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Research Papers: Design of Mechanisms and Robotic Systems

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

[+] Author and Article Information
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

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

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

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 139(6), 062304 (Apr 25, 2017) (12 pages) Paper No: MD-16-1857; doi: 10.1115/1.4036306 History: Received December 27, 2016; Revised March 10, 2017

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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Figures

Grahic Jump Location
Fig. 1

General structure of epicyclic gear train

Grahic Jump Location
Fig. 2

(a) Functional schematic, (b) Graph representation, (c) Rotation graph for (a), and (d) Assigning parameters to edges

Grahic Jump Location
Fig. 3

(a) Graph G1, (b) Graph G2, (c) Five-link gear train 1, and (d) Five-link gear train 2

Grahic Jump Location
Fig. 4

(a) Rotation graph of Fig. 3(c) and (b) Rotation graph of Fig. 3(d)

Grahic Jump Location
Fig. 5

(a) Possibilities of addition of new link, (b) 3GT1-1334, (c) 3GT1-1314, (d) 3GT1-1224, (e) 3GT1-1214, (f) 3GT1-2324, and (g) 3GT1-2334

Grahic Jump Location
Fig. 6

(a) 4EGT1 with axis a and axis b for gears 2, 3, and 4 and (b) Functional schematic for 4EGT1 in (a)

Grahic Jump Location
Fig. 7

(a) Adding a new link to existing four-link EGT, (b) 5-link alternative 1, and (c) 5-link alternative 2

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