Skip to main content
SpringerLink
Log in

Derivation of Input/Output Relationships for the Bennett 6R Linkages Based on the Method of Decomposition

  • Conference paper
New Advances in Mechanisms, Transmissions and Applications

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 17))

Abstract

The Bennett overconstrained 6R linkages are the double-planar, the double-spherical and the plano-spherical 6R linkages. These mechanisms are obtained by combining simple planar and/or spherical mechanisms and then removing one of the common links. This paper presents the derivation of the input/output relationships for these mechanisms using the decomposition method. This method is based on writing the input/output equations for the two imaginary loops comprising the 6R mechanism and then eliminating the imaginary joint variable. It is found that the resulting input/output equations contain up to 4th power of trigonometric terms, such as cos4 θ.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Sarrus, P.T.: Note sur la transformation des mouvements rectilignes alternatifs, en mouvements circulaires, et reciproquement. Academie des Sciences 36, 1036–1038 (1853)

    Google Scholar 

  2. Selvi, Ö.: Structural and kinematic synthesis of overconstrained mechanisms. PhD Thesis in Mechanical Engineering, İzmir Institute of Technology (2012)

    Google Scholar 

  3. Bennett, G.T.: The parallel motion of Sarrus and some allied mechanisms. Philosophy Magazine, 6th Series 9, 803–810 (1905)

    Article  Google Scholar 

  4. Chen, Y., You, Z.: Spatial overconstrained linkages—the lost jade. In: Koetsier, T., Ceccarelli, M. (eds.) Explorations in the History of Machines and Mechanisms. HMMS, vol. 15, pp. 535–550. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Baker, J.E.: Displacement-closure equations of the unspecialized double Hooke’s-joint linkage. Mech. Mach. Theory 37, 1127–1144 (2002)

    Article  Google Scholar 

  6. Alizade, R.I., Aydazade, K.P., Novruzbekov, I.G.: Analysis and synthesis of planar mechanisms by using decomposition method. J. Mechanics of Machines, The Academy of Sciences of the USSR 57, 26–32 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. İzmir Institute of Technology, İzmir, Turkey

    R. I. Alizade, G. Kiper, M. İ. C. Dede & E. Uzunoğlu

Authors
  1. R. I. Alizade
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Kiper
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. İ. C. Dede
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. Uzunoğlu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. I. Alizade .

Editor information

Editors and Affiliations

  1. Mechanical Engineering Department, University of the Basque Country, Bilbao, Spain

    Victor Petuya

  2. Mechanical Engineering Department, University of the Basque Country, Bilbao, Spain

    Charles Pinto

  3. Mechanical Engineering Faculty, Politehnica University of Timişoara, Timisoara, Romania

    Erwin-Christian Lovasz

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Alizade, R.I., Kiper, G., Dede, M.İ.C., Uzunoğlu, E. (2014). Derivation of Input/Output Relationships for the Bennett 6R Linkages Based on the Method of Decomposition. In: Petuya, V., Pinto, C., Lovasz, EC. (eds) New Advances in Mechanisms, Transmissions and Applications. Mechanisms and Machine Science, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7485-8_28

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-7485-8_28

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7484-1

  • Online ISBN: 978-94-007-7485-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation