A Comparitive Study of a Few Tests for Isomorphism in Planetary Gear Trains
Keywords:characteristic polynomial, Eigen values, hamming number, row transformation matrix
AbstractGraph theory and Matrix methods are widely used by various kinematicians for synthesis and analysis of PGTs. Characteristic polynomial coefficients are used to detect isomorphism in Planetary Gear Trains (PGT). With the Eigen values and Eigen vectors method multiple matrix calculations are required. In case of Hamming number method a single Hamming matrix is enough to detect isomorphism in two PGTs and also determine structural aspects like symmetry easily . Further using the Hamming matrix for a PGT, the number of possible combinations of levels that can be assigned to a given PGT  is identified. A review and comparison of Characteristic polynomial, Eigen vectors and Eigen value and Hamming number methods is presented.
I. Rajasri, YVD Rao and AVSSKS. Gupta, “Structural Aspects of Symmetry and Its Effects on Generation of Planetary Gear Trains,” 2011 International Conference on Mechanical and Aerospace Engineering, March 2011, pp. 530-533.
I. Rajasri, Dr. AVSSKS Gupta, Dr.YVD Rao “Influence of structural aspects on the generation process in planetary gear trains,” International Journal Of Scientific Research, vol. 3, pp. 1018-1021, October 2011.
Z. Levai, “Structure and Analysis of planetary gear trains,” J. Mech., vol. 3, pp. 131-148, 1968.
Uicker and A.Raicu, “A method for the identification and recognition of equivalence of kinematic chains,” Mach. Theory, vol. 10, pp. 375-383, 1975.
Ashok Dargar., Ali Hasan., R.A.Khan., “Mobility analysis of inematic chains,” Kathmandu university journal of science, vol. 6, pp. 25-32, March 2010.
Ali Hasan, Khan. R. A., Aas Mohd, “A new method to detect isomorphism in kinematic chains,” Kathmandu university journal of science, vol. 1, pp. 1-11, January 2007.
L.W.Tsai, “An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains,” ASME Journal of Mechanisms, Transactions and Automation in Design, vol. 199, pp. 329-336, 1987.
A.G.Ambekar and V.P.Agrawal, “On canonical numbering of kinematic chains and isomorphism problem: Max code,” ASME paper.
J.N.Yadav, C.R.Pratap and V.P.Agrawal, “Detection of isomorphism among kinematic chains using the distance concept,” J. Mech. Design, ASME Trans, vol.117, pp. 607-611, 1995.
H.S.Yan and W.M.Hwang, “Linkage path code,” Mech. Mach. Theory, vol.19, pp. 425-429, 1984.
J. P. Cubillo and Jinbao Wan. “Comments on mechanism kinematics chain isomorphism identification using adjacent matrices,” Mech and Mach Theory, vol.40, pp. 131-139, 2004.
R. P Sunkari and L.C. Schmidt. “Reliability and efficiency of the existing spectral methods for isomorphism detection,” J. Mech. Design, ASME Trans, vol. 128, pp. 1246-1252, November 2006.
Zongyu Chang, Ce Zhang, Yuhu Yang, Yuxin Wang, “A new method to mechanism kinematic chain isomorphism identification,” Mech and Mach Theory, vol. 37, pp. 411-417, 2000.
Rao. A. C., 2000, “A Genetic Algorithm for epicyclic Gear Trains,” Mech. Mach. Theory, vol. 38, pp, 135-147, 2000.
Rao. A. C., 2000, “Application of Fuzzy Logic for the study of Isomorphism, Inversions, symmetry, parallelism and mobility in kinematic chains,” Mech. Mach. Theory, vol. 35, pp, 1103-1116, 2000.
A.C.Rao, “Hamming number technique I: Further applications,” Mech. Mach. Theory, vol. 32, pp. 477-488, 1997.
A.C.Rao and D.Varada Raju, “Application of the Hamming number technique to detect isomorphism among kinematic chains and inversions,” Mech. Mach. Theory, vol. 26, pp. 55-75, 1991.
A.C.Rao, “Comparison of plane and spatial kinematic chains for structural error performance using pseudo-Hamming distances,” Indian J.Tech, vol.26, pp.155-160, 1988.
A C Rao & Y V D Rao. “Symmetry in planetary gear trains,” Indian Journal of Engineering & Material Sciences, vol.9, pp.
-314, October 2002.
T. S. Mruthyunjaya, and M. R. Raghavan, “Structural analysis of kinematic chains and mechanisms based on matrix representation,” ASME, J. Mech. Design, vol. 101, pp. 488-494, 1979.
J.K.Shin and S. Krishnamurty, “On identification and canonical numbering of pin jointed kinematic chains,” J. Mech. Design, ASME Trans, vol. 116, pp. 182-188, 1994.
H. S. Yan and A.S.Hall, “Linkage characteristic polynomials: definition, coefficients by inspection,” J. Mech. Design, vol. 103, pp. 578-584, 1981.
T.S.Mruthyunjaya and H.R. Balasubramanian, “Inquest of a reliable and efficient computational test for detection of isomorphism in kinematic chains,” Mach. Theory, vol. 22, pp. 131-139, 1987.
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