's College London, Western Road 17, Sutton, SM1 2TE, United Kingdom

    Jian S Dai

  2. University of Genova, Via Opera Pia 15A, Genova, Italy

    Matteo Zoppi

  3. , School of Engineering and, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom

    Xianwen Kong

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© 2012 Springer-Verlag London

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Rodriguez-Leal, E., Dai, J.S., Pennock, G.R. (2012). A Study of the Instantaneous Kinematics of the 5-RSP Parallel Mechanism Using Screw Theory. In: Dai, J., Zoppi, M., Kong, X. (eds) Advances in Reconfigurable Mechanisms and Robots I. Springer, London. https://doi.org/10.1007/978-1-4471-4141-9_32

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  • DOI: https://doi.org/10.1007/978-1-4471-4141-9_32

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4140-2

  • Online ISBN: 978-1-4471-4141-9

  • eBook Packages: EngineeringEngineering (R0)

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