Skip to main content

A Numerical Approach to Find Distinct Mechanisms of a Planar Kinematic Chain Using Linkage Coordinates

  • Conference paper
  • First Online:
Advances in Mechanical and Materials Technology (EMSME 2020)

Abstract

In a planar kinematic chain, different mechanisms are possible when on link’s mobility is restricted by fixing it. These mechanisms obtained are called as inversions. In the present paper, a numerical approach is proposed which is based on new concept defined as ‘linkage coordinates’ related to connectivity of a link in a closed planar kinematic chain. The proposed method is tested on various linkages (8, 9, 10) with varying degree of freedom (DoF) for which identified inversions are in correlation with earlier results in the literature. The proposed method can be applied to analyze other characteristics of kinematic chains with higher linkages and higher DoF. 8-link 1-DoF completed results are presented in the results section of the paper.

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 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
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

Similar content being viewed by others

References

  1. Rao AC, Varada Raju D (1991) Application of the hamming number technique to detect isomorphism among kinematic chains and inversions. Mech Mach Theory 26(1):55–75

    Google Scholar 

  2. Kui CJ, Qing CW (1994) Identification of Isomorphism among kinematic chains and inversions using link’s adjacent-chain-table. Mech Mach Theory 29(1):53–58

    Article  Google Scholar 

  3. Rao AC (2000) Application of fuzzy logic for the study of isomorphism, inversions, symmetry, parallelism and mobility in kinematic chains. Mech Mach Theory 35:1103–1116

    Article  MATH  Google Scholar 

  4. Ali H, Khan RA, Dargar AK (2007) Isomorphism and inversions of kinematic chains up to 10-Links. In: 13th national conference on mechanisms and machines (NaCoMM07), IISc, Bangalore, India

    Google Scholar 

  5. Mohammad A, Khan RA, Agrawal VP (2007) Identification of kinematic chains and distinct mechanisms using extended adjacency matrix. Proc IMechE Part C J Mech Eng Sci 221:81–88

    Google Scholar 

  6. Bedi GS, Sanyal S (2010) Joint connectivity: a new approach for detection of isomorphism and inversions of planar kinematic chains. J Inst Eng (India) 90:23–26

    Google Scholar 

  7. Sanyal S (2011) Structural identification of distinct inversions of planar kinematic chains. IIUM Eng J 85–92

    Google Scholar 

  8. Bal JS, Deshmukh PB, Jagadeesh A (2013) Link invariant functions and detection of isomorphism and inversions of kinematic chains. In: Proceedings of the 1st international and 16th national conference on machines and mechanisms (iNaCoMM2013), IIT Roorkee, India

    Google Scholar 

  9. Hasan A(2013) Determination of the distinct mechanisms from a given kinematic chain. i-Manager’s J Mech Eng 3(3):8–14. https://doi.org/10.26634/jme.3.3.2366

  10. Rizvi SSH, Hasan A, Khan RA (2016) An efficient algorithm for distinct inversions and isomorphism detection in kinematic chains. Persp Sci 8:251–253

    Google Scholar 

  11. Rai RK, Punjabi S (2017) An elusive method to identify isomorphism and inversions of kinematic chains and mechanisms. Indian J Sci Technol 10(18):1–13

    Article  Google Scholar 

  12. Shukla A, Sanyal S (2017) Gradient method for identification of isomorphism of planar kinematic chains. Aust J Mech Eng. https://doi.org/10.1080/14484846.2017.1374815

  13. Kamesh VV (2018) A novel algorithm to find distinct mechanisms of a planar kinematic chain. Int J Innov Res Explor 5(2):27–31

    Google Scholar 

  14. Kamesh VV, Prasad DVSSSV (2020) A novel algorithm to find distinct mechanisms of a kinematic chain using link polynomial. In: Proceedings of the national conference on recent technologies in engineering and basic sciences-2020 (NCRTEBS-2020). BVC Engineering College(A), Odalarevu, AP

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Appendix

Appendix

Distinct chains 8-link 1-DOF (16 no.)

Chain 1

Chain 2

Chain 3

Chain 4

Chain 5

Chain 6

Chain 7

Chain 8

Chain 9

Chain 10

Chain 11

Chain 12

Chain 13

Chain 14

Chain 15

Chain 16

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kamesh, V.V., Srinivasa Rao, V., Prasad, D.V.S.S.S.V., Ranjit, P.S. (2022). A Numerical Approach to Find Distinct Mechanisms of a Planar Kinematic Chain Using Linkage Coordinates. In: Govindan, K., Kumar, H., Yadav, S. (eds) Advances in Mechanical and Materials Technology . EMSME 2020. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-2794-1_114

Download citation

  • DOI: https://doi.org/10.1007/978-981-16-2794-1_114

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-2793-4

  • Online ISBN: 978-981-16-2794-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics