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

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

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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Levai, Z. , 1968, “ Structure and Analysis of Planetary Gear Trains,” J. Mech., 3(3), pp. 131–148. [CrossRef]
Buchsbaum, F. , and Freudenstein, F. , 1970, “ Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanisms,” J. Mech. Mach. Theory, 5(3), pp. 357–392.
Freudenstein, F. , 1971, “ An Application of Boolean Algebra to the Motion of Epicyclic Drives,” ASME J. Eng. Ind., 93(1), pp. 176–182. [CrossRef]
Ravisankar, R. , and Mruthyunjaya, T. S. , 1985, “ Computerized Synthesis of the Structure of Geared Kinematic Chains,” Mech. Mach. Theory, 20(5), pp. 367–387. [CrossRef]
Tsai, L. W. , 1987, “ An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Train,” ASME J. Mech., Transm. Autom. Des., 109(3), pp. 329–336. [CrossRef]
Chattarjee, G. , and Tsai, L. W. , 1994, “ Enumeration of Epicyclic-Type Automatic Transmission Gear Trains,” SAE Technical Paper No. 941012.
Chattarjee, G. , and Tsai, L. W. , 1996, “ Computer-Aided Sketching of Epicyclic-Type Automatic Transmission Gear Trains,” ASME J. Mech. Des., 118(3), pp. 405–411. [CrossRef]
Rao, A. C. , and Rao, Y. V. D. , 2002, “ Symmetry in Planetary Gear Trains,” Indian J. Eng. Mater. Sci., 9(5), pp. 311–314.
Rao, A. C. , 2003, “ A Genetic Algorithm for Epicyclic Gear Trains,” Mech. Mach. Theory, 38(2), pp. 135–147. [CrossRef]
Rao, Y. V. D. , and Rao, A. C. , 2008, “ Generation of Epicyclic Gear Trains of One Degree of Freedom,” ASME J. Mech. Des., 130(5), p. 052604. [CrossRef]
Reddy, R. , Gupta, A. V. S. S. K. S. , and Rao, Y. V. D. , 2011, “ Influence of Structural Aspects on the Generation Process in Planetary Gear Trains,” J. Eng., 3(10), pp. 1018–1021. [CrossRef]
Rajasri, I. , Rao, Y. V. D. , and Gupta, A. , 2011, “ Structural Aspects of Symmetry and Its Effects on Generation of Planetary Gear Trains,” International Conference on Mechanical and Aerospace Engineering, New Delhi, India, Mar. 21–23, pp. 530–533.
Rajasri, I. , Gupta, A. V. S. S. K. S. , and Rao, Y. V. D. , 2014, “ Symmetry and Its Effects on Structures of Planetary Gear Trains,” J. Inst. Eng. (India): Ser. C, 95(1), pp. 77–81. [CrossRef]
Prasad Raju Pathapati, V. V. N. R. , and Rao, A. C. , 2002, “ A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains,” ASME J. Mech. Des., 124(4), pp. 662–675. [CrossRef]
Srinath, A. , 2005, “ Improved Synthesis of Planetary Gear Trains,” J. Inst. Eng. (India): Mech. Eng. Div., 86, pp. 172–174.
El-Gayyar, M. S. , El-Eashy, H. M. , and Zaki, M. , 2006, “ Structural Synthesis and Enumeration of Epicyclic Gear Mechanisms Up to 12-Links Using Acyclic Graph Method,” ASME Paper No. GT2006-91136.
Del Castillo, J. M. , 2002, “ Enumeration of 1-DOF Planetary Gear Train Graphs Based on Functional Constraints,” ASME J. Mech. Des., 124(4), pp. 723–732. [CrossRef]
Liu, C. P. , and Chen, D. Z. , 2001, “ On the Application of Kinematic Units to the Topological Analysis of Geared Mechanisms,” ASME J. Mech. Des., 123(2), pp. 240–246. [CrossRef]
Hsu, C. H. , 1999, “ Systematic Enumeration of Epicyclic Gear Mechanisms for Automotives,” JSME Int. J., Ser. C, 42(1), pp. 225–233. [CrossRef]
Hsu, C. H. , and Wu, Y. C. , 1997, “ Automatic Detection of Embedded Structure in Planetary Gear Trains,” ASME J. Mech. Des., 119(2), pp. 315–318. [CrossRef]
Kim, J. U. , and Kwak, B. M. , 1990, “ Application of Edge Permutation Group to Structural Synthesis of Epicyclic Gear Trains,” Mech. Mach. Theory, 25(5), pp. 563–573. [CrossRef]
Shin, J. K. , and Krishnamurthy, S. , 1993, “ Standard Code Technique in the Enumeration of Epicyclic Gear Trains,” Mech. Mach. Theory, 28(3), pp. 347–355. [CrossRef]
Hsu, C. H. , and Lam, K. T. , 1993, “ Automatic Analysis of the Kinematic Structure of Planetary Gear Trains,” ASME J. Mech. Des., 115(3), pp. 631–638. [CrossRef]
Varadaraju, D. , and Mohankumar, Ch. , 2016, “ Split Hamming String as an Isomorphism Test for One Degree-of-Freedom Planar Simple-Jointed Kinematic Chains Containing Sliders,” ASME J. Mech. Des., 138(8), p. 082301. [CrossRef]
Wilson, R. J. , 1996, Introduction to Graph Theory, 4th ed., Addison Wesley Longman Limited, Harlow, UK.
Balakrishnan, R. , and Ranganathan, K. , 2012, A Textbook of Graph Theory, 2nd ed., Springer, New York.
Henley, E. J. , and Williams, R. A. , 1973, Graph Theory in Modern Engineering, Vol. 98, Academic Press/Elsevier, New York.
Wallis, W. D. , 2000, A Beginner's Guide to Graph Theory, Springer Science+ Business Media LLC, New York.


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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