Skip to main content
SpringerLink
Log in

A computerized loop based approach for identification of isomorphism and type of mobility in planar kinematic chains

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

Some new invariants like chain string, link identification string, loop participation of joint frequency string and loop size frequency string of simple jointed kinematic chains are presented. The first step of the proposed method is to identify all possible loops of a kinematic chain and then these new invariants are developed. A modified loop-joint approach is proposed in this work as compared to the previous work in literature where loop-link matrix is formulated to search all the loops present in a kinematic chain. A computer program has been developed for formulating loop-joint matrix of kinematic chain and its all invariants. This method takes into consideration all the loops present, associated joints and links and is able to test isomorphism among kinematic chains and their inversions and also to detect type of mobility of multi degree of freedom kinematic chains. The proposed method is successfully tested for all kinematic chains upto five independent loops having any number of degree of freedom and no counter example is found. The detailed results of 9-link, M = 2 (mobility) and 10 link, M = 3 kinematic chains are provided with five types of mobility and results are in accordance with the results published in literature. The method is also explained with the help of some complex examples and presented in this paper.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  • Agrawal V P and Rao J S 1987 Fractionated freedom kinematic chains and mechanisms. Mechanism and Machine Theory 22(2): 125–130

  • Ambekar A and Agrawal V P 1986 On canonical numbering of kinematic chains and isomorphism problem: Max code. ASME Mechanisms Conference

  • Ambekar A and Agrawal V P 1987 Canonical numbering of kinematic chains and isomorphism problem: min code. Mechanism and Machine Theory 22(5): 453–461

  • Ding H, Huang Z and Mou D 2008 Computer-aided structure decomposition theory of kinematic chains and its applications. Mechanism and Machine Theory 43: 1596–1609

  • Eric A B and Chris H 2005 Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: Application to 12- and 14-bar single degree-of-freedom chains. Mechanism and Machine Theory 40(9): 1030–1050

  • Huafeng D and Zhen H 2007 A new theory for the topological structure analysis of kinematic chains and its applications. Mechanism and Machine Theory 42(10): 1264–1279

  • Kong F G, Li Q and Zhang W J 1999 An artificial neural network approach to mechanism kinematic chain isomorphism identification. Mechanism and Machine Theory 34(2): 271–283

  • Marin G G, Casermeiro E M and Rodriguez D L 2007 Improving neural networks for mechanism kinematic chain isomorphism identification. J. Neural Process Lett. 26(2): 133–143

  • Mruthyunjaya T S 1984a A computerized methodology for structural synthesis of kinematic chains: Part 1 – Formulation. Mechanism and Machine Theory 19(6): 487–495

  • Mruthyunjaya T S 1984b A computerized methodology for structural synthesis of kinematic chains: Part 2 – Application to several fully or partial known cases. Mechanism and Machine Theory 19(6): 497–505

  • Mruthyunjaya T S 1984c A computerized methodology for structural synthesis of kinematic chains: Part 3 – Application to new case of 10- link, three-freedom chains. Mechanism and Machine Theory 19(6): 507–530

  • Mruthyunjaya T S 2003 Kinematic structure of mechanisms revisited. Mechanism and Machine Theory 38: 279–320

  • Mruthyunjaya T and Balasubramanzan H R 1987 In quest of a reliable and efficient computational test for detection of isomorphism in kinematic chains. Mechanism and Machine Theory 22(2): 131–140

  • Rajesh P S and Linda C S 2006 Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm. Mechanism and Machine Theory 41(9): 1021–1030

  • Rao A C 2000a Genetic algorithm for characteristics of kinematic chains. ASME J. Mech. Des. 122(2): 228–231

  • Rao A C 2000b Application of fuzzy logic for the study of isomorphism, inversions, symmetry, parallelism and mobility in kinematic chains. Mechanism and Machine Theory 35(8): 1103–1116

  • Rao A C 2004 Parallelism in planar kinematic chains (manipulators). Mechanism and Machine Theory 39: 1111–1122

  • Rao A C and Raju V V N R P 2000 Loop based detection of isomorphism among chains, inversions and type of freedom in multi degree of freedom chain. ASME J. Mech. Des. 122: 31–42

  • Rao A C and Rao C N 1992a Loop based pseudo hamming values – 1. Testing isomorphism and rating kinematic chains. Mechanism and Machine Theory 28(1): 113–127

  • Rao A C and Rao C N 1992b Loop based pseudo hamming values – 2. Inversions, preferred frames and actuator. Mechanism and Machine Theory 28(1): 129–143

  • Rao A C and Varada Raju D 1991 Application of the hamming number technique to detect isomorphism among kinematic chains and inversion. Mechanism and Machine Theory 26(1): 55–75

  • Tang C and Liu T 1993 Degree code; a new mechanism identifier. ASME J. Mech. Des. 115(3): 627–630

  • Tischler C R, Samuel A E and Hunt K H 1995 Kinematic chains for robot hands—II, kinematic constraints, classification, connectivity and actuation. Mechanism and Machine Theory 30(8): 1217–1239

  • Uicker J J and Raicu A 1975 A method for the identification of and recognition of equivalence of kinematic chains. Mechanism and Machine Theory 10(5): 375–383

  • Yan H S and Hall A S 1981 Linkage characteristic polynomials: definitions, coefficients by inspection. ASME J. Mech. Des. 103(3): 578–584

  • Yan H S and Hall A S 1982 Linkage characteristic polynomials: assembly, theorems, uniqueness. ASME J. Mech. Des. 104(1): 11–20

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Jamia Millia Islamia University, New Delhi, 110 025, India

    MANOJ K LOHUMI, AAS MOHAMMAD & IRSHAD A KHAN

  2. Department of Mechanical Engineering, Galgotias College of Engineering and Technology, Knowledge Park-2, Greater Noida, 201 306, India

    MANOJ K LOHUMI

Authors
  1. MANOJ K LOHUMI
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. AAS MOHAMMAD
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. IRSHAD A KHAN
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to MANOJ K LOHUMI.

Appendices

Appendix I

Figure 9
figure 9

Nine link. M = 2. Kinematic chains.

Full size image

Appendix II

Figure 10
figure 10

Ten link. M = 3. Kinematic chains.

Full size image
Figure 11
figure 11

Ten link. M = 3. Kinematic chains.

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

LOHUMI, M.K., MOHAMMAD, A. & KHAN, I.A. A computerized loop based approach for identification of isomorphism and type of mobility in planar kinematic chains. Sadhana 40, 335–350 (2015). https://doi.org/10.1007/s12046-015-0344-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-015-0344-z

Keywords

Search

Navigation