Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.
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June 2017
Research-Article
Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial
Vinjamuri Venkata Kamesh,
Vinjamuri Venkata Kamesh
Associate Professor
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: venkatakamesh.vinjamuri@aec.edu.in
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: venkatakamesh.vinjamuri@aec.edu.in
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Kuchibhotla Mallikarjuna Rao,
Kuchibhotla Mallikarjuna Rao
Professor
Mechanical Engineering,
College of Engineering,
JNTUK University,
East Godavari District,
Kakinada 533 003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com
Mechanical Engineering,
College of Engineering,
JNTUK University,
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: venkatakamesh.vinjamuri@aec.edu.in
Mechanical Engineering,
Aditya Engineering College,
East Godavari District,
Surampalem 533 437, Andhra Pradesh, India
e-mail: venkatakamesh.vinjamuri@aec.edu.in
Kuchibhotla Mallikarjuna Rao
Professor
Mechanical Engineering,
College of Engineering,
JNTUK University,
East Godavari District,
Kakinada 533 003, Andhra Pradesh, India
e-mail: rangaraokuchibhotla@gmail.com
Mechanical Engineering,
College of Engineering,
JNTUK University,
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
1Corresponding author.
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 27, 2016; final manuscript received March 10, 2017; published online April 25, 2017. Assoc. Editor: Dar-Zen Chen.
J. Mech. Des. Jun 2017, 139(6): 062304 (12 pages)
Published Online: April 25, 2017
Article history
Received:
December 27, 2016
Revised:
March 10, 2017
Citation
Kamesh, V. V., Mallikarjuna Rao, K., and Srinivasa Rao, A. B. (April 25, 2017). "Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial." ASME. J. Mech. Des. June 2017; 139(6): 062304. https://doi.org/10.1115/1.4036306
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