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TECHNICAL PAPERS

A New Technique Based on Loops to Investigate Displacement Isomorphism in Planetary Gear Trains

[+] Author and Article Information
V. V. N. R. Prasad Raju Pathapati

Mechanical Engr. Dept., B.V. Raju Institute of Technology, Narsapur, Medak (Dt), A.P, India-502 313e-mail: raju_pathapati@yahoo.com

A. C. Rao

K.L. College of Engineering, Vaddeswaram, Guntur District, AP, India-522 502

J. Mech. Des 124(4), 662-675 (Nov 26, 2002) (14 pages) doi:10.1115/1.1503373 History: Received December 01, 2000; Online November 26, 2002
Copyright © 2002 by ASME
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References

Buchsbaum,  F., and Freudenstein,  F., 1970, “Synthesis of Kinematic Structure of Geared Kinematic Chains and Other Mechanisms,” J. Mec., 5, pp. 357–392.
Freudenstein,  F., 1971, “An Application of Boolean Algebra to the Motion of Epicyclic Drives,” ASME J. Eng. Ind., 93B, pp. 176–182.
Ravishanker,  R., and Mruthunjaya,  T. S., 1985, “Computerized Synthesis of the Structure of Geared Kinematic Chains,” Mech. Mach. Theory, 20(5), pp. 367–387.
Tsai,  L. W., 1987, “An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains,” ASME J. Mech., Transm., Autom. Des., 25(5), pp. 563–573.
Kim,  J. U., and Kwak,  B. M., 1990, “Application of Edge Permutation Group to the Stuctural Synthesis of Epicyclic Gear Trains,” Mech. Mach. Theory, 25(5), pp. 563–573.
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.
Tsai,  L. W., and Lin,  C. C., 1989, “The Creation of Non Fractionated, Two D.O.F., Epicyclic Gear Trains,” ASME J. Mech., Transm., Autom. Des., 3, pp. 524–529.
Chatterjee, G., and Tsai, L. W., 1994, “Computer Aided Sketching of Epicyclic Type Automatic Transmission Gear Trains,” SAE transactions, Paper No. 941012.
Chatterjee,  G., and Tsai,  L. W., 1996, “Computer Aided Sketching of Epicyclic Type Automatic Transmission Gear Trains,” ASME J. Mech. Des., 3, pp. 405–411.
Olson, D. G., Erdman, A. G., and Riley, D. R., 1987, “A New Graph Theory Representation for the Topological Analysis of Planetary Gear Trains,” Proceedings of 7th World Congress on the Theory of Machines and Mechanisms, Seville, Spain, Vol. 3, pp. 1421–1425.
Olson,  D. G., Erdman,  A. G., and Riley,  D. R., 1991, “Topological Analysis of Single D.O.F., Planetary Gear Trains,” ASME J. Mech. Des., 113, pp. 10–16.
Yan,  H. S., and Hsu,  C. H., 1988, “Contracted Graphs of Kinematic Chains With Multiple Joints,” Math. Comput. Modell., 10, pp. 681–695.
Hsu,  C. H., and Lam,  K. T., 1992, “A New Graph Representation for the Automatic Kinematic Analysis of Planetary Gear Trains,” ASME J. Mech. Des., 114, pp. 196–200.
Hsu,  C. H., and Lam,  K. T., 1993, “Automatic Analysis of Kinematic Structure of Planetary Gear Trains,” ASME J. Mech. Des., 115, pp. 631–638.
Hsu,  C. H., 1994, “Displacement Isomorphism of Planetary Gear Trains,” Mech. Mach. Theory, 129(4), pp. 513–523.
Hsu,  C. H., 1993, J. Franklin Inst., 330, pp. 913–927.
Hsu,  C. H., and Hsu,  J. J., 1997, “An Efficient Methodology for the Structural Synthesis of Geared Kinematic Chains,” Mech. Mach. Theory, 32(8), pp. 957–973.
Rao,  A. C., and Pathapati,  V. V. N. R. Prasad Raju, 2000, “Loop Based Detection of Isomorphism Among Chains, Inversions and Type of Freedom in Multi Degree of Freedom Chains,” ASME J. Mech. Des., 122, pp. 31–42.
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Figures

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Linearly non-isomorphic & rotationally isomorphic graphs
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Linearly isomorphic & rotationally isomorphic graphs
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6 Link, PGTs given in Ref. 17
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Corrected graph in conventional form
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Corrected graph in new form
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A graph numbered 16-5 in Ref. 17
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A graph which cannot be produced by recursive generation method
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Redrawn conventional graph of Fig. 21
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Two pseudo-isomorphic graphs having different standard codes but having same G.C.L.H.S.
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Two pseudo-isomorphic graphs having same G.C.L.H.S.
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Functional graph representation of a 6-Link PGT
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Conventional graph representation
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Rotation graph representation
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Revised Representation of rotation graph
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Alternative conventional graph representation of Fig. 1
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Alternative functional graph representation of Fig. 1
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New graph representation of PGT shown in Fig. 1
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Acyclic graph representation of Fig. 7
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Depiction of redrawing a conventional graph
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Depiction of redrawing a conventional graph
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5 Link, PGT in conventional form
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6 Link, PGT in conventional graph form
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6 Link, PGT in new graph form
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Linearly non-isomorphic & rotationally non-isomorphic graphs

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