Skip to main content

Workspace Analysis of a Reconfigurable Mechanism Generated from the Network of Bennett Linkages

  • Conference paper
  • First Online:
Advances in Reconfigurable Mechanisms and Robots II

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 36))

Abstract

In this paper, a workspace triangle is introduced to evaluate the workspace of a reconfigurable mechanism generated from the network of Bennett linkages. Three evaluation indexes of workspace including movement locus of the joint, surface swept by the link and helical tube enveloped by the workspace triangle have been discussed. The comparison between the workspace of the reconfigurable mechanism and the sum of five resultant 5 R /6 R linkages including generalized Goldberg 5 R linkage, generalized variant of the L -shape Goldberg 6 R linkage, Waldron’s hybrid 6 R linkage, isomerized generalized L -shape Goldberg 6 R linkage and generalized Wohlhart’s double-Goldberg 6 R linkage is accomplished by using the evaluation indexes and mapping the workspace to the joint space which is defined by a vector whose components are joint variables.

The erratum of this chapter can be found under DOI 10.1007/978-3-319-23327-7_94

An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-319-23327-7_94

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Kong, X., Huang, C.: Type synthesis of single-DOF single-loop mechanisms with two operation modes. In: Proceedings of the 2009 ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, pp. 136–141. London (2009)

    Google Scholar 

  2. Wohlhart, K.: Multifunctional 7R Linkages. In: Proceedings of the International Symposium on Mechanisms and Machine Theory, pp. 85–91. AzCIFToMM, Izmir, Turkey (2010)

    Google Scholar 

  3. Goldberg, M.: A three-dimensional analog of a plane kempe linkage. J. Math. Phys. 25 , 96–110 (1946)

    Article  MathSciNet  Google Scholar 

  4. Song, C.Y., Feng, H.J., Chen, Y., Chen, I.M., Kang, R.J.: Reconfigurable mechanism generated from the network of Bennett linkages. Mech. Mach. Theory 88 , 49–62 (2015)

    Article  Google Scholar 

  5. Kumar, A., Waldron, K.J.: The workspace of a mechanical manipulator. J. Mech. Des.-T. ASME 103 (3), 665–672 (1981)

    Google Scholar 

  6. Bonev, I.A., Ryu, J.: A new approach to orientation workspace analysis of 6-DOF parallel manipulators. Mech. Mach. Theory 36 , 15–28 (2001)

    Article  MATH  Google Scholar 

  7. Gosselin, C.: Determination of the workspace of 6-DOF parallel manipulators. J. Mech. Des.-T. ASME 112 (3), 331–336 (1990)

    Google Scholar 

  8. Bajpai, A., Roth, B.: Workspace and mobility of a closed-loop manipulator. Int. J. Robot. Res. 5 (2), 131–142 (1986)

    Article  Google Scholar 

  9. Fallahi, B., Lai, H.Y., Naghibi, R., Wang, Y.: A study of the workspace of five-bar closed loop manipulator. Mech. Mach. Theory 29 (5), 759–765 (1994)

    Article  Google Scholar 

  10. Dai, J.S., Wang, D.L., Cui, L.: Orientation and workspace analysis of the multifingered metamorphic hand—metahand. IEEE T. Robot. 25 (4), 942–946 (2009)

    Article  Google Scholar 

  11. Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices. J. Appl. Mech. 23 , 215–221 (1955)

    MathSciNet  MATH  Google Scholar 

  12. Baker, J.E.: The Bennett, Goldberg and Myard linkages-in perspective. Mech. Mach. Theory 14 , 239–253 (1979)

    Article  Google Scholar 

  13. Borouchaki, H., Lo, S.H.: Fast Delaunay triangulation in three dimensions. Comput. Method Appl. M. 128 (1), 153–167 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge the support of the National Natural Science Foundation of China under grant codes of 51275334 and 51290293 and of Tianjin Municipal Science and Technology Department Program under grant codes of 13JCZDJC26400 and 14JCYBJC19300. The first author would like to acknowledge the support of Tianjin University for providing the University Graduate Scholarship.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yan Chen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Fen, H., Kang, R., Chen, Y. (2016). Workspace Analysis of a Reconfigurable Mechanism Generated from the Network of Bennett Linkages. In: Ding, X., Kong, X., Dai, J. (eds) Advances in Reconfigurable Mechanisms and Robots II. Mechanisms and Machine Science, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-319-23327-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23327-7_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23326-0

  • Online ISBN: 978-3-319-23327-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics