Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four-, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature.
Skip Nav Destination
Article navigation
December 2017
Research-Article
An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory
Vinjamuri Venkata Kamesh,
Vinjamuri Venkata Kamesh
Associate Professor
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: kameshvv@gmail.com
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: kameshvv@gmail.com
Search for other works by this author on:
Kuchibhotla Mallikarjuna Rao,
Kuchibhotla Mallikarjuna Rao
Professor
Mechanical Engineering,
University College of Engineering,
JNTUK,
East Godavari District,
Kakinada 533 003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com
Mechanical Engineering,
University College of Engineering,
JNTUK,
East Godavari District,
Kakinada 533 003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com
Search for other works by this author on:
Annambhotla Balaji Srinivasa Rao
Annambhotla Balaji Srinivasa Rao
Professor
Mechanical Engineering,
Sri Vasavi Institute of Engineering
and Technology,
Pedana Mandal,
Krishna District,
Nandamuru 521369, Andhra Pradesh India
e-mail: absrao71@gmail.com
Mechanical Engineering,
Sri Vasavi Institute of Engineering
and Technology,
Pedana Mandal,
Krishna District,
Nandamuru 521369, Andhra Pradesh India
e-mail: absrao71@gmail.com
Search for other works by this author on:
Vinjamuri Venkata Kamesh
Associate Professor
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: kameshvv@gmail.com
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: kameshvv@gmail.com
Kuchibhotla Mallikarjuna Rao
Professor
Mechanical Engineering,
University College of Engineering,
JNTUK,
East Godavari District,
Kakinada 533 003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com
Mechanical Engineering,
University College of Engineering,
JNTUK,
East Godavari District,
Kakinada 533 003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com
Annambhotla Balaji Srinivasa Rao
Professor
Mechanical Engineering,
Sri Vasavi Institute of Engineering
and Technology,
Pedana Mandal,
Krishna District,
Nandamuru 521369, Andhra Pradesh India
e-mail: absrao71@gmail.com
Mechanical Engineering,
Sri Vasavi Institute of Engineering
and Technology,
Pedana Mandal,
Krishna District,
Nandamuru 521369, Andhra Pradesh India
e-mail: absrao71@gmail.com
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 7, 2017; final manuscript received August 3, 2017; published online October 3, 2017. Assoc. Editor: Massimo Callegari.
J. Mech. Des. Dec 2017, 139(12): 122301 (11 pages)
Published Online: October 3, 2017
Article history
Received:
February 7, 2017
Revised:
August 3, 2017
Citation
Venkata Kamesh, V., Mallikarjuna Rao, K., and Balaji Srinivasa Rao, A. (October 3, 2017). "An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory." ASME. J. Mech. Des. December 2017; 139(12): 122301. https://doi.org/10.1115/1.4037628
Download citation file:
Get Email Alerts
Related Articles
Compound Topological Invariant Based Method for Detecting Isomorphism in Planar Kinematic Chains
J. Mechanisms Robotics (October,2020)
Studying the Optimal Layout of Topological Graphs to Facilitate the Automatic Sketching of Kinematic Chains
J. Mech. Des (August,2017)
The Database Generation for Planar 2-DOF Fractionated Multiple-Joint Kinematic Chains
J. Mechanisms Robotics (December,2024)
Related Proceedings Papers
Related Chapters
An Improved String Matching Algorithm Based on Suffix Array
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Prevention of Textual Plagiarism
International Conference on Computer and Computer Intelligence (ICCCI 2011)
Creative Design of the Sewing Machine’s Feeding Mechanism Based on Topological Characteristics of Kinematic Chains
International Conference on Advanced Computer Theory and Engineering, 5th (ICACTE 2012)