Isomorphism canonical adjacency matrices and characteristics number strings to

identification in epicyclic gear trains (EGTs) has found a lot of attention for
doing analysis and synthesis of mechanism during last few decades. It is one of
the basic ways to improve the performance of the mechanism by graph analysis.
Graph theory is being used for analyzing the graphs conventionally. With the
help of graph theory the kinematic diagram is converted into graphical form and
then by using various methods of identifying the isomorphism among geared
kinematic mechanisms 1-4.

synthesis and analysis of geared kinematic mechanisms is a rigorous process.
The basic applications of graph theory in the design and analysis of epicyclic
gear mechanisms have made the process more efficient and effectiveness. A
comprehensive study of structural synthesis of gear kinematic chains were carried
out by various authors is presented here.

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Buchsbaum and
Freudenstein 1 were developed a method for the enumeration and classification
of geared kinematic structures using network theorems and combinatorial
analysis. The complete detail comprises of application and implementation of
the theory to gear transmissions and differential drives. I. Rajasri et al. 2 were suggested about hamming
number technique to detect the isomorphism in EGTs. Generation of one-degree of
freedom EGTs with upto seven links was presented. E. Pennestri et al. 3 dealt
about graph theory based algorithms for analysis of mechanisms and gear trains.
H. Ding et al. 4 were suggested about automatic method for the structural synthesis
of EGTs. It was required to canonical adjacency matrices and characteristics
number strings to identify isomorphism for synthesis and analysis of geared
mechanisms. A new procedure for analysis of the graphs of single degree
of freedom epicyclic gear trains was presented based on functional constraints
as given in 5. Another procedure for the topological characteristics of the
fractionated geared differential mechanism was presented in 6. Chen et al. 7
were suggested a process for the modular design of geared robot manipulators.
Hsu and Hsu 8 have developed a new model for synthesis of the kinematic
structure of geared kinematic chains with any number of links using cyclic graphs.
The work in proposed a new graphical representation to represent the kinematic
structure of a planetary spur-gear train 9. It becomes easier to analyze the epicyclic
spur gear trains with graphical representation. A method for the identification
of the displacement isomorphism of planetary gear trains with any number of
gear pairs was suggested by Hsu 10. I. Rajasri et al. 11 were suggested
about identification of isomorphism in planetary gear trains based on adjacency
symmetrical matrix. A Hamming matrix was used to identify structural aspect of
symmetry in PGTs. A computer program for the automatic test of structural
analysis in planetary gear trains was put forwarded by Hsu and Wu 12. A new method
based on edge
permutation concept which was used to identify the non-isomorphic
graphs in epicyclic gear trains 13. Identification of rotational and
displacement isomorphism is one of the important step in structural synthesis
of EGTs. Discrepancy in results was reported in EGTs having higher number of
elements. A. C. Rao et al. 14 were presented a method using the hamming
number technique and loops for study of displacement and rotational isomorphism
in EGTs. The new idea of genetic algorithm to detect the isomorphism among
geared kinematic chains and extended the work to check different
characteristics of gears like speed ratios and transmission efficiency 15. Mruthyunjaya
and Ravishankar 16 dealt about the computerized technique for structural
synthesis of geared kinematic chains which is useful to derive epicyclic gear
drives. Shin and Krishnamurty 17 were introduced an efficient solution method
for the classification of epicyclic gear trains based on the standard code
model. The detailed description of application of graphs theory in mechanism
design was presented for epicyclic gear trains in 18-19.  A. Hasan et al. 20 were developed a new
method based on joint-joint matrix approach to detect isomorphism among planer
kinematic chains. A brief discussion was done on structural analysis of EGTs by
new procedure based on path matrix was developed by for detect isomorphism
among geared kinematic chains 21.

it has observed from various recent reviews that several methodologies for
synthesis and analysis of geared kinematic mechanisms have been brought to study
by researchers. The major problem was faced during synthesis of geared
mechanism is to identify the isomorphism among generated alternatives.


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