volume ii, issue vi, june 2015 an atlas of 12-link, 1 ...keywords– kinematic chain, structural...

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Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705 www.rsisinternational.org/IJRSI.html Page 17 An Atlas of 12-Link, 1Freedom Simple Jointed Kinematic Chains and Mechanisms Vijayananda Kaup Department of Mechanical Engineering, CMR Institute of Technology, Bengaluru, India Abstract Simple Jointed Kinematic chains have long since been established as an important conceptual entity useful in the creative synthesis of mechanisms, machines and power transmission systems. The task of generating and analysing kinematic chains, popularly termed as the structural synthesis and analysis of chains is a mammoth task especially when there are more than nine links in the chain. By reporting all the structural variants of the simple jointed kinematic chains (SJKCs) belonging to 12-link, 1-freedom category along with the distinct mechanisms derivable from each, the results of this work mainly serves to relieve machine designers from the efforts of performing structural synthesis and analysis of chains, and also from getting into the intricacies of the isomorphism problem associated with the number synthesis of the chains. Instead, they can direct their efforts towards finding ways to convert SJKCs to the desired mechanisms having different machine elements. A total of 6856 chains were generated using a computer program developed by the author followed by detection of 75397 distinct mechanisms from the given category of chains. These findings are reported in this paper by employing a concise notation for representing the chains. The paper also discusses the findings that emerged by applying characteristics polynomial based isomorphism tests on all the 6856 chains using the link-adjacency, degree and structural matrices. It reports two cases where the degree- and structural matrix based isomorphism tests yield identical counter examples. KeywordsKinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION ne possible reason which can be attributed to non- availability of the complete collection of the structural variants of 12-link, 1-freedom simple jointed kinematic chains (SJKCs) in the published literature is the large volume of associated data required to be published [1]. Owing to its potential use in the preliminary design phase of the product design cycle, which is the phase during which the machine design engineer has to bring out innovation in the artefact that is being designed, kinematic chains have been found to assist in the creative synthesis of solutions in an objective and systematized manner [2]. It is also found to help in spawning newer ideas and novel mechanical configurations regardless of the complexity of the underlying mechanism. It has been shown in literature that the chains, which in its primitive form consist of simple links connected by means of the turning joints, can be transformed into mechanisms consisting of gears, cams, belts, chains, and so on [3]. Several researchers in the past have attempted structural synthesis of chains, and have proposed various methods to enumerate them [4-17]. But for very few instances [13,16] wherein the drawing of the kinematic chain structures are reported, the results reported thus far is predominantly restricted to describing the methodology of synthesis, their application to several cases of links and degree of freedom, followed by the tabulations of the total number of chains that could be generated in each category of SJKCs. The mechanism designers, on the other hand, would prefer to have all the structural variants presented to them so that they can further work upon the chains to produce actual mechanisms. One possible reason for the non-availability of a chain catalogue as a sketch or an alternative representation of the chain is the sheer difficulty to report the substantial results given the page-space constraints. This paper chooses to provide the complete structural information about the chains and the number of mechanisms that each kinematic chain can yield in a form that enables easy sketching of the structure of SJKCs and identification of the links which yield distinct mechanisms (or alternatively, the links which yield identical mechanism). To this end a concise notation for the chain is proposed. The notation enables representation of the chain and the possible distinct mechanisms derivable from it by means of an alpha-numeric string of 12 characters length. A short FORTRAN program that can decode the chain into a form that is convenient to sketch, as compared to the link adjacency matrix representation, is also included in the paper. While searching across all the 6856 chains for cospectral examples it is found that when characteristic polynomial of link adjacency matrix [18] is employed as an isomorphism index there were 15 triplets of 12-link, 1- freedom SJKCs, and 183 instances of pairs of cospectral chains. A similar search for cospectral examples using the degree matrix [20] and structural matrix [19] representations revealed two pairs of counter-examples to isomorphism tests. A surprising discovery in the study was that both the tests failed to distinguish the same pairs of kinematic chains. These chains are also reported in this paper. II. BRIEF REVIEWOF LITERATURE Referring to "Table 1: Current status of enumeration of kinematic chains" in the review paper by Mruthyunjaya [1], it may be observed that several researchers have in the past attempted enumeration of chains adopting different approaches and have reportednearly identical results. Restricting the survey of literature to those contributions that emphasized computer-based methodologies of number synthesis and also to those that deal with SJKCs possessing greater than 9 links, Tuttle et al. [3,4] introduced group theory to the study of kinematic structure for the enumeration of chains and mechanisms.Mruthyunjaya[11-13, 16] presented the method O

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Page 1: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 17

An Atlas of 12-Link, 1–Freedom Simple Jointed

Kinematic Chains and Mechanisms

Vijayananda Kaup

Department of Mechanical Engineering, CMR Institute of Technology, Bengaluru, India

Abstract – Simple Jointed Kinematic chains have long since

been established as an important conceptual entity useful in the

creative synthesis of mechanisms, machines and power

transmission systems. The task of generating and analysing

kinematic chains, popularly termed as the structural synthesis

and analysis of chains is a mammoth task especially when there

are more than nine links in the chain. By reporting all the

structural variants of the simple jointed kinematic chains

(SJKCs) belonging to 12-link, 1-freedom category along with

the distinct mechanisms derivable from each, the results of this

work mainly serves to relieve machine designers from the

efforts of performing structural synthesis and analysis of

chains, and also from getting into the intricacies of the

isomorphism problem associated with the number synthesis of

the chains. Instead, they can direct their efforts towards finding

ways to convert SJKCs to the desired mechanisms having

different machine elements. A total of 6856 chains were

generated using a computer program developed by the author

followed by detection of 75397 distinct mechanisms from the

given category of chains. These findings are reported in this

paper by employing a concise notation for representing the

chains. The paper also discusses the findings that emerged by

applying characteristics polynomial based isomorphism tests on

all the 6856 chains using the link-adjacency, degree and

structural matrices. It reports two cases where the degree- and

structural matrix based isomorphism tests yield identical

counter examples.

Keywords– Kinematic chain, structural synthesis, mechanisms,

isomorphism, Degree matrix, Structural matrix.

I. INTRODUCTION

ne possible reason which can be attributed to non-

availability of the complete collection of the structural

variants of 12-link, 1-freedom simple jointed kinematic

chains (SJKCs) in the published literature is the large

volume of associated data required to be published [1].

Owing to its potential use in the preliminary design phase of

the product design cycle, which is the phase during which

the machine design engineer has to bring out innovation in

the artefact that is being designed, kinematic chains have

been found to assist in the creative synthesis of solutions in

an objective and systematized manner [2]. It is also found to

help in spawning newer ideas and novel mechanical

configurations regardless of the complexity of the underlying

mechanism. It has been shown in literature that the chains,

which in its primitive form consist of simple links connected

by means of the turning joints, can be transformed into

mechanisms consisting of gears, cams, belts, chains, and so

on [3].

Several researchers in the past have attempted

structural synthesis of chains, and have proposed various

methods to enumerate them [4-17]. But for very few

instances [13,16] wherein the drawing of the kinematic chain

structures are reported, the results reported thus far is

predominantly restricted to describing the methodology of

synthesis, their application to several cases of links and

degree of freedom, followed by the tabulations of the total

number of chains that could be generated in each category of

SJKCs. The mechanism designers, on the other hand, would

prefer to have all the structural variants presented to them so

that they can further work upon the chains to produce actual

mechanisms.

One possible reason for the non-availability of a

chain catalogue – as a sketch or an alternative representation

of the chain – is the sheer difficulty to report the substantial

results given the page-space constraints. This paper chooses

to provide the complete structural information about the

chains and the number of mechanisms that each kinematic

chain can yield in a form that enables easy sketching of the

structure of SJKCs and identification of the links which yield

distinct mechanisms (or alternatively, the links which yield

identical mechanism). To this end a concise notation for the

chain is proposed. The notation enables representation of the

chain and the possible distinct mechanisms derivable from it

by means of an alpha-numeric string of 12 characters length.

A short FORTRAN program that can decode the chain into a

form that is convenient to sketch, as compared to the link

adjacency matrix representation, is also included in the

paper.

While searching across all the 6856 chains for

cospectral examples it is found that when characteristic

polynomial of link adjacency matrix [18] is employed as an

isomorphism index there were 15 triplets of 12-link, 1-

freedom SJKCs, and 183 instances of pairs of cospectral

chains. A similar search for cospectral examples using the

degree matrix [20] and structural matrix [19] representations

revealed two pairs of counter-examples to isomorphism

tests. A surprising discovery in the study was that both the

tests failed to distinguish the same pairs of kinematic chains.

These chains are also reported in this paper.

II. BRIEF REVIEWOF LITERATURE

Referring to "Table 1: Current status of enumeration of

kinematic chains" in the review paper by Mruthyunjaya [1],

it may be observed that several researchers have in the past

attempted enumeration of chains adopting different

approaches and have reportednearly identical results.

Restricting the survey of literature to those

contributions that emphasized computer-based

methodologies of number synthesis and also to those that

deal with SJKCs possessing greater than 9 links, Tuttle et al.

[3,4] introduced group theory to the study of kinematic

structure for the enumeration of chains and

mechanisms.Mruthyunjaya[11-13, 16] presented the method

O

Page 2: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 18

based on transformation of binary chains for structural

synthesis of simple- and multiple-jointed chains with

positive, zero or negative freedom. Complete collection of 9-

link, 2-freedom and 10-link, 1-freedom chains were derived

in this work through a computer program implementing the

method.Mruthyunjaya et al. [16] have reported the sketches

of all 11-link, two-freedom chains, derived by applying

transformation of binary chains for structural synthesis. The

complete collection of 839 simple-jointed chains found in

the category including 65 with total freedom, 688 with

partial freedom and 86 with fractionated freedom were

presented. References [13,16] illustrates the amount of space

required to publish the kinematic structure of mechanisms.

III. SYNTHESIS METHODOLOGY ADOPTED IN THIS

WORK

In his doctoral dissertation, the corresponding author

Vijayananda [17] had developed a structural synthesis

method in which a chain having a given number of links and

degree of freedom is built up by augmenting a specially

constructed assemblage of links called the link-patterns to a

valid chain having fewer number of links called the parent

kinematic chain. The parent kinematic chain is a closed

chain with positive freedom and free from immobile sub-

chains while the link-pattern is either an open structure with

two free elements or a quasi-closed structure with one free

element. The interrelation among the degrees of freedom and

amongst the number of links of the chain to be derived, the

parent kinematic chain and the link pattern to be added are

presented and the rules to be followed while adding the link

patterns are formulated. The method is applicable for

synthesis of chains with positive, zero or negative freedom.

It has been expressed in analytical terms using concepts from

graph theory and computerized to enable synthesis of chains

with positive freedom incorporating an isomorphism test

developed by the corresponding author [17]. The program

has been applied to generate chains with up to 13 links and

having different freedoms. Another advantage of this method

is that it also generates valuable information required to

identify type of freedom of the derived chains. See also

Mruthyunjaya [1].

IV. STRUCTURALSYNTHESIS OF 12-LINK, 1

FREEDOM SJKC

As mentioned in the above section, synthesis of 12-link, 1

freedom SJKCs are generated using the complete collection

of 10-link, 1 freedom and 11-link, 2-freedom parent

kinematic chains. It should be observed that the number

synthesis being dealt with and reported in this work is

restricted to generating closed and connected chains

possessing no redundant sub-chains having zero or negative

freedom.

By using a dyad link-pattern (two binary links in

series) that adds two binary links and three simple joints to

the 10-link, 1 freedom parent chains, SJKCs having 12-link

and 1 freedom can be generated. Note that by applying

Gruebler’s criterion, this augmentation will not alter the

number of degrees of freedom of the parent chain. This

operation is performed in turn on each of the complete

collection of 10-link, 1-dof chains. Chains so produced will

have at least one dyad in it.

Similarly, by adding one binary link to 11-link, 2-

dof chain, two additional joints will be introduced. Now by

applying Gruebler’s criterion, one dof (3×1–2×2 = –1) will

be removed from the original 2-dof chain rendering the final

chain to possess 12-link and 1-dof. It may be observed that

addition of one binary link need be done to only those 11-

link 2-dof chains that will yield chains without dyads. The

latter lends a significant computational time saving avenue.

V. RESULTS OF NUMBER SYNTHESIS &

COSPECTRALCASESAMONG 12-LINK, 1-

FREEDOMCHAINS

This paper reports the structure of 6856 SJKCs, and the

75397 distinct mechanisms that can be derived from the

complete collection of 12-link, 1-freedon chains (Table 4).

These chains are arranged column-wise in blocks of 640

chains. For example, chain no. 90 is J4oA8H8+241. The

order of listing is to be particularly noted since the cospectral

chain numbers shown in Tables 1 and 2 is as per the stated

order.

As a further exercise, characteristic polynomial of

the degree matrix proposed in [20] and that of the structural

matrix proposed in [19] was examined by applying it to all

the 12-link, 1-freedom chains. The intent of the study was to

check for the existence of any counter examples. It was

found that there existed two pairs of chains wherein both the

tests failed to distinguish the two structures. A surprising

discovery from this exercise is that both of the above two

tests had the same cases of counterexamples. The two cases

of counter-examples shown in Fig. 1 were common to both

isomorphism tests.

Counter-example # 1

Counter-example # 2

Figure 1: Counter-examples for the degree matrix [3] and structural matrix [2] based approaches

It may be noted that the size of structural matrix

(which is equal to the sum of number of links and joints in

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Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 19

the chain) is larger than that of the degree matrix for the

same chain (which is the size of the link adjacency matrix).

That is, for a 12-link, 1-freedom category the structural

matrix is a square matrix of size 28 while it is 12 in the case

of degree matrix. Although the degree matrix of a chain is

easily derivable from its link adjacency matrix, the former

contain some additional information in it. The latter, loaded

with extra information, serves as the better starting point for

the computation of the characteristic coefficients. It is due to

this that the characteristic polynomial of degree matrix has

been found to have fewer counter-examples.

In the same manner the structural matrix of the

chain, although derivable from link-adjacency matrix,

contains a lot more information about the chain in its initial

form itself. The method, in fact, generates a matrix which is

larger in size than what the representation requires. The

objective was to pack as much information about the chain

as possible into the matrix representation from which

characteristic polynomial of the matrix is computed. The

test based on this matrix is believed to have no counter-

examples. The findings of the present work in the 12-link, 1-

freedom category reveals that the degree matrix based test

[20], despite its smaller size, is computationally as efficient

as the method of characteristic polynomial of link adjacency

matrix suggested in [18], and as robust as that of structural

matrix based method [19]. From the above it can be concluded that despite its

relatively smaller size (N × N), isomorphism test based on

the degree matrix is as good as the isomorphism test based

on structural matrix whose size is [(N+J) × (N+J) ], where N

is the number of links, and J is the number of joints in the

chain.

Table 1: 15 CASES OF COSPECTRAL TRIPLETS AMONG 12-LINK, 1-FREEDOM CHAINS [225, 561, 6165],[1522,4517,4832],[2166,2575,2611],[2167,2168,2201],[2193,2284,2285]

[2395,2426,2600],[2428,2450,2618],[2449,2453,2475],[3219,3321,3863],[3536,3548,3642]

[3537,3551,3571],[5314,6678,6735],[5486,6817,6825],[5934,6720,6332],[6025,6725,6846]

Table 2: 183 CASES OF COSPECTRAL PAIRS AMONG 12-LINK, 1-FREEDOM CHAINS

[ 27,3981],[ 50,3851],[ 279, 927],[ 303, 471],[ 340, 443],[ 365,6070],[ 382,3881],[ 391,3877]

[ 400, 428],[ 409, 499],[ 437,5361],[ 497,6088],[ 517,5011],[ 522,6142],[ 524, 527],[ 535, 577]

[ 544,6146],[ 576,5319],[ 601,6167],[ 605,5573],[ 775,1733],[ 836, 934],[ 905,1802],[1061,1101]

[1125,4212],[1154,1363],[1214,1333],[1306,5641],[1318,4172],[1550,5676],[1559,5528],[1601,1636]

[1668,2029],[1710,1951],[1731,1766],[1755,2742],[1808,1897],[1921,2071],[2152,2153],[2157,2158]

[2162,2163],[2203,2708],[2230,4423],[2233,4439],[2240,5822],[2257,2315],[2264,2613],[2286,2425]

[2291,4955],[2318,3339],[2326,5756],[2329,2601],[2330,4546],[2335,4536],[2386,2564],[2422,2616]

[2424,2604],[2430,2621],[2439,2628],[2582,3736],[2615,3737],[2643,5806],[2660,5085],[2692,2925]

[2745,4486],[2937,6229],[2944,4457],[2945,2947],[2946,5840],[2967,3056],[2970,6236],[3088,4516]

[3120,3460],[3128,3466],[3148,4222],[3157,4219],[3164,3190],[3186,5539],[3196,4294],[3212,6679]

[3220,4290],[3252,4186],[3253,6650],[3255,4184],[3293,5708],[3304,4115],[3306,4141],[3311,6020]

[3314,5937],[3320,4304],[3348,6216],[3384,4688],[3389,4659],[3420,4698],[3431,4692],[3439,3760]

[3440,4697],[3528,3533],[3531,3565],[3535,3544],[3596,5100],[3611,4021],[3635,3810],[3653,4493]

[3658,4492],[3664,3691],[3678,6431],[3680,4778],[3683,3684],[3685,4783],[3692,3694],[3705,4724]

[3710,4745],[3735,3817],[3743,4702],[3753,3814],[3761,4701],[3766,3789],[3862,5344],[3864,5348]

[3886,5905],[3890,5907],[3910,4849],[3923,4854],[3927,5986],[3936,6673],[4329,5927],[4459,5094]

[4539,6254],[4720,6363],[4780,6339],[4809,5977],[4811,5976],[5001,5132],[5002,5152],[5021,6546]

[5064,5208],[5066,5222],[5189,5276],[5190,5294],[5205,6618],[5323,5326],[5341,6707],[5365,6709]

[5369,5370],[5399,5400],[5413,6759],[5415,6784],[5434,5436],[5437,5527],[5456,5457],[5471,5510]

[5473,5512],[5481,6792],[5493,5675],[5552,6168],[5553,6166],[5901,6303],[5916,6163],[5918,6177]

[5928,6151],[5934,6720],[5984,6332],[5985,6364],[5990,6330],[6024,6726],[6033,6716],[6461,6574]

[6481,6571],[6514,6604],[6516,6580],[6517,6600],[6519,6605],[6520,6606],[6562,6647],[6566,6839]

[6641,6737],[6680,6734],[6681,6730],[6683,6732],[6684,6692],[6724,6727],[6848,6853]

VI. CONCISE NOTATION FORREPORTING SJKCs – APROPOSAL

A compact notation is proposed to represent SJKCs and the

number of distinct mechanisms they yield. The notation

helps in greatly reducing the space requirements for

reporting the results. To illustrate the notation we consider

the example of the 12-link, 3-d.o.f chain shown in Fig. 2

along with its link adjacency matrix.

Figure 2: 10-Link, 3-DOF SJKC and its Link-Adjacency Matrix

The compact notation for this chain

is+A+iAm4K+A4,B. The letters included in the notation

are interpreted by the following procedure.

Commencing from row-1 of the upper triangular link

adjacency matrix (diagonal elements excluded), the matrix

elements are first written row by row as a single binary

string as follows: 000000001010000000101100001010110000000100010100000

000001010000100 The above binary string is then divided into smaller

units containing six binary digits. A 12-link KC represented

by 12×12 matrix will have 66 binary digits (=11×122)

leading to eleven six-bit-units as shown below.

[000000][001010][000000][101100][001010][110000][00

0100][010100][000000][001010][000100]

0 0 0 0 0 0 0 0 0 1

0 1

0 0 0 0 0 0 0 0 0 1

0 1

0 0 0 1 0 0 0 0 1 0

1 0

0 0 1 0 1 1 0 0 0 0

0 0

0 0 0 1 0 0 1 0 0 0

1 0

0 0 0 1 0 0 1 0 0 0

0 0

0 0 0 0 1 1 0 0 0 0

0 0

0 0 0 0 0 0 0 0 1 0 1 0

0 0 1 0 0 0 0 1 0 0

0 0

1 1 0 0 0 0 0 0 0 0 1 0

0 0 1 0 1 0 0 1 0 1

0 0

1 1 0 0 0 0 0 0 0 0

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Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 20

Letx1x2x3x4x5x6represent a six-bit-unitwherexi(i =

1,2,…,6) are the six binary digits. From thexi's we

cangenerate an integerdjas follows.

𝑑𝑗 = 𝑥𝑖 × 26−𝑖

6

𝑖=1

Dependinguponthe six-bit-units xi's, djcan take any

integer value from 0 (zero) through 63 (26 – 1). Knowingdj

the followingsubstitutionis carried out.

If dj = 0, substitute with the ‘+’ character. This is to

avoid confusion between ‘0’ (zero) with the alphabet

‘O’.

If dj = 1, 2, 3, ..., 9, no substitution needbe made.

If dj = 10,11,12,…, 35, substitute it with the upper

case alphabets A, B, C,…, Z respectively.

If dj = 36, 37, 38 ..., 61, substitute it with the lower

case alphabets a, b, c,…, y, z respectively.

If dj = 62, 63, substitute them with the characters ‘*’,

‘=’ respectively.

After the above substitutions, concatenatedj (j = 1, 2,...,

11) obtained from the eleven six-bit-units. The sequence of

occurrence ofdj'sis to be retained. The string consisting of

eleven characters given above(+A+iAm4K+A4)provides

information about the structure of kinematic chain in the

condensed notation.

The second part of the notation, B (following the

comma), provides details about the number of distinct

mechanisms possible from the chain, and also which of the

links yield structurally identically mechanism upon fixation.

The meaning conveyed by each of these codes is tabulated in

Table 3.

Table 3: Mechanisms: Symbols and their meaning

Code Meaning of the symbol A All mechanisms are distinct B 1=2,3,4,5,6,7,8,9,10,11,12

C 1=2=3=4,5=6=7=8,9=10,11=12

D 1=2,3=4,5=6,7,8,9,10,11,12

E 1=2,3=4,5=6,7=8,9=10,11=12

F 1=2=3=4=5=6=7=8,9=10=11=12

G 1=2,3=4,5,6,7,8,9,10,11,12

H 1=2=3=4,5=6,7=8,9=10,11=12

I 1=2=3=4=5=6,7=8,9=10,11=12

J 1=2=3=4,5=6=7=8,9=10=11=12

K 1=2,3=4,5=6,7=8,9=10,11,12

L 1=2,3=4,5=6,7=8,9,10,11,12

M 1=2=3=4,5=6,7=8,9=10,11,12

N 1=2=3=4=5=6,7=8,9=10,11,12

O 1=2=3=4,5=6,7=8,9,10,11,12

P 1=2=3,4=5=6,7,8,9,10,11,12

Q 1=2=3=4,5=6=7=8,9=10,11,12

R 1=2=3=4=5=6=7=8=9=10,11=12

S 1=2=3=4,5=6,7,8,9,10,11,12

T 1=2=3=4=5=6=7=8,9=10,11=12

U 1=2=3,4=5=6,7=8,9,10,11,12

V 1=2=3,4=5=6,7=8=9,10,11,12

W 1=2=3=4=5=6,7=8=9,10=11,12

In the present example the meaning of letter B is that links 1

and 2 have identical disposition with reference to the

remaining 10 links in the chain while the links 3 through 12

have distinct location within the chain. This is indicated in

Table 3 as (1=2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12).

VII. FORTRAN PROGRAM FORDECODING THE

NOTATION

In order to facilitate extraction of the chain from its notation,

a FORTRAN code block has been included below. The

program reads the notation made up with eleven characters

from an input text file named 12LINK.INP. The output of the

program will list pairs of links which are adjacent to each

other. For example, if the input is+A+iAm4K+A4,then the

output would be (1,10), (1,12), (2,10), (2,12), (3,4), (3,9),

(3,11), (4,5), (4,6), (5,7), (5,11), (6,7), (8,9), (8,11), (10,11)

VIII. SUMMARY AND CONCLUSION

The paper reports the structures of 6856 SJKCs belonging to

12-link, 1-dof category along with 75397 distinct

mechanisms. A concise notation developed for the purpose

has been used. The paper also reports all the distinct

mechanisms possible from each chain. This was made

possible through a unique way of labelling of the links of the

chain. A FORTRAN program which enables quick decoding of

the notation into a form that facilitates easy sketching of

chains is also presented. A logical extension of this work is

to automate the sketching of the chains. While testing the

above chains collection using the characteristic polynomial

based tests it is found that there existed 15 triplets and 183

cases of cospectral pairs of chains when link adjacency

matrix was used for chain representation. However, with the

degree matrix and structural matrix representations of chains

there were only two pairs of cospectral chains where the

tests could not distinguish. Both tests were found to fail for

the same pairs of chains.

ACKNOWLEDGEMENT

The corresponding author is thankful to CMR Institute of

Technology for motivating and providing an opportunity to

conduct this work.

REFERENCES

[1]. T S Mruthyunjaya,(2003). Kinematicstructureof mechanisms

revisited,Mech. Mach. Theory, 38,279–320.

[2]. R CJohnson, (1971). Mechanical Design Synthesis with Optimization Applications,Van Nostrand Reinhold Company, New York.

[3]. R F Pryor, SGDhande, G N Sandor, (1979). On the classification and enumeration of six-link and eight-link cammodulated linkages, in:

Proceedings of the 5th World Congress on Theory of Machines and

Mechanisms, 1315–1321. [4]. F R E Crossley,(1964). The permutations of 10 link plane kinematic

chains, Antriebstechnik 3, 181.

[5]. N IManolescu, (1964). A unitary method for construction of the kinematic plane chains and plane mechanisms with different degrees

of mobility, Revue Roumaine des Sciences Techniques, Serie de

MecaniqueAppliquee 9, 1263–1313 (in French). [6]. F R E Crossley, (1965). Permutations of kinematic chains with eight

members or less from graph-theoretic view point, in: Developments in

Theoretical and Applied Mechanics, vol. 2, Pergamon Press, Oxford,

467–486.

[7]. N IManolescu, (1973). A method based on Baranov trusses and using

graph theory to find the set of planar jointed kinematic chains and mechanisms, Mech. Mach. Theory8, 3–22.

[8]. G Kiper, D Schian, (1975). The Twelve-Link Gruebler-Type

Kinematic Chains,VDI-Z, (117), 283–288. [9]. GKiper, (1979). Computer-aided type synthesis and compilation of

specific mechanisms of lowest complexity, in: Proceedings of the 5th

World Congress on Theory of Machines and Mechanisms,1097–1100.

Page 5: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

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[10]. M Mayourin, F Freudenstein, (1984). The development of an atlas of

kinematic structures of mechanisms, J. Mechanisms, Transmissions, Automat.Des. 106, 458–461.

[11]. T S Mruthyunjaya, (1984). A computerized methodology for structural

synthesis of kinematic chains: Part 1: Formulation, Mech. Mach. Theory, 19, 487–495.

[12]. T SMruthyunjaya, (1984). A computerized methodology for structural

synthesis of kinematic chains: Part 2: Application to several fully or partially known cases, Mech. Mach. Theory 19, 497–505.

[13]. T S Mruthyunjaya, (1984). A computerized methodology for structural

synthesis of kinematic chains: Part 3: Application to new case of 10-link three freedom chains, Mech. Mach. Theory 19, 507–530.

[14]. ER Tuttle, S W Peterson, (1987). Symmetry group

theory applied to kinematic chain enumeration, Proceedings of the 10th

Applied Mechanisms Conference, Vol. 2, Sec IV-B, New Orleans, LA. [15]. ER Tuttle, SW Peterson, J E, Titus, (1989). Enumeration of basic

kinematic chains using the theory of finite groups, J. Mechanisms,

Transmissions, Automat.Des. ASME Trans. 111, 498–503. [16]. TSMruthyunjaya, H R Balasubramnian, K.Vijayananda, (1992).

Computerised Structural Synthesis and Analysis of Eleven-link, Two-

freedom Kinematic Chains, Revue Roumaine des Sciences Techniques, Serie de MécaniqueAppliquée, Vol. 37, No. 2,91-106.

[17]. KVijayananda,(1994). Computer-Aided Structural Synthesis of

Linkages and Epicyclic Gear Transmissions,Ph.D Thesis, Indian Institute of Science, India.

[18]. J JUicker, ARaicu,(1975). A Method for the Recognition of

Equivalence of Kinematic Chains,Mech. Mach. Theory10,375–383. [19]. H SYan, W MHwang,(1983). A Method for the Identification of

Planar Linkage Chains,ASME Journal of Mechanisms, Transmissions

and Automation in Design.105,658–662. [20]. T S Mruthyunjaya,H R Balasubramanian, (1987). In Quest of a

Reliable and Efficient Computational Test for Detection of

Isomorphism in Kinematic Chains, Mech. Mach. Theory22(2),131–139.

!------ THIS PROGRAM READS THE STRING (For example: +A+iAm4K+A4) AND

!------ OUTPUTS THE LINK LABELS THAT ARE ADJACENT TO EACH OTHER

INTEGER*4 M

CHARACTER KCN*11, MATRIX*66, BINUM*6

OPEN(UNIT=5,FILE='12LINK.INP',STATUS='OLD',ACCESS='SEQUENTIAL')

READ(5,*) KCN ! THE STRING IS READ HERE

DO I = 1,11

M =ICHAR(KCN(I:I))

IF(M == 43)THEN !if ‘+’, set M to 0

M = 0

ELSEIF(M >48 .AND. M <58)THEN !if ‘1-9’ do not change

M = M - 48

ELSEIF(M >64 .AND. M <91)THEN !if ‘A-Z’ set to ‘10-35’ resp.

M = M - 55

ELSEIF(M >96 .AND. M <123)THEN !if ‘a-z’ set to ’36-61’ resp.

M = M - 61

ELSEIF(M == 42) THEN !if ‘*’ set to 62

M = 62

ELSEIF(M == 61) THEN !if ‘=’ set to 63

M = 63

ENDIF

BINUM = '000000'

CALL TOMATRIX(M,BINUM)

MATRIX(6*(I-1)+1:6*I) = BINUM(1:6)

ENDDO

IENT = 0

DO I = 1,11

DO J = I+1,12

IENT = IENT + 1

IF(MATRIX(IENT:IENT) == '1')THEN

WRITE(*,*) I,J ! OUTPUTS ADJACENT LINKS

ENDIF

ENDDO

ENDDO

STOP

END

!$$$$$$ =======================================================

SUBROUTINE TOMATRIX(M,BINUM)

INTEGER*4 M, IDIV, IREM

CHARACTER BINUM*6

DO J = 1,6

IDIV = M/2

IREM = MOD(M,2)

IF(IREM == 1)THEN

BINUM(7-J:7-J)= '1'

ELSE

BINUM(7-J:7-J)= '0'

ENDIF

IF(IDIV /= 0) THEN

M = IDIV

ELSE

RETURN

ENDIF

ENDDO

END

Table 4: 12–LINK, 1–DOF KINEMATIC CHAINS AND MECHANISMS

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Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 22

============================ CHAIN NUMBERS 1 – 640 =================

X42E1Ge+4+p,C fH262G8W41X,A fH26+G8+L1X,A JKo2+H884+X,A JGo2+G8W4+p,A JGo22G8844X,A J+o28G8Ga1X,A J+oI+G9+5+Z,A

K8eW2+e+3P5,D fH262G8W4+f,A fH26+G8+L+f,A JKo2+H8+C+X,A G4WGG44ICIo,G JGo22G8+C4X,A J+o28G8Ga+f,A J+o22G9+5+f,A

GKWe42CZ4+X,E fH262G8W4+Z,A fH26+G8+L+Z,A JKo2+H8+4GX,A JKo2+G8+aGX,A JGo22G8+4KX,A J+o28G8Ga+Z,A J+o22G9+5+Z,A

WK+a81Ch4+X,A fH26+Gee4+X,A fH26+G8+5Wf,A JKo2+H8+41X,A JKo2+G8+a1X,A JGo22G8+45X,A J+o28G8+qGX,A J+o2+Gf+5+f,A

WK+a81CZC+X,A fH26+GeWC+X,A fH26+G8+5WZ,A JKo2+H8+4+f,A JKo2+G8+a+f,A JGo22G8+44f,A J+o28G8+q1X,A J+o2+Gf+5+Z,A

WK+a81CZ4GX,A fH26+GeW4GX,A fH26+G8+52f,A JKo2+H8+4+Z,A JKo2+G8+a+Z,A JGo22G8+44Z,A J+o28G8+q+f,A H+a+824ICIo,G

WK+a81CZ41X,A mmab+W4I8+I,E fH26+G8+52Z,A JGoY1Ge+4+I,E JGoY+G88K+I,E JGo2+Ge844X,A J+o28G8+q+Z,A J+o2+G9G51X,A

WK+a81CZ4+f,A fH26+GeW4+f,A G6WQWK1Go4+,K JGoI+H884+X,A JGoI+G8+aGX,A JGo2+Ge+C4X,A J+o28G8+aXX,A J+o2+G9G5+f,A

WK+a81CZ4+Z,A fH26+GeW4+Z,A G4WG41CAK+p,G JGoI+H8+C+X,A JGoI+G8+a1X,A JGo2+Ge+4KX,A J+o28G8+aWf,A J+o2+G9G5+Z,A

W4+C2+P+c4j,F J4oA8H8+241,E fL26+G8+44f,A JGoI+H8+4GX,A JGoI+G8+a+f,A JGo2+Ge+45X,A J+o28G8+aWZ,A J+o2+G9+LGX,A

GGX+41Cp4GX,G fH26+G8m4GX,A fL26+G8+44Z,A JGoI+H8+41X,A JGoI+G8+a+Z,A JGo2+Ge+44f,A J+o28G8+a2f,A J+o2+G9+aXI,E

GGX+41Cp41X,G fH26+G8m41X,A fH2c+G8+4II,E JGoI+H8+4+f,A JGo22GO+a+X,A JGo2+Ge+44Z,A J+o28G8+a2Z,A J+o2+G9+L+f,A

GGX+41Cp4+f,G fH26+G8m4+f,A fH2M+G8+44f,A JGoI+H8+4+Z,A JGo22G8+i+X,A JGo2+G8GC4X,A J+o28G8+a+p,A J+o2+G9+L+Z,A

GGX+41Cp4+Z,G fH26+G8m4+Z,A fH2M+G8+44Z,A CL8mX4K2++X,K JGo22G8+aGX,A JGo2+G8G4KX,A J4o28G8+5+f,A J+o2+G9+5XX,A

WG+a81CZ4XX,H fH26+G8WKGX,A QHmWG842+II,E JGo22H884+X,A JGo22G8+a1X,A JGo2+G8G45X,A J4o28G8+5+Z,A J+o2+G9+5Wf,A

GGX+41CZ4Wf,G fH26+G8WK1X,A fH262G8+44f,A JGo22H8+C+X,A JGo22G8+a+f,A JGo2+G8G44f,A J+oI8G8+5+f,A J+o2+G9+5WZ,A

GGX+41CZ4WZ,G fH26+G8WK+f,A fH262G8+44Z,A JGo22H8+4GX,A JGo22G8+a+Z,A JGo2+G8G44Z,A J+oI8G8+5+Z,A J+o2+G9+52f,A

W4+C2+OGEMX,I fH26+G8WK+Z,A mmab+W4AG+I,E JGo22H8+41X,A JGo2+Ge8a+X,A JGo2+G8+KKX,A K+m+824ICIo,G J+o2+G9+52Z,A

W4+C2+GvQM+,H fH26+G8W4XX,A fH26+Ge+44f,A JGo22H8+4+f,A JGo2+Ge+i+X,A JGo2+G8+K5X,A J+o2AG8+51X,A J+o2+G9+5+p,A

QLmWG8K2++X,A fH26+G8W4Wf,A fH26+Ge+44Z,A JGo22H8+4+Z,A JGo2+Ge+aGX,A JGo2+G8+K4f,A J+o2AG8+5+f,A J4o2+G9+44f,A

QLmWG84A++X,A fH26+G8W4WZ,A fH26+G8GC4X,A JGo2+He84+X,A JGo2+Ge+a1X,A JGo2+G8+K4Z,A J+o2AG8+5+Z,A J4o2+G9+44Z,A

QLmWG8428+X,A fH26+G8W42f,A fH26+G8G4KX,A JGo2+He+C+X,A JGo2+Ge+a+f,A JGo2+G8+4bX,A J+o28Ge+5GX,A J+oI+G9+44f,A

QLmWG842+GX,A fH26+G8W42Z,A fH26+G8G45X,A JGo2+He+4GX,A JGo2+Ge+a+Z,A JGo2+G8+4af,A J+o28H8+4XI,E J+oI+G9+44Z,A

QLmWG842+1X,A fH26+G8W4+p,A fH26+G8G44f,A JGo2+He+41X,A JGo2+G8Gi+X,A JGo2+G8+4aZ,A J+o28Ge+5+f,A J+o22G9+44f,A

QLmWG842++f,A G4WGG4CAK+p,G fH26+G8G44Z,A JGo2+He+4+f,A JGo2+G8GaGX,A JGo2+G8+46f,A J+o28Ge+5+Z,A J+o22G9+44Z,A

QLmWG842++Z,A fL26+G8+aGX,A fH26+G8+KKX,A JGo2+He+4+Z,A JGo2+G8Ga1X,A JGo2+G8+46Z,A J+o28G8GD+X,A J+o2+Gf+44f,A

QHmWI8K2++X,J fL26+G8+a1X,A fH26+G8+K5X,A JGo2+H8GC+X,A 972Q8H+8A4+,K JGo2+G8+44p,A J+o28G8G5GX,A J+o2+Gf+44Z,A

QHmWI84A++X,A fL26+G8+a+f,A fH26+G8+K4f,A JGo2+H8G4GX,A JGo2+G8Ga+Z,A KCf+e58+4GX,A J+o28G8G51X,A H+a+414ICIo,G

QHmWI8428+X,A fL26+G8+a+Z,A fH26+G8+K4Z,A JGo2+H8G41X,A JGo2+G8+qGX,A KCf+e58+41X,A J+o28G8G5+f,A J+o2+G9G44f,A

QHmWI842+GX,A fH2c+G88K+I,E fH26+G8+4af,A JGo2+H8G4+f,A JGo2+G8+q1X,A K8f+e58GC+X,E J+o28G8G5+Z,A J+o2+G9G44Z,A

QHmWI842+1X,A fH2M+G8+aGX,A fH26+G8+4aZ,A JGo2+H8G4+Z,A JGo2+G8+q+f,A a894e54I8+X,E J+o28G8+LGX,A J+o2+G9+aII,E

QHmWI842++f,A fH2M+G8+a1X,A fH26+G8+46f,A JGo2+H8+KGX,A JGo2+G8+q+Z,A C58GX4L2W+X,K J+o28G8+L1X,A J+o2+G9+K4f,A

QHmWI842++Z,A fH2M+G8+a+f,A fH26+G8+46Z,A JGo2+H8+K1X,A JGo2+G8+aXX,A K8f+e58G4+f,A J+o28G8+L+f,A J+o2+G9+K4Z,A

QHmWG84I8+X,E fH2M+G8+a+Z,A fH26+G8+44p,A JGo2+H8+K+f,A JGo2+G8+aWf,A K8f+e58G4+Z,A J+o28G8+L+Z,A J+o2+G9+4bX,A

QHmWG84I+GX,A fH262G88a+X,A aC94e58+4GX,A JGo2+H8+K+Z,A JGo2+G8+aWZ,A K8f+e58+4+p,C J+o28G8+5XX,A J+o2+G9+4af,A

QHmWG84I+1X,A fH262G8+i+X,A aC94e58+41X,A JGo2+H8+4XX,A JGo2+G8+a2f,A J4o28G8W4+f,A J+o28G8+5Wf,A J+o2+G9+4aZ,A

QHmWG84I++f,A QHmWG842+XI,E f126+G9+aXX,J JGo2+H8+4Wf,A JGo2+G8+a2Z,A 4I8f3Wm+2c+,K J+o28G8+5WZ,A J+o2+G9+46f,A

QHmWG84I++Z,A fH262G8+a+f,A K8f+e54I8+X,E JGo2+H8+4WZ,A G4WG824ICIo,G J+oI8G8W4+f,A J+o28G8+52f,A J+o2+G9+46Z,A

QHmWG842+XX,E fH262G8+a+Z,A K4eGX4L2W+X,K JGo2+H8+42f,A JKo2+G8+51X,A J+oI8G8W4+Z,A J+o28G8+52Z,A J+o2+G9+44p,A

QHmWG842+Wf,A fH26+Ge8a+X,A Q5m+G852W+f,A JGo2+H8+42Z,A JKo2+G8+5+f,A K+m+W84ICIo,G J+o28G8+5+p,A J4o2+G8+64f,A

QHmWG842+WZ,A fH26+Ge+i+X,A Q5m+G852W+Z,A JGo2+H8+4+p,A JKo2+G8+5+Z,A J+o2AG8WC+X,A J4o28G8+44f,A J4o2+G8+64Z,A

QHmWG842++p,E mmab+W42+XI,E Q1m+I852W+f,A G4WGW84ICIo,G JGoI+G8+5GX,A J+o2AG8W4GX,A J4o28G8+44Z,A J+o22G8+64f,A

W4+C2+QKA4D,H fH26+Ge+a+f,A Q1m+I852W+Z,A JKo2+G8WC+X,A JGoY+G8+4XI,E J+o2AG8W41X,A J+oI8G8+44f,A J+o22G8+64Z,A

mqab+W4A++X,A fH26+Ge+a+Z,A X+24W4+vQM+,H JKo2+G8W4GX,A JGoI+G8+5+f,A J+o2AG8W4+f,A J+oI8G8+44Z,A J+o2+G8G64f,A

mqab+W428+X,A KKemX4K2++X,K Q1m+G85IW1X,A JKo2+G8W41X,A JGoI+G8+5+Z,A J+o2AG8W4+Z,A K+m+414ICIo,G J+o2+G8G64Z,A

mqab+W42+GX,A fH26+G8GaGX,A Q1m+G85IW+f,A JKo2+G8W4+f,A JGo22GO+5+X,A J+o28Gee4+X,A J+o2AG8+44f,A WG+a814ICIo,H

mqab+W42+1X,A fH26+G8Ga1X,A Q1m+G85IW+Z,A JKo2+G8W4+Z,A JGo22G885+X,A J+o28H8GC+I,E J+o2AG8+44Z,A J+o2+G8+6af,A

mqab+W42++f,A fH26+G8Ga+f,A Q1m+G852WXX,J JGoI+G8e4+X,A JGo22G8+D+X,A J+o28GeW4GX,A J+o28H8+4II,E J+o2+G8+6aZ,A

mqab+W42++Z,A fH26+G8Ga+Z,A Q1m+G852WWf,A JGoY+G8GC+I,E JGo22G8+5GX,A J+o28GeW41X,A J+o28Ge+44f,A J+o2+G8+64p,E

G2WG429+aXp,F fH26+G8+qGX,A Q1m+G852WWZ,A JGoI+G8W4GX,A JGo22G8+51X,A J+o28GeW4+f,A J+o28Ge+44Z,A XG2aW44IGHX,K

mmab2W4A++X,A fH26+G8+q1X,A Q1m+G852W+p,E JGoI+G8W41X,A JGo22G8+5+f,A J+o28GeW4+Z,A J+o28G8GC4X,A KWg+828+2bb,D

mmab2W428+X,A fH26+G8+q+f,A maa5+W52W+f,A JGoI+G8W4+f,A JGo22G8+5+Z,A J+o28G8mC+X,A J+o28G8G4KX,A HGYWG84IGHX,K

mmab2W42+GX,A fH26+G8+q+Z,A maa5+W52W+Z,A JGoI+G8W4+Z,A JGo2+Ge85+X,A J+o28G8m4GX,A J+o28G8G45X,A X424W44gY8X,A

mmab2W42+1X,A fH26+G8+aXX,A mWa52W52W+f,A JGo22GOW4+X,A JGo2+Ge+D+X,A J+o28G8m41X,A J+o28G8G44f,A X424W44Yg8X,A

mmab2W42++f,A fH26+G8+aWf,A mWa52W52W+Z,A JGo22G8e4+X,A JGo2+Ge+5GX,A J+o28G8m4+f,A J+o28G8G44Z,A X424W44YYOX,A

mmab2W42++Z,A fH26+G8+aWZ,A X+24W4AKA4D,H JGo22G8WC+X,A JGo2+Ge+51X,A AGu3G8++q+Z,B J+o28G8+KKX,A X424W44YY9X,A

mmab+W4I8+X,E fH26+G8+a2f,A mWa5+W5IW+f,A JGo22G8W4GX,A JGo2+Ge+5+f,A J+o28G8WKGX,A J+o28G8+K5X,A X424W44YY8f,A

mmab+W4I+GX,A fH26+G8+a2Z,A mWa5+W5IW+Z,A JGo22G8W41X,A JGo2+Ge+5+Z,A J+o28G8WK1X,A J+o28G8+K4f,A X424W44YY8Z,A

mmab+W4I+1X,A fH26+G8+a+p,A mWa5+W52WXX,J JGo22G8W4+f,A JGo2+G8GD+X,A J+o28G8WK+Z,A J+o28G8+K4Z,A X+24W45ImHX,M

mmab+W4I++f,A G4WG82CAK+p,G mWa5+W52WWf,A JGo22G8W4+Z,A JGo2+G8G5GX,A J+o28G8W4XX,A J+o28G8+4bX,A H+a+G44oY8f,G

mmab+W4I++Z,A fL26+G8+51X,A mWa5+W52WWZ,A JGo2+Gee4+X,A JGo2+G8G51X,A J+o28G8W4Wf,A J+o28G8+4af,A H+a+G44oY8Z,G

mmab+W42+XX,E fL26+G8+5+f,A mWa5+W52W+p,E JGo2+GeWC+X,A JGo2+G8G5+f,A J+o28G8W4WZ,A J+o28G8+4aZ,A WG+a819+YLL,N

mmab+W42+Wf,A fL26+G8+5+Z,A WK+i8152b81,E JGo2+GeW4GX,A JGo2+G8G5+Z,A J+o28G8W42f,A J+o28G8+46f,A H+a+G44YYef,G

mmab+W42+WZ,A fH2M+G8+5GX,A K8eW2+e+2hY,D JGo2+GeW41X,A JGo2+G8+LGX,A J+o28G8W42Z,A J+o28G8+46Z,A H+a+G44YYeZ,G

mmab+W42++p,E fH2M+G8+5+f,A GKWe4252b81,E JGo2+GeW4+f,A JGo2+G8+L1X,A J4o28G8+a+f,A J+o28G8+44p,A X+24W44YY8p,O

G4WGW8CAK+p,G fH2M+G8+5+Z,A WK+a815Ab81,A JGo2+GeW4+Z,A JGo2+G8+L+f,A J4o28G8+a+Z,A HGZ+414A8+p,L G4WGW8+miXu,G

fL26+G8WC+X,A QHmWG84AG+I,E WK+a8152j81,A JGo2+G8mC+X,A JGo2+G8+L+Z,A J+oI8G8+a+f,A J4o2+G9+a+Z,A LKi+G48WC+X,A

fL26+G8W4GX,A fH262G8+D+X,A WK+a8152bO1,A JGo2+G8m4GX,A JGo2+G8+5XX,A J+oI8G8+a+Z,A J+o22G9+a+f,A LKi+G48W4GX,A

fL26+G8W41X,A fH262G8+5+f,A WK+a8152b91,A JGo2+G8m41X,A JGo2+G8+5Wf,A K+m+G44ICIo,G Wm4YYKI44+I,E LKi+G48W41X,A

fL26+G8W4+f,A fH262G8+5+Z,A WK+a8152b89,A JGo2+G8m4+f,A JGo2+G8+5WZ,A J+o2AG8+aGX,A X+24W44ICIo,H LKi+G48W4+f,A

fL26+G8W4+Z,A fH26+Ge85+X,A WK+a8152b83,A JGo2+G8m4+Z,A JGo2+G8+52f,A J+o2AG8+a1X,A J+o2+G9GaGX,A LKi+G48W4+Z,A

fH2M+G8e4+X,A mmab+W42+II,E WG+a815Ij81,H JGo2+G8WKGX,A JGo2+G8+52Z,A J+o2AG8+a+f,A J+o2+G9Ga1X,A LGiGG48e4+X,A

fH2c+G8GC+I,E fH26+Ge+5+f,A GGX+415IbO1,G JGo2+G8WK1X,A JGo2+G8+5+p,A J+o2AG8+a+Z,A J+o2+G9Ga+f,A L4gG1+P+Y41,K

fH2M+G8W4GX,A fH26+Ge+5+Z,A GGX+415Ib91,G JGo2+G8WK+f,A G4WG414ICIo,G J+o28H88K+I,E J+o2+G9Ga+Z,A LGiGG48W4GX,A

fH2M+G8W41X,A fH26+G8GD+X,A GGX+415Ib83,G JGo2+G8WK+Z,A JKo2+G8+44f,A J+o28Ge+aGX,A J+o2+G9+aXX,E LGiGG48W41X,A

fH2M+G8W4+f,A fH26+G8G5GX,A WG+a8152bf1,H JGo2+G8W4XX,A JKo2+G8+44Z,A J+o28Ge+a1X,A J+o2+G9+aWf,A LGiGG48W4+f,A

fH2M+G8W4+Z,A fH26+G8G51X,A GGX+4152be9,G JGo2+G8W4Wf,A JGoY+G8+4II,E J+o28Ge+a+f,A J+o2+G9+aWZ,A LGiGG48W4+Z,A

fH262G8e4+X,A fH26+G8G5+f,A GGX+4152be3,G JGo2+G8W4WZ,A JGoI+G8+44f,A J+o28Ge+a+Z,A J4o2+G9+5+f,A LGi+I4OW4+X,A

fH262G8WC+X,A fH26+G8G5+Z,A W4+C2+OGAbi,I JGo2+G8W42f,A JGoI+G8+44Z,A J+o28G8Gi+X,A J4o2+G9+5+Z,A LGi+I48e4+X,A

QHmWG84I8+I,E fH26+G8+LGX,A G4WH+G4ICIo,G JGo2+G8W42Z,A JGo22GO+44X,A J+o28G8GaGX,A J+oI+G9+5+f,A LGi+I48WC+X,A

============================ CHAIN NUMBERS 641 – 1280 =================

LGi+I48W4GX,A LGi+G4e+5+f,A L+i+O48WK+f,A L+i+O48+K4f,A GGX+Y8C2D8X,A ZGG62GA+4KX,A Z+H6+GAG5+f,A Z4G68GA+5+f,A

LGi+I48W41X,A LGi+G4e+5+Z,A L+i+O48WK+Z,A L+i+O48+K4Z,A GGX+Y8C25OX,A ZGG62GA+45X,A Z+H6+GAG5+Z,A Z4G68GA+5+Z,A

LGi+I48W4+f,A LGi+G48GD+X,A L+i+O48W4XX,A L+i+O48+4bX,A GGX+Y8C259X,A ZGG62GA+44f,A Z+H6+GA+LGX,A Z+GM8GA+5+f,A

LGi+I48W4+Z,A LGi+G48G5GX,A L+i+O48W4Wf,A L+i+O48+46f,A GGX+Y8C258f,A ZGG62GA+44Z,A Z+H6+GA+L1X,A Z+GM8GA+5+Z,A

LGi+G4ee4+X,A LGi+G48G51X,A L+i+O48W4WZ,A L+i+O48+46Z,A GGX+Y8C258Z,A ZGG6+Gg844X,A Z+H6+GA+L+f,A K+m+82C25In,G

LGi+G4eWC+X,A LGi+G48G5+f,A L+i+O48W42f,A KCeW82C24GX,A GGX+W8CI5OX,G ZGG6+Gg+C4X,A Z+H6+GA+L+Z,A Z+G6AGA+51X,A

Page 7: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 23

LGi+G4eW4GX,A LGi+G48G5+Z,A L+i+O48W42Z,A KCeW82C241X,A GGX+W8CI59X,G ZGG6+Gg+4KX,A Z+H6+GA+5XX,A Z+G6AGA+5+f,A

LGi+G4eW41X,A LGi+G48+LGX,A L+i+O48W4+p,A K8eWA2C24GX,A GGX+W8C2LOX,G ZGG6+Gg+45X,A Z+H6+GA+5Wf,A Z+G6AGA+5+Z,A

LGi+G4eW4+f,A LGi+G48+L1X,A L4i+O48+a+f,A K8eWA2C241X,A GGX+W8C2L9X,G ZGG6+Gg+44f,A Z+H6+GA+5WZ,A Z+G68Gg85+X,A

LGi+G4eW4+Z,A LGi+G48+L+f,A L4i+O48+a+Z,A X+24W41Gs4B,M G4WG825314j,L ZGG6+Gg+44Z,A Z+H6+GA+52f,A Z+G68Gg+D+X,A

LGi+G48mC+X,A LGi+G48+L+Z,A L+iGO48+a+f,A K8eW82CI4GX,A 84GH221164j,P H+a+G4BK5+Z,G Z+H6+GA+52Z,A Z+G68Gg+5GX,A

LGi+G48m4GX,A LGi+G48+5XX,A L+iGO48+a+Z,A K8eW82CI41X,A G2W82+aII4U,K ZGG6+GAG4KX,A Z+H6+GA+5+p,A Z+G68Gg+51X,A

LGi+G48m41X,A LGi+G48+5Wf,A K+m+G4+miXu,G K8eW82CI4+f,A G8WW8252WYU,M ZGG6+GAG45X,A Z4H6+GA+44f,A Z+G68Gg+5+f,A

LGi+G48m4+f,A LGi+G48+5WZ,A L+i+Q48+aGX,A K8eW82CI4+Z,A GGX+W8C25AZ,G ZGG6+GAG44f,A Z4H6+GA+44Z,A Z+G68Gg+5+Z,A

LGi+G48m4+Z,A 36IQ9HG+24+,K L+i+Q48+a1X,A K4eG1+S264X,K 9T3Y+GH14+1,A ZGG6+GAG44Z,A G2W841C25In,G Z+G68GAGD+X,A

LGi+G48WKGX,A G4WG41+miXu,G L+i+Q48+a+f,A K8eW82C24Wf,A 9T3Y+G11C+1,A ZGG6+GA+KKX,A Z+HM+GA+44f,A Z+G68GAG5GX,A

LGi+G48WK1X,A LKi+G48+44f,A L+i+Q48+a+Z,A K8eW82C24WZ,A 9T3Y+G114G1,A ZGG6+GA+K5X,A Z+HM+GA+44Z,A Z+G68GAG51X,A

LGi+G48WK+f,A LKi+G48+44Z,A K4eGX4OX241,K K8eW82C24+p,L 9T3Y+G11411,A ZGG6+GA+K4f,A Z+H62GA844X,A Z+G68GAG5+f,A

LGi+G48WK+Z,A L4gG1+O+24B,K L+i+O4e+aGX,A L4i+G49+5+f,A I+e+2+c1OdW,G ZGG6+GA+K4Z,A Z+H62GA+C4X,A Z+G68GAG5+Z,A

LGi+G48W4XX,A LGiGG48+44f,A L+i+O4e+a1X,A L4i+G49+5+Z,A 972Q8H+8C+W,K ZGG6+GA+4bX,A Z+H62GA+4KX,A Z+G68GA+LGX,A

LGi+G48W4Wf,A LGiGG48+44Z,A L+i+O4e+a+f,A L+iGG49+5+f,A 9P3Y2G11C+1,A ZGG6+GA+4af,A Z+H62GA+45X,A Z+G68GA+L1X,A

LGi+G48W4WZ,A LGi+I4O+44X,A L+i+O4e+a+Z,A L+iGG49+5+Z,A 9P3Y2G114G1,A ZGG6+GA+4aZ,A Z+H62GA+44f,A Z+G68GA+L+f,A

LGi+G48W42f,A LGi+I48844X,A L+i+O48Gi+X,A L+i+I49+5+f,A 9P3Y2G11411,A ZGG6+GA+46f,A Z+H62GA+44Z,A Z+G68GA+L+Z,A

LGi+G48W42Z,A LGi+I48+C4X,A L+i+O48GaGX,A L+i+I49+5+Z,A 9P3Y2G114+9,A ZGG6+GA+46Z,A Z+H6+Gg844X,A Z+G68GA+5XX,A

LGi+G48W4+p,A LGi+I48+4KX,A L+i+O48Ga1X,A L+i+G4f+5+f,A 972Q+G18i+W,K ZGG6+GA+44p,A Z+H6+Gg+C4X,A Z+G68GA+5Wf,A

G4WGG4+miXu,G LGi+I48+45X,A L+i+O48Ga+f,A L+i+G4f+5+Z,A 9P3Y+G1H4G1,A 3aM2GKG+24X,A Z+H6+Gg+4KX,A Z+G68GA+5WZ,A

LKi+G48+aGX,A LGi+I48+44f,A L+i+O48Ga+Z,A H+a+82+miXu,G 9P3Y+G1H411,A 3aM2GK++A4X,A Z+H6+Gg+45X,A Z+G68GA+52f,A

LKi+G48+a1X,A LGi+I48+44Z,A L+i+O48+qGX,A L+i+G49G51X,A 9P3Y+G1H4+9,A G8WX+G4XaCJ,G Z+H6+Gg+44f,A Z+G68GA+52Z,A

LKi+G48+a+f,A LGi+G4e844X,A L+i+O48+q1X,A L+i+G49G5+f,A 972Q+G+8E+W,K 3aM2GK++24f,A Z+H6+Gg+44Z,A Z+G68GA+5+p,A

LKi+G48+a+Z,A LGi+G4e+C4X,A L+i+O48+q+f,A L+i+G49G5+Z,A 9P3Y+G114W9,A 3aM2GK++24Z,A H+a+G4B4L+Z,G Z4G68GA+44f,A

L4gG1+OX241,K LGi+G4e+4KX,A L+i+O48+q+Z,A K4eG1+S224L,K 9P3Y+G114W3,A 2IHAeM++4+M,L Z+H6+GAG4KX,A Z4G68GA+44Z,A

LGiGG48+aGX,A LGi+G4e+45X,A L+i+O48+aXX,A L+i+G49+L1X,A 9P3Y+G114+J,L 3WM2IK++A4X,A Z+H6+GAG45X,A Z+GM8GA+44f,A

LGiGG48+a1X,A LGi+G4e+44f,A L+i+O48+aWf,A L+i+G49+L+f,A G4WG82C25In,G 3WM2IK++25X,A Z+H6+GAG44f,A Z+GM8GA+44Z,A

LGiGG48+a+f,A LGi+G4e+44Z,A L+i+O48+aWZ,A L+i+G49+L+Z,A ZKG6+GA+51X,A 3WM2IK++24f,A Z+H6+GAG44Z,A K+m+41C25In,G

LGiGG48+a+Z,A LGi+G48GC4X,A L+i+O48+a2f,A L+i+G49+5XX,A ZKG6+GA+5+f,A 3WM2IK++24Z,A Z+H6+GA+KKX,A Z+G6AGA+44f,A

LGi+I4O+a+X,A LGi+G48G4KX,A L+i+O48+a2Z,A L+i+G49+5Wf,A ZKG6+GA+5+Z,A 2IHA8I424+M,L Z+H6+GA+K5X,A Z+G6AGA+44Z,A

LGi+I488a+X,A LGi+G48G45X,A L+i+O48+a+p,A L+i+G49+5WZ,A 3WM2GK++2af,D 3WM2GK+G25X,A Z+H6+GA+K4f,A Z+G68Gg844X,A

LGi+I48+i+X,A LGi+G48G44f,A L4i+O48+5+f,A L+i+G49+52f,A ZGGM+GA+D+X,A 3WM2GK+G24f,A Z+H6+GA+K4Z,A Z+G68Gg+C4X,A

LGi+I48+aGX,A LGi+G48G44Z,A L4i+O48+5+Z,A L+i+G49+52Z,A ZGGM+GA+5GX,A 3WM2GK+G24Z,A Z+H6+GA+4bX,A Z+G68Gg+4KX,A

LGi+I48+a1X,A LGi+G48+KKX,A L+iGO48+5+f,A L+i+G49+5+p,A ZGGM+GA+51X,A 3WM2GK++26f,D Z+H6+GA+4af,A Z+G68Gg+45X,A

LGi+I48+a+f,A LGi+G48+K5X,A L+iGO48+5+Z,A L4i+G49+44f,A ZGGM+GA+5+f,A 3WM2GK++26Z,D Z+H6+GA+4aZ,A Z+G68Gg+44f,A

LGi+I48+a+Z,A LGi+G48+K4f,A K+m+82+miXu,G L4i+G49+44Z,A ZGGM+GA+5+Z,A 3WM2GK++24p,D Z+H6+GA+46f,A Z+G68Gg+44Z,A

LGi+G4e8a+X,A LGi+G48+K4Z,A L+i+Q48+51X,A L+iGG49+44f,A ZGG62GA85+X,A Z4I6+G9+Y51,A Z+H6+GA+46Z,A Z+G68GAGC4X,A

LGi+G4e+i+X,A LGi+G48+4bX,A L+i+Q48+5+f,A L+iGG49+44Z,A ZGG62GA+D+X,A Z4I6+G9+Y43,A Z+H6+GA+44p,A Z+G68GAG4KX,A

LGi+G4e+aGX,A LGi+G48+4af,A L+i+Q48+5+Z,A L+i+I49+44f,A ZGG62GA+5GX,A Z+I62G98Y41,A Z4G68GAW4+f,A Z+G68GAG45X,A

LGi+G4e+a1X,A LGi+G48+4aZ,A K4eGX4O+24L,K L+i+I49+44Z,A ZGG62GA+51X,A Z+I62G9+g41,A Z4G68GAW4+Z,A Z+G68GAG44f,A

LGi+G4e+a+f,A LGi+G48+46f,A L+i+O4e+51X,A L+i+G4f+44f,A ZGG62GA+5+f,A Z+I62G9+YK1,A Z+GM8GAW4+f,A Z+G68GAG44Z,A

LGi+G4e+a+Z,A LGi+G48+46Z,A L+i+O4e+5+f,A L+i+G4f+44Z,A ZGG62GA+5+Z,A Z+I62G9+Y51,A Z+GM8GAW4+Z,A Z+G68GA+KKX,A

LGi+G48Gi+X,A LGi+G48+44p,A L+i+O4e+5+Z,A H+a+41+miXu,G ZGG6+Gg85+X,A Z+I62G9+Y49,A K+m+W8C25In,G Z+G68GA+K5X,A

LGi+G48GaGX,A KKf+a58+4GX,A L+i+O48GD+X,A L+i+G49G44f,A ZGG6+Gg+D+X,A Z+I62G9+Y43,A Z+G6AGAW4GX,A Z+G68GA+K4f,A

LGi+G48Ga1X,A KKf+a58+41X,A L+i+O48G5GX,A L+i+G49G44Z,A ZGG6+Gg+5GX,A X+24W4B4aXI,H Z+G6AGAW41X,A Z+G68GA+K4Z,A

LGi+G48Ga+f,A K2e8Y4f+a+X,K L+i+O48G51X,A K4eG1+S224B,K ZGG6+Gg+51X,A Z+I6+G9GYK1,A Z+G6AGAW4+f,A Z+G68GA+4bX,A

LGi+G48Ga+Z,A aG8ae54I8+X,E L+i+O48G5+f,A L+i+G49+K4f,A ZGG6+Gg+5+f,A Z+I6+G9GY51,A Z+G6AGAW4+Z,A Z+G68GA+4af,A

LGi+G48+qGX,A CH8We54I8+X,E L+i+O48G5+Z,A L+i+G49+K4Z,A ZGG6+Gg+5+Z,A Z+I6+G9GY49,A Z+G68GgW4GX,A Z+G68GA+4aZ,A

LGi+G48+q1X,A KGf+a58G4+f,A L+i+O48+LGX,A L+i+G49+4bX,A H+a+G4BK5+f,G Z+I6+G9GY43,A Z+G68GgW41X,A Z+G68GA+46f,A

LGi+G48+q+f,A KGf+a58G4+Z,A L+i+O48+L1X,A L+i+G49+4af,A ZGG6+GAG5GX,A Z+I6+G9+Yb1,E Z+G68GAmC+X,A Z+G68GA+46Z,A

LGi+G48+q+Z,A KGf+a58+4+p,C L+i+O48+L+f,A L+i+G49+4aZ,A ZGG6+GAG51X,A Z+I6+G9+Ya9,A Z+G68GAm4GX,A Z+G68GA+44p,A

LGi+G48+aXX,A L4i+O48W4+f,A L+i+O48+L+Z,A L+i+G49+46f,A ZGG6+GAG5+f,A Z+I6+G9+Ya3,A Z+G68GAm41X,A KCeW8242A8X,A

LGi+G48+aWf,A L4i+O48W4+Z,A L+i+O48+5XX,A L+i+G49+46Z,A ZGG6+GAG5+Z,A Z+I6+G9+Y4J,E J+o+1+GOQ4A,K KCeW824229X,A

LGi+G48+aWZ,A L+iGO48W4+f,A L+i+O48+5Wf,A L+i+G49+44p,A ZGG6+GA+LGX,A Z4H6+GA+5+f,A Z+G68GAm4+Z,A K4eG1+L2WHX,K

LGi+G48+a2f,A L+iGO48W4+Z,A L+i+O48+5WZ,A H4YG1+KYW+j,L ZGG6+GA+L1X,A Z4H6+GA+5+Z,A Z+G68GAWKGX,A K8eW824I2OX,A

LGi+G48+a2Z,A K+m+W8+miXu,G L+i+O48+52f,A X42AAHG8I41,E ZGG6+GA+L+f,A G2W882C25In,G Z+G68GAWK1X,A K8eW824I29X,A

LGi+G48+a+p,A L+i+Q48WC+X,A L+i+O48+52Z,A L+i+G48G64f,A ZGG6+GA+L+Z,A Z+HM+GA+51X,A Z+G68GAW4XX,A K8eW824I28f,A

G4WG82+miXu,G L+i+Q48W4GX,A L+i+O48+5+p,A L+i+G48G64Z,A ZGG6+GA+5XX,A Z+HM+GA+5+f,A Z+G68GAW4Wf,A K8eW824I28Z,A

LKi+G48+51X,A L+i+Q48W41X,A CH8W3+m8Ac+,K K4eG1+O+2cB,K ZGG6+GA+5Wf,A Z+HM+GA+5+Z,A Z+G68GAW4WZ,A K4eG1+K22LX,K

LKi+G48+5+f,A L+i+Q48W4+f,A L+iGO48+44f,A L+i+G48+6af,D ZGG6+GA+5WZ,A Z+H62GA85+X,A Z+G68GAW42f,A K8eW82422ef,A

LKi+G48+5+Z,A L+i+Q48W4+Z,A L+iGO48+44Z,A L+i+G48+6aZ,D ZGG6+GA+52f,A Z+H62GA+D+X,A Z+G68GAW42Z,A K8eW82422eZ,A

L4gG1+O+24L,K L+i+O4ee4+X,A K+m+41+miXu,G L+i+G48+66f,D ZGG6+GA+52Z,A Z+H62GA+5GX,A J4o2+G9+Y51,A K8eW824228p,L

LGiGG48+51X,A K4eGX4P+Y41,K L+i+Q48+44f,A L+i+G48+66Z,D ZGG6+GA+5+p,A Z+H62GA+51X,A J4o2+G9+Y43,A Z4G6+IA+a+f,A

LGiGG48+5+f,A L+i+O4eW4GX,A L+i+Q48+44Z,A K8eWG48+2Ra,D G4WG41C25In,G Z+H62GA+5+f,A J+o22G9+Y51,A Z4G6+IA+a+Z,A

LGiGG48+5+Z,A L+i+O4eW41X,A K4eGX4O+24B,K GKX+X8C258X,A ZKG6+GA+44f,A Z+H62GA+5+Z,A J+o22G9+Y43,A Z+GM+IA+a+f,A

LGi+I4O+5+X,A L+i+O4eW4+f,A L+i+O4e+44f,A GKX+W8S258X,A ZKG6+GA+44Z,A Z+H6+Gg85+X,A J+o2+G9Gg41,E Z+GM+IA+a+Z,A

LGi+I4885+X,A L+i+O4eW4+Z,A L+i+O4e+44Z,A GKX+W8CA58X,A 3WM2GK++2aZ,D Z+H6+Gg+D+X,A J+o2+G9GYK1,A I+e+G4C25In,G

LGi+I48+D+X,A L+i+O48mC+X,A L+i+O48GC4X,A GKX+W8C2D8X,A ZGGM+GA+C4X,A Z+H6+Gg+5GX,A J+o2+G9GY51,A Z+G6+Ig+aGX,A

LGi+I48+5GX,A L+i+O48m4GX,A L+i+O48G4KX,A GKX+W8C25OX,A ZGGM+GA+4KX,A Z+H6+Gg+51X,A J+o2+G9GY49,A Z+G6+Ig+a1X,A

LGi+I48+5+f,A L+i+O48m41X,A L+i+O48G45X,A GKX+W8C259X,A ZGGM+GA+45X,A Z+H6+Gg+5+f,A J+o2+G9GY43,A Z+G6+Ig+a+f,A

LGi+G4e85+X,A L+i+O48m4+f,A L+i+O48G44f,A GKX+W8C258f,A ZGGM+GA+44f,A Z+H6+Gg+5+Z,A J+o2+G9+Yb1,E H2Y9+W+vQ4+,K

LGi+G4e+D+X,A L+i+O48m4+Z,A L+i+O48G44Z,A GKX+W8C258Z,A ZGGM+GA+44Z,A H+a+G4B4L+f,G J+o2+G9+Ya9,A Z+G6+IAGi+X,A

LGi+G4e+5GX,A L+i+O48WKGX,A L+i+O48+KKX,A G8WYGK8+2Ra,D ZGG62GA844X,A Z+H6+GAG5GX,A J+o2+G9+Ya3,A Z+G6+IAGaGX,A

LGi+G4e+51X,A L+i+O48WK1X,A L+i+O48+K5X,A GGX+Y8CA58X,A ZGG62GA+C4X,A Z+H6+GAG51X,A J+o2+G9+Y4J,E Z+G6+IAGa1X,A

============================= CHAIN NUMBERS 1281 – 1920 =================

Z+G6+IA+qGX,A Z+G6+GB+5Wf,A Z+G6+GA+66f,A 1W61Ke25G+Z,B XG24W46c+Wf,A K8ma++A51f1,G OHW1+eA+a+p,A O1W18egW41X,B

Z+G6+IA+q1X,A Z+G6+GB+5WZ,A Z+G6+GA+66Z,A aG8ae58+4+U,C XG24W46c+WZ,A K8ma++A51e9,G G4WG822TT+W,G O1W18egW4+f,B

Z+G6+IA+q+Z,A Z+G6+GB+52f,A Z+G6+GA+64p,A XG2aY46E++X,A XG24W46c+2f,A M+u4++52aXI,E OLW1+eA+51X,A O1W18egW4+Z,B

Z+G6+IA+aXX,A Z+G6+GB+52Z,A ej5A4I42++1,E 1W61KeY5+GX,B XG24W46c+2Z,A K8ma++A51A9,G OLW1+eA+5+f,A O1W18eAmC+X,B

Z+G6+IA+aWf,A Z+G6+GB+5+p,A I+e+G44gI5a,G 1W61KeY5+1X,B XG24W46c++p,A K8ma++A51A3,G OLW1+eA+5+Z,A O1W18eAm4GX,B

Z+G6+IA+aWZ,A Z4G6+GB+44f,A ej524I42+11,A 1W61KeY5++f,B GmZ4++A15IC,G K8ma++A518J,G G6WQ+G115Ie,D O1W18eAm41X,B

Z+G6+IA+a2f,A Z4G6+GB+44Z,A GMWwGO1+WY+,K 1W61KeY5++Z,B 1a61Ge251+f,A G4WGW82TT+W,G OHWH+eA+51X,A O1W18eAm4+f,B

Z+G6+IA+a2Z,A Z+GM+GB+44f,A ef526I428+1,A XG2aW46M8+X,E 1a61Ge251+Z,A OLW1+eAWC+X,A OHWH+eA+5+f,A O1W18eAm4+Z,B

Z4G6+IA+5+f,A Z+GM+GB+44Z,A ef526I42+11,A XG2aW46M++f,A 1W61Ie251GX,E OLW1+eAW4GX,A OHWH+eA+5+Z,A O1W18eAWKGX,B

Z4G6+IA+5+Z,A Z+G62GB+44f,A ef524I4I8+1,E WG+a819GhC1,H 1W64KAC2+XI,E OLW1+eAW41X,A OHW12eA85+X,A O1W18eAWK1X,B

Z+GM+IA+5+f,A Z+G62GB+44Z,A ef524I4I+11,A 1W61Ke25+Wf,B 1W61Ie251+f,B OLW1+eAW4+f,A OHW12eA+D+X,A O1W18eAWK+f,B

Z+GM+IA+5+Z,A Z+G6+Gh+44f,A ef524I4I++9,A 1W61Ke25+WZ,B 1W61Ie251+Z,B OLW1+eAW4+Z,A OHW12eA+5GX,A O1W18eAWK+Z,B

Z+G62IA+5+f,A Z+G6+Gh+44Z,A ef524I42+X1,E XG2aW466++p,E +6+P1WIKI4K,K G6WQ+G445Ie,D OHW12eA+51X,A O1W18eAW4XX,B

Z+G62IA+5+Z,A H+a+41C25In,G ef524I42+W9,A WG+a811GmpA,M 1W61GeY511X,B OHWH+eAWC+X,A OHW12eA+5+f,A O1W18eAW4Wf,B

I+e+82C25In,G Z+G6+GBG44f,A I4e+4169XC1,A +O1YKI1Cq+1,B 1W61GeY51+f,B OHWH+eAW4GX,A OHW12eA+5+Z,A O1W18eAW4WZ,B

Page 8: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 24

Z+G6+Ig+51X,A Z+G6+GBG44Z,A I4e+4161XS1,A HCYW821fa+1,A 1W61GeY51+Z,B OHWH+eAW41X,A OHW1+eg85+X,A O1W18eAW42f,B

Z+G6+Ig+5+f,A Z+G6+GB+KKX,A I+e+6169XC1,A +O1YKI14qG1,B 1W61Ge2L1GX,B OHWH+eAW4+f,A OHW1+eg+D+X,A O1W18eAW42Z,B

Z+G6+Ig+5+Z,A Z+G6+GB+K5X,A I+e+6161XS1,A +O1YKI14q11,B 1W61Ge2b+XI,E OHWH+eAW4+Z,A OHW1+eg+5GX,A O1W18eAW4+p,B

Z+G6+IAGD+X,A Z+G6+GB+K4f,A G8WX1WK2+Hp,L +O1YKI14q+9,B 1W61Ge2L1+f,B OHW12eAe4+X,A OHW1+eg+51X,A +A+g4H224qO,D

Z+G6+IAG5GX,A Z+G6+GB+K4Z,A 8WI1G+G8B3E,P +O1YKI14q+3,B 1W61Ge2L1+Z,B OHW12eAWC+X,A OHW1+eg+5+f,A O1W1Ie9+YK1,B

Z+G6+IAG51X,A Z+G6+GB+4bX,A I+e+4161Xi3,G K2e8Y4e+4+U,C +O1YGK111QC,D OHW12eAW4GX,A OHW1+eg+5+Z,A O1W1Ie9+Y51,B

Z+G6+IAG5+f,A Z+G6+GB+4af,A 4G9+a5+88HU,Q H8YWA21fa+1,A 1W61Ge25H1X,B OHW12eAW41X,A OHW1+eAGD+X,A O1W1Ie9+Y49,B

Z+G6+IAG5+Z,A Z+G6+GB+4aZ,A 8T1YWK114G1,A +O1YKIX4aG1,B 1W61Ge25H+f,B OHW12eAW4+f,A OHW1+eAG5GX,A O1W1Ie9+Y43,B

Z+G6+IA+LGX,A Z+G6+GB+46f,A 8T1YWK11411,A +O1YKIX4a11,B 1W61Ge25H+Z,B OHW12eAW4+Z,A OHW1+eAG51X,A O1W1Ge9Gg41,E

Z+G6+IA+L1X,A Z+G6+GB+46Z,A a+86+G4Z+YU,M +O1YKIX4a+9,B +O1Y8I+WBA9,D I+e+W83baGH,G OHW1+eAG5+f,A O1W1Ge9GYK1,B

Z+G6+IA+L+f,A Z+G6+GB+44p,A 8P1YYK11C+1,A +O1YKIX4a+3,B 1W61Ge251Wf,B OHW1+egWC+X,A OHW1+eAG5+Z,A O1W1Ge9GY51,B

Z+G6+IA+L+Z,A Z4G6+GA15+f,A 8P1YYK114G1,A H4YG1+HOy+W,K 1W61Ge251WZ,B OHW1+egW4GX,A OHW1+eA+LGX,A O1W1Ge9GY49,B

Z+G6+IA+5XX,A Z4G6+GA15+Z,A 8P1YYK11411,A H8YW821naG1,A 1W61Ge2512f,B OHW1+egW41X,A OHW1+eA+L1X,A O1W1Ge9GY43,B

Z+G6+IA+5Wf,A Z+GM+GA15+f,A 87+QWK18i+W,K H4YG1+GOU4W,K 1W61Ge2512Z,B OHW1+egW4+f,A OHW1+eA+L+f,A O1W1Ge9+Yb1,E

Z+G6+IA+5WZ,A Z+GM+GA15+Z,A 8P1YWK1H4G1,A +O1YKI14aW9,B 1W61Ge251+p,B OHW1+egW4+Z,A OHW1+eA+L+Z,A O1W1Ge9+Ya9,B

Z+G6+IA+52f,A Z+G62GA15+f,A 8P1YWK1H411,A +O1YKI14aW3,B GmZ4++A15GS,G OHW1+eAmC+X,A OHW1+eA+5XX,A O1W1Ge9+Ya3,B

Z+G6+IA+52Z,A Z+G62GA15+Z,A 8P1YWK1H4+9,A H8YW821Xa+J,L 1a61Ge25+4f,A OHW1+eAm4GX,A OHW1+eA+5Wf,A O1W1Ge9+Y4J,E

Z+G6+IA+5+p,A Z+G6+Gg15+f,A 87+QWK+8E4W,K W4+C2+GnBCI,H 1a61Ge25+4Z,A OHW1+eAm41X,A OHW1+eA+5WZ,A O5W18eA+5+f,A

Z4G6+IA+44f,A Z+G6+Gg15+Z,A 8P1YWK114W9,A HKYWG86E++X,A 1W64KAC2+II,E OHW1+eAm4+f,A OHW1+eA+52f,A O5W18eA+5+Z,A

Z4G6+IA+44Z,A Z+G6+GAH5+f,A 8P1YWK114W3,A 1W62KK45GGX,B 1W61Ie25+4f,B OHW1+eAm4+Z,A OHW1+eA+52Z,A +6+Q2GX15Ie,D

Z+GM+IA+44f,A Z+G6+GAH5+Z,A 9b628G22W+f,A 1W62KK45G1X,B 1W61Ie25+4Z,B OHW1+eAWKGX,A OHW1+eA+5+p,A O1W1AeA+51X,B

Z+GM+IA+44Z,A GWY+82C25In,G 9b628G22W+Z,A 1W62KK45G+f,B +6+P1WIKI4A,K OHW1+eAWK1X,A G4WG412TT+W,G O1W1AeA+5+f,B

Z+G62IA+44f,A Z+G6+GA1L1X,A 9X6I8G22W+f,A 1W62KK45G+Z,B 1W61GeY5+4f,B OHW1+eAWK+f,A OLW1+eA+44f,A O1W1AeA+5+Z,B

Z+G62IA+44Z,A Z+G6+GA1L+f,A 9X6I8G22W+Z,A KGeWa68+4+U,C 1W61GeY5+4Z,B OHW1+eAWK+Z,A OLW1+eA+44Z,A O1W18eg85+X,B

I+e+41C25In,G Z+G6+GA1L+Z,A K+m+G44AH4U,G HGYWI86E++X,A 1W61Ge2b+II,E OHW1+eAW4XX,A G6WQ+G+WbIe,D O1W18eg+D+X,B

Z+G6+Ig+44f,A Z+G6+GA15XX,A 9X62AG22W+f,A 1W62KKa5+GX,B 1W61Ge2L+4f,B OHW1+eAW4Wf,A OHWH+eA+44f,A O1W18eg+5GX,B

Z+G6+Ig+44Z,A Z+G6+GA15Wf,A 9X62AG22W+Z,A 1W62KKa5+1X,B 1W61Ge2L+4Z,B OHW1+eAW4WZ,A OHWH+eA+44Z,A O1W18eg+51X,B

Z+G6+IAGC4X,A Z+G6+GA15WZ,A 87+QWK+fA4+,K 1W62KKa5++f,B +O1YGK+WXQC,D OHW1+eAW42f,A OHW12eA844X,A O1W18eg+5+f,B

Z+G6+IAG4KX,A Z+G6+GA152f,A 9X628GY2W+f,A 1W62KKa5++Z,B 1W61Ge25G4f,B OHW1+eAW42Z,A OHW12eA+C4X,A O1W18eg+5+Z,B

Z+G6+IAG45X,A Z+G6+GA152Z,A 9X628GY2W+Z,A HGYWG86M8+X,E 1W61Ge25G4Z,B OHW1+eAW4+p,A OHW12eA+4KX,A O1W18eAGD+X,B

Z+G6+IAG44f,A Z+G6+GA15+p,A 9X628G2Ie+X,A HGYWG86M++f,A +O1Y8I+WbA3,D G4WGG42TT+W,G OHW12eA+45X,A O1W18eAG5GX,B

Z+G6+IAG44Z,A Z4G6+GA144f,A 9X628G2IW1X,A HGYWG866+XX,E 1W61Ge25+af,B OLW1+eA+aGX,A OHW12eA+44f,A O1W18eAG51X,B

Z+G6+IA+KKX,A Z4G6+GA144Z,A 9X628G2IW+f,A 1W62KK45+Wf,B 1W61Ge25+aZ,B OLW1+eA+a1X,A OHW12eA+44Z,A O1W18eAG5+f,B

Z+G6+IA+K5X,A Z+GM+GA144f,A 9X628G2IW+Z,A 1W62KK45+WZ,B 1W61Ge25+6f,B OLW1+eA+a+f,A OHW1+eg844X,A O1W18eAG5+Z,B

Z+G6+IA+K4f,A Z+GM+GA144Z,A 9X628G22m1X,A HGYWG866++p,E 1W61Ge25+6Z,B OLW1+eA+a+Z,A OHW1+eg+C4X,A O1W18eA+LGX,B

Z+G6+IA+K4Z,A Z+G62GA144f,A 9X628G22m+f,A G4WGW89+ZCJ,G 1W61Ge25+4p,B G6WQ+G225Ie,D OHW1+eg+4KX,A O1W18eA+L1X,B

Z+G6+IA+4bX,A Z+G62GA144Z,A 9X628G22m+Z,A 4O9YGK++1QC,D X424W476W+f,A OHWH+eA+aGX,A OHW1+eg+45X,A O1W18eA+L+f,B

Z+G6+IA+4af,A Z+G6+Gg144f,A 9X628G22WWf,A XK24W46c+GX,A W4+C2+P+c4U,F OHWH+eA+a1X,A OHW1+eg+44f,A O1W18eA+L+Z,B

Z+G6+IA+4aZ,A Z+G6+Gg144Z,A 9X628G22WWZ,A XK24W46c+1X,A a+86+G661Af,S OHWH+eA+a+f,A OHW1+eg+44Z,A O1W18eA+5XX,B

Z+G6+IA+46f,A Z+G6+GAH44f,A 9X628G22W2f,A XK24W46c++f,A a+86+G661AZ,S OHWH+eA+a+Z,A OHW1+eAGC4X,A O1W18eA+5Wf,B

Z+G6+IA+46Z,A Z+G6+GAH44Z,A 9X628G22W2Z,A XK24W46c++Z,A WG+a819+Zj1,I OHW12eA8a+X,A OHW1+eAG4KX,A O1W18eA+5WZ,B

Z+G6+IA+44p,A GWY+41C25In,G 9X628G22W+p,A b+A6+G+OQ4A,K H+a+G476WWf,G OHW12eA+aGX,A OHW1+eAG45X,A O1W18eA+52f,B

8GH181+Wbef,P Z+G6+GA1K4f,A 8T1Y+G534G1,A XG2aW46M8+I,E X+24W476W+p,H OHW12eA+a1X,A OHW1+eAG44f,A O1W18eA+52Z,B

H+a+G4B45Wf,G Z+G6+GA1K4Z,A 8T1Y+G53411,A XG2KW46c+GX,A W4+C2+OGCXU,T OHW12eA+a+f,A OHW1+eAG44Z,A O1W18eA+5+p,B

H+a+G4B45WZ,G Z+G6+GA14bX,A 8P1Y2G534G1,A XG2KW46c+1X,A i994W44AG+I,E OHW12eA+a+Z,A OHW1+eA+KKX,A O5W18eA+44f,A

H+a+G4B452f,G Z+G6+GA14af,A 8P1Y2G53411,A XG2KW46c++f,AKCma++Q5181,A I+e+W83ba1H,G OHW1+eA+K5X,A O5W18eA+44Z,A

H+a+G4B452Z,G Z+G6+GA14aZ,A X+24W44Z+YU,M XG2KW46c++Z,A KCma++A5981,A OHW1+eg+i+X,A OHW1+eA+K4f,A +6+Q2GWWbIe,D

H+a+G4B45+p,G Z+G6+GA146f,A 8P1Y+G5J4G1,A KGf+4142+YU,L KCma++A51O1,A OHW1+eg+aGX,A OHW1+eA+K4Z,A O1W1AeA+44f,B

Z4G6+GB+5+f,A Z+G6+GA146Z,A 8P1Y+G5J411,A H4YG1+HOw4+,K KCma++A5191,A OHW1+eg+a1X,A OHW1+eA+4bX,A O1W1AeA+44Z,B

Z4G6+GB+5+Z,A Z+G6+GA144p,A 8P1Y+G5J4+9,A XG24Y46c+GX,A KCma++A5189,A OHW1+eg+a+f,A OHW1+eA+4af,A O1W18eg844X,B

Z+GM+GB+5+f,A Z4G6+GA+64f,A 87+Q+G4AE4W,K XG24Y46c+1X,A G6WU+G8+5Ie,D OHW1+eg+a+Z,A OHW1+eA+4aZ,A O1W18eg+C4X,B

Z+GM+GB+5+Z,A Z4G6+GA+64Z,A 8P1Y+G534W9,A XG24Y46c++f,A K8ma2+AD181,A OHW1+eAGi+X,A OHW1+eA+46f,A O1W18eg+4KX,B

Z+G62GB+5+f,A Z+GM+GA+64f,A 8P1Y+G534W3,A XG24Y46c++Z,A K8ma2+A5981,A OHW1+eAGaGX,A OHW1+eA+46Z,A O1W18eg+45X,B

Z+G62GB+5+Z,A Z+GM+GA+64Z,A C58G1+L2WYX,K L+g1+W+OQ4A,K K8ma2+A51O1,A OHW1+eAGa1X,A OHW1+eA+44p,A O1W18eg+44f,B

Z+G6+Gh+5+f,A Z+G62GA+64f,A C98W824I15X,A HGYWG86M8+I,E K8ma2+A5191,A OHW1+eAGa+f,A O5W18eAW4+f,A O1W18eg+44Z,B

Z+G6+Gh+5+Z,A Z+G62GA+64Z,A C58G1+K22cX,K XG24W4cc+GX,A K8ma2+A5189,A OHW1+eAGa+Z,A O5W18eAW4+Z,A O1W18eAGC4X,B

H+a+82C25In,G Z+G6+Gg+64f,A 26GQXKG+24A,K XG24W4cc+1X,A K8ma2+A5183,A OHW1+eA+qGX,A +6+Q2Ga45Ie,D O1W18eAG4KX,B

Z+G6+GBG51X,A Z+G6+Gg+64Z,A W2+K2+OGCXp,R XG24W4cc++f,AGAWi++4YWYS,L OHW1+eA+q1X,A O1W1AeAWC+X,B O1W18eAG45X,B

Z+G6+GBG5+f,A Z+G6+GAG64f,A W4+C2+P+ZCJ,H XG24W4cc++Z,A K8ma++AL1O1,G OHW1+eA+q+f,A O1W1AeAW4GX,B O1W18eAG44f,B

Z+G6+GBG5+Z,A Z+G6+GAG64Z,A 1W61KeI5G+X,B XG24W46s8+X,A K8ma++AL191,G OHW1+eA+q+Z,A O1W1AeAW41X,B O1W18eAG44Z,B

Z+G6+GB+LGX,A Z+G6+GA+M4f,A 1W61Ke2DG+X,B XG24W46s++f,A K8ma++AL189,G OHW1+eA+aXX,A O1W1AeAW4+f,B O1W18eA+KKX,B

Z+G6+GB+L1X,A Z+G6+GA+M4Z,A XK2aW46E++X,A XG24W46s++Z,A K8ma++A5HO1,G OHW1+eA+aWf,A O1W1AeAW4+Z,B O1W18eA+K5X,B

Z+G6+GB+L+f,A GGX+41C25In,G 1W61Ke25GGX,B XG24W46cG+f,A K8ma++A5H91,G OHW1+eA+aWZ,A +O1Y4H445OH,D O1W18eA+K4f,B

Z+G6+GB+L+Z,A Z+G6+GA+6af,A 1W61Ke25G1X,B XG24W46cG+Z,A K8ma++A5H89,G OHW1+eA+a2f,A O1W18egWC+X,B O1W18eA+K4Z,B

Z+G6+GB+5XX,A Z+G6+GA+6aZ,A 1W61Ke25G+f,B GGX+419GZS1,G K8ma++A5H83,G OHW1+eA+a2Z,A O1W18egW4GX,B O1W18eA+4bX,B

============================ CHAIN NUMBERS 1921 – 2560 =================

O1W18eA+4af,B O1W1+gA+K4Z,B O1W1+eA15Wf,B OHW1+eeY4GX,A OHW1+e825XX,A O1W1Ae8244f,B O5W1+e92a+Z,A O1W12e8344Z,B

O1W18eA+4aZ,B O1W1+gA+4bX,B O1W1+eA15WZ,B OHW1+eeY41X,A OHW1+e825Wf,A O1W1Ae8244Z,B O1W12e92a+f,B O1W1+ee344f,B

O1W18eA+46f,B O1W1+gA+4af,B O1W1+eA152f,B OHW1+eeY4+f,A OHW1+e825WZ,A O1W18ee2C4X,B O1W12e92a+Z,B O1W1+ee344Z,B

O1W18eA+46Z,B O1W1+gA+4aZ,B O1W1+eA152Z,B OHW1+eeY4+Z,A OHW1+e8252f,A O1W18ee24KX,B O1W1+ef2a+f,B O1W1+e8J44f,B

O1W18eA+44p,B O1W1+gA+46f,B O1W1+eA15+p,B OHW1+e8oC+X,A OHW1+e8252Z,A O1W18ee245X,B O1W1+ef2a+Z,D O1W1+e8J44Z,B

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+O1Y6H445O1,B O5W1+eB+a+Z,A O1W12eA144Z,B OHW1+e8o4+Z,A OLW1+e8244Z,A O1W18e8I4KX,B O1W1+e9Ia+f,B O1W1+e834bX,B

+O1Y6H44591,B O1W12eB+a+f,B O1W1+eg144f,B OHW1+e8YKGX,A G6WQ+G+WaMe,D O1W18e8I45X,B O1W1+e9Ia+Z,B O1W1+e834af,B

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+C+o2GaAC+f,L O1W1+eh+a+f,B O1W1+eAH44f,B OHW1+e8YK+f,A OHWH+e8244Z,A O1W18e8I44Z,B O1W1+e92q1X,B O1W1+e8346f,B

+O1Y4H4K5O1,B O1W1+eh+a+Z,B O1W1+eAH44Z,B OHW1+e8YK+Z,A OHW12e8A44X,A O1W18e82KKX,B O1W1+e92q+f,B O1W1+e8346Z,B

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+O1Y4H4K583,B O1W1+eBGaGX,B O1W1+eA1K4f,B OHW1+e8Y4Wf,A OHW12e8245X,A O1W18e82K4f,B O1W1+e92aXX,B O5W1+e8264f,A

+O1Y4H445f1,D O1W1+eBGa1X,B O1W1+eA1K4Z,B OHW1+e8Y4WZ,A OHW12e8244f,A O1W18e82K4Z,B O1W1+e92aWf,B O5W1+e8264Z,A

82G91211+pi,U O1W1+eBGa+f,B O1W1+eA14bX,B OHW1+e8Y42f,A OHW12e8244Z,A O1W18e824bX,B O1W1+e92aWZ,B O1W12e8264f,B

+O1Y4H445A3,D O1W1+eBGa+Z,B O1W1+eA14af,B OHW1+e8Y42Z,A OHW1+ee2C4X,A O1W18e824af,B O1W1+e92a2f,B O1W12e8264Z,B

O5W1+gA+a+f,A O1W1+eB+qGX,B O1W1+eA14aZ,B OHW1+e8Y4+p,A OHW1+ee24KX,A O1W18e824aZ,B O1W1+e92a2Z,B O1W1+ee264f,B

O5W1+gA+a+Z,A O1W1+eB+q1X,B O1W1+eA146f,B G4WGG42TS4W,G OHW1+ee245X,A O1W18e8246f,B O1W1+e92a+p,B O1W1+ee264Z,B

O1W12gA+a+f,B O1W1+eB+q+f,B O1W1+eA146Z,B OLW1+e82aGX,A OHW1+ee244f,A O1W18e8246Z,B O5W1+e925+f,A O1W1+e8I64f,B

O1W12gA+a+Z,B O1W1+eB+q+Z,B O1W1+eA144p,B OLW1+e82a1X,A OHW1+ee244Z,A O1W18e8244p,B O5W1+e925+Z,A O1W1+e8I64Z,B

+6+Q1GI25Ie,D O1W1+eB+aXX,B O5W1+eA+64f,A OLW1+e82a+f,A OHW1+e8IC4X,A +C+oYKX14+f,L O1W12e925+f,B O1W1+e82M4f,B

O1W1+gg+aGX,B O1W1+eB+aWf,B O5W1+eA+64Z,A OLW1+e82a+Z,A OHW1+e8I4KX,A +O1Y6H2A581,B O1W12e925+Z,B O1W1+e82M4Z,B

Page 9: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 25

O1W1+gg+a1X,B O1W1+eB+aWZ,B O1W12eA+64f,B G6WQ+G224Me,D OHW1+e8I45X,A +O1Y6H22D81,B O1W1+ef25+f,B +6+Q8I+WaMe,D

O1W1+gg+a+f,B O1W1+eB+a2f,B O1W12eA+64Z,B OHWH+e82aGX,A OHW1+e8I44f,A +O1Y6H225O1,B O1W1+ef25+Z,B O1W1+e826af,B

O1W1+gg+a+Z,B O1W1+eB+a2Z,B O1W1+eg+64f,B OHWH+e82a1X,A OHW1+e8I44Z,A +O1Y6H22591,B +6+QWO114Me,D O1W1+e826aZ,B

O1W1+gAGi+X,B O1W1+eB+a+p,B O1W1+eg+64Z,B OHWH+e82a+f,A OHW1+e82KKX,A +O1Y6H22583,B O1W1+e9I51X,B O1W1+e8266f,B

O1W1+gAGaGX,B O5W1+eB+5+f,A O1W1+eAG64f,B OHWH+e82a+Z,A OHW1+e82K5X,A +C+o2Gb34+f,L O1W1+e9I5+f,B O1W1+e8266Z,B

O1W1+gAGa1X,B O5W1+eB+5+Z,A O1W1+eAG64Z,B OHW12e82aGX,A OHW1+e82K4f,A +O1Y4H2I5O1,B O1W1+e9I5+Z,B O1W1+e8264p,B

O1W1+gAGa+f,B O1W12eB+5+f,B O1W1+eA+M4f,B OHW12e82a1X,A OHW1+e82K4Z,A +O1Y4H2I591,B O1W1+e92LGX,B G4WG821OyXW,G

O1W1+gAGa+Z,B O1W12eB+5+Z,B O1W1+eA+M4Z,B OHW12e82a+f,A OHW1+e824bX,A +O1Y4H2I583,B O1W1+e92L1X,B GCWqW44IG+f,L

O1W1+gA+qGX,B O1W1+eh+5+f,B +6+Q8I+WbIe,D OHW12e82a+Z,A OHW1+e824af,A +O1Y4H225f1,D O1W1+e92L+f,B SLe+W48+5+f,A

O1W1+gA+q1X,B O1W1+eh+5+Z,B O1W1+eA+6af,B I+e+G43ba1H,G OHW1+e824aZ,A 82G911+WWpi,U O1W1+e92L+Z,B SLe+W48+5+Z,A

O1W1+gA+q+f,B +6+QWO115Ie,D O1W1+eA+6aZ,B OHW1+ee2aGX,A OHW1+e8246f,A O5W1+g825+f,A O1W1+e925XX,B K6eS++4228i,L

O1W1+gA+q+Z,B O1W1+eBG51X,B O1W1+eA+66f,B OHW1+ee2a1X,A OHW1+e8246Z,A O5W1+g825+Z,A O1W1+e925Wf,B SHeWW48+4XI,E

O1W1+gA+aXX,B O1W1+eBG5+f,B O1W1+eA+66Z,B OHW1+ee2a+f,A OHW1+e8244p,A O1W12g825+f,B O1W1+e925WZ,B SHeGW48+5+f,A

O1W1+gA+aWf,B O1W1+eBG5+Z,B O1W1+eA+64p,B OHW1+ee2a+Z,A +A+g4H444MO,D O1W12g825+Z,B O1W1+e9252f,B SHeGW48+5+Z,A

O1W1+gA+aWZ,B O1W1+eB+LGX,B i994W442+II,E OHW1+e8Ii+X,A O1W1Ie8X2K1,B +6+Q1GH14Me,D O1W1+e9252Z,B iH8aW44AG+I,E

O1W1+gA+a2f,B O1W1+eB+L1X,B KCma++A4B81,A OHW1+e8IaGX,A O1W1Ie8X251,B O1W1+ge251X,B O1W1+e925+p,B SHe+Y48+D+X,A

O1W1+gA+a2Z,B O1W1+eB+L+f,B KCma++A43O1,A OHW1+e8Ia1X,A O1W1Ie8X249,B O1W1+ge25+f,B O5W1+e9244f,A SHe+Y48+5+f,A

O1W1+gA+a+p,B O1W1+eB+L+Z,B KCma++A4391,A OHW1+e8Ia+f,A O1W1Ie8X243,B O1W1+ge25+Z,B O5W1+e9244Z,A SHe+Y48+5+Z,A

O5W1+gA+5+f,A O1W1+eB+5XX,B KCma++A4389,A OHW1+e8Ia+Z,A O1W1Ge8nA41,E O1W1+g8ID+X,B O1W12e9244f,B iH8aW442+II,E

O5W1+gA+5+Z,A O1W1+eB+5Wf,B G6WU+G8+4Me,D OHW1+e82qGX,A O1W1Ge8n2K1,B O1W1+g8I5GX,B O1W12e9244Z,B SHe+W4e+5+f,A

O1W12gA+5+f,B O1W1+eB+5WZ,B K8ma2+AC381,A OHW1+e82q1X,A O1W1Ge8n251,B O1W1+g8I51X,B O1W1+ef244f,B SHe+W4e+5+Z,A

O1W12gA+5+Z,B O1W1+eB+52f,B K8ma2+A4B81,A OHW1+e82q+f,A O1W1Ge8n249,B O1W1+g8I5+f,B O1W1+ef244Z,B SHe+W48GD+X,A

+6+Q1GH15Ie,D O1W1+eB+52Z,B K8ma2+A43O1,A OHW1+e82q+Z,A O1W1Ge8n243,B O1W1+g8I5+Z,B +6+QWO+WaMe,D SHe+W48G5GX,A

O1W1+gg+51X,B O1W1+eB+5+p,B K8ma2+A4391,A OHW1+e82aXX,A O1W1Ge8X2b1,E O1W1+g82LGX,B O1W1+e9I44f,B SHe+W48G51X,A

O1W1+gg+5+f,B O5W1+eB+44f,A K8ma2+A4389,A OHW1+e82aWf,A O1W1Ge8X2a9,B O1W1+g82L1X,B O1W1+e9I44Z,B SHe+W48G5+f,A

O1W1+gg+5+Z,B O5W1+eB+44Z,A K8ma2+A4383,A OHW1+e82aWZ,A O1W1Ge8X2a3,B O1W1+g82L+f,B O1W1+e92KKX,B SHe+W48G5+Z,A

O1W1+gAGD+X,B O1W12eB+44f,B GAWi++4YY8S,L OHW1+e82a2f,A O1W1Ge8X24J,E O1W1+g82L+Z,B O1W1+e92K5X,B SHe+W48+LGX,A

O1W1+gAG5GX,B O1W12eB+44Z,B K8ma++AK391,G OHW1+e82a2Z,A O5W18e825+f,A O1W1+g825XX,B O1W1+e92K4f,B SHe+W48+L1X,A

O1W1+gAG51X,B O1W1+eh+44f,B K8ma++AK389,G OHW1+e82a+p,A O5W18e825+Z,A O1W1+g825Wf,B O1W1+e92K4Z,B SHe+W48+L+f,A

O1W1+gAG5+f,B O1W1+eh+44Z,B K8ma++A4JO1,G G4WG822TS4W,G +6+Q2GX14Me,D O1W1+g825WZ,B O1W1+e924bX,B SHe+W48+L+Z,A

O1W1+gAG5+Z,B +6+QWO+WbIe,D K8ma++A4J91,G OLW1+e8251X,A O1W1Ae8251X,B O1W1+g8252f,B O1W1+e924af,B SHe+W48+5XX,A

O1W1+gA+LGX,B O1W1+eBG44f,B K8ma++A4J89,G OLW1+e825+f,A O1W1Ae825+f,B O1W1+g8252Z,B O1W1+e924aZ,B SHe+W48+5Wf,A

O1W1+gA+L1X,B O1W1+eBG44Z,B M+u4++52aII,E OLW1+e825+Z,A O1W1Ae825+Z,B O1W1+g825+p,B O1W1+e9246f,B SHe+W48+5WZ,A

O1W1+gA+L+f,B O1W1+eB+KKX,B K8ma++A43f1,G G6WQ+G114Me,D O1W18ee2D+X,B O5W1+g8244f,A O1W1+e9246Z,B SHe+W48+52f,A

O1W1+gA+L+Z,B O1W1+eB+K5X,B K8ma++A43e9,G OHWH+e8251X,A O1W18ee25GX,B O5W1+g8244Z,A O1W1+e9244p,B SHe+W48+52Z,A

O1W1+gA+5XX,B O1W1+eB+K4f,B K8ma++A43A9,G OHWH+e825+f,A O1W18ee251X,B O1W12g8244f,B O5W1+e835+f,A SHe+W48+5+p,A

O1W1+gA+5Wf,B O1W1+eB+K4Z,B K8ma++A43A3,G OHWH+e825+Z,A O1W18ee25+f,B O1W12g8244Z,B O5W1+e835+Z,A KWo4++8L5+f,G

O1W1+gA+5WZ,B O1W1+eB+4bX,B K8ma++A438J,G OHW12e8A5+X,A O1W18ee25+Z,B +6+Q1GGWaMe,D O1W12e835+f,B KWo4++8L5+Z,G

O1W1+gA+52f,B O1W1+eB+4af,B G4WGW82TS4W,G OHW12e825GX,A O1W18e8ID+X,B O1W1+ge244f,B O1W12e835+Z,B S1e+Y49+a+f,A

O1W1+gA+52Z,B O1W1+eB+4aZ,B OLW1+e8YC+X,A OHW12e8251X,A O1W18e8I5GX,B O1W1+ge244Z,B O1W1+ee35+f,B X+24W41OyXW,H

O1W1+gA+5+p,B O1W1+eB+46f,B OLW1+e8Y4GX,A OHW12e825+f,A O1W18e8I51X,B O1W1+g8IC4X,B O1W1+ee35+Z,B S1e+W49GaGX,A

O5W1+gA+44f,A O1W1+eB+46Z,B OLW1+e8Y41X,A OHW12e825+Z,A O1W18e8I5+f,B O1W1+g8I4KX,B O1W1+e8J5+f,B KWo4++85L+f,G

O5W1+gA+44Z,A O1W1+eB+44p,B OLW1+e8Y4+f,A OHW1+ee2D+X,A O1W18e8I5+Z,B O1W1+g8I45X,B O1W1+e8J5+Z,B KWo4++85L+Z,G

O1W12gA+44f,B O5W1+eA15+f,A OLW1+e8Y4+Z,A OHW1+ee25GX,A O1W18e82LGX,B O1W1+g8I44f,B +6+QGK114Me,D S1e+W49+aXX,J

O1W12gA+44Z,B O5W1+eA15+Z,A G6WQ+G444Me,D OHW1+ee251X,A O1W18e82L1X,B O1W1+g8I44Z,B O1W1+e83L1X,B S1e+W49+aWf,A

+6+Q1GGWbIe,D O1W12eA15+f,B OHWH+e8YC+X,A OHW1+ee25+f,A O1W18e82L+f,B O1W1+g82KKX,B O1W1+e83L+f,B S1e+W49+a+p,E

O1W1+gg+44f,B O1W12eA15+Z,B OHWH+e8Y4GX,A OHW1+ee25+Z,A O1W18e82L+Z,B O1W1+g82K5X,B O1W1+e83L+Z,B i584W452W+f,A

O1W1+gg+44Z,B O1W1+eg15+f,B OHWH+e8Y41X,A OHW1+e8ID+X,A O1W18e825XX,B O1W1+g82K4f,B O1W1+e835XX,B i584W452W+Z,A

O1W1+gAGC4X,B O1W1+eg15+Z,B OHWH+e8Y4+f,A OHW1+e8I5GX,A O1W18e825Wf,B O1W1+g82K4Z,B O1W1+e835Wf,B i184Y452W+f,A

O1W1+gAG4KX,B O1W1+eAH5+f,B OHWH+e8Y4+Z,A OHW1+e8I51X,A O1W18e825WZ,B O1W1+g824bX,B O1W1+e835WZ,B i184Y452W+Z,A

O1W1+gAG45X,B O1W1+eAH5+Z,B OHW12e8g4+X,A OHW1+e8I5+f,A O1W18e8252f,B O1W1+g824af,B O1W1+e8352f,B X+24W498ob1,H

O1W1+gAG44f,B +6+QGK115Ie,D OHW12e8Y4GX,A OHW1+e8I5+Z,A O1W18e8252Z,B O1W1+g824aZ,B O1W1+e8352Z,B GKXKW44A8+E,L

O1W1+gAG44Z,B O1W1+eA1L1X,B OHW12e8Y41X,A OHW1+e82LGX,A O1W18e825+p,B O1W1+g8246f,B O1W1+e835+p,B i184W45IW+f,A

O1W1+gA+KKX,B O1W1+eA1L+f,B OHW12e8Y4+f,A OHW1+e82L1X,A O5W18e8244f,A O1W1+g8246Z,B O5W1+e8344f,A i184W45IW+Z,A

O1W1+gA+K5X,B O1W1+eA1L+Z,B OHW12e8Y4+Z,A OHW1+e82L+f,A O5W18e8244Z,A O1W1+g8244p,B O5W1+e8344Z,A i184W452WXX,J

O1W1+gA+K4f,B O1W1+eA15XX,B I+e+G43baGH,G OHW1+e82L+Z,A +6+Q2GWWaMe,D O5W1+e92a+f,A O1W12e8344f,B i184W452WWf,A

============================ CHAIN NUMBERS 2561 – 3200 =================

i184W452WWZ,A S1f+Y+A+51X,A GOXaW44oWG1,A S1e+W49GY49,A S1eGW+B+5+f,A S5e+W+A+64f,A S1e+8+i25+f,A GeYa++66IGX,G

i184W452W+p,E S1f+Y+A+5+f,A GOXaW44oW11,A S1e+W49GY43,A S1eGW+B+5+Z,A S5e+W+A+64Z,A S1e+8+i25+Z,A GeYa++66I1X,G

G4WG821OTXW,G S1f+Y+A+5+Z,A GOXaW44oW+9,A S1e+W49+Yb1,E S1e+Y+B+5+f,A S1eGW+A+64f,A S1e+8+CID+X,A GeYa++66I+f,G

SLe+W+A+51X,A S1f+W+g85+X,A GOXaW44oW+3,A S1e+W49+Ya9,A S1e+Y+B+5+Z,A S1eGW+A+64Z,A S1e+8+CI5GX,A GeYa++66I+Z,G

SLe+W+A+5+f,A S1f+W+g+D+X,A G6WSW44II4W,K S1e+W49+Ya3,A S1e+W+h+5+f,A S1e+Y+A+64f,A S1e+8+CI51X,A 4K9G92S24+6,L

SLe+W+A+5+Z,A S1f+W+g+5GX,A GOXaW44YWW9,A S1e+W49+Y4J,E S1e+W+h+5+Z,A S1e+Y+A+64Z,A S1e+8+CI5+f,A 1W61Kb8G2GX,B

SHeGW+A+5GX,A S1f+W+g+51X,A GOXaW44YWW3,A S5e+W2A+5+f,A H+a+821OTXW,G S1e+W+g+64f,A S1e+8+CI5+Z,A 1W61Kb8G21X,B

SHeGW+A+51X,A S1f+W+g+5+f,A S5e+e+A+5+f,A S5e+W2A+5+Z,A S1e+W+BG51X,A S1e+W+g+64Z,A S1e+8+C2LGX,A 1W61Kb8G2+f,B

SHeGW+A+5+f,A S1f+W+g+5+Z,A S5e+e+A+5+Z,A S1eGW2A+5+f,A S1e+W+BG5+f,A S1e+W+AG64f,A S1e+8+C2L1X,A 1W61Kb8G2+Z,B

SHeGW+A+5+Z,A S1f+W+AGD+X,A S1eGe+A+5+f,A S1eGW2A+5+Z,A S1e+W+BG5+Z,A S1e+W+AG64Z,A S1e+8+C2L+f,A 4eAWmC8+2XX,D

SHe+Y+A85+X,A S1f+W+AG5GX,A S1eGe+A+5+Z,A S1e+Y2A+5+f,A S1e+W+B+LGX,A S1e+W+A+M4f,A S1e+8+C2L+Z,A 4eAWmC8+2Wf,D

SHe+Y+A+D+X,A S1f+W+AG51X,A K+m+821OTXW,G S1e+Y2A+5+Z,A S1e+W+B+L1X,A S1e+W+A+M4Z,A S1e+8+C25XX,A 4eAWmC8+2WZ,D

SHe+Y+A+5GX,A S1f+W+AG5+f,A S1e+g+A+51X,A I+e+821OTXW,G S1e+W+B+L+f,A GGX+411OTXW,G S1e+8+C25Wf,A 4eAWmC8+22f,D

SHe+Y+A+51X,A S1f+W+AG5+Z,A S1e+g+A+5+f,A S1e+W2g+51X,A S1e+W+B+L+Z,A S1e+W+A+6af,A S1e+8+C25WZ,A 4eAWmC8+22Z,D

SHe+Y+A+5+f,A S1f+W+A+LGX,A S1e+g+A+5+Z,A S1e+W2g+5+f,A S1e+W+B+5XX,A S1e+W+A+6aZ,A S1e+8+C252f,A 4eAWmC8+2+p,D

SHe+Y+A+5+Z,A S1f+W+A+L1X,A S1e+e+g85+X,A S1e+W2g+5+Z,A S1e+W+B+5Wf,A S1e+W+A+66f,A S1e+8+C252Z,A WG+a814AAcA,M

SHe+W+g85+X,A S1f+W+A+L+f,A S1e+e+g+D+X,A S1e+W2AGD+X,A S1e+W+B+5WZ,A S1e+W+A+66Z,A S1e+8+C25+p,A 4YAA8I++3YA,D

SHe+W+g+D+X,A S1f+W+A+L+Z,A S1e+e+g+5GX,A S1e+W2AG5GX,A S1e+W+B+52f,A S1e+W+A+64p,A X42CW41Xc41 , 5CAY4H194+1,A

SHe+W+g+5GX,A S1f+W+A+5XX,A S1e+e+g+51X,A S1e+W2AG51X,A S1e+W+B+52Z,A O5W1+YC25GX,A H2Y882+mq+Q,L 5CAY4H11C+1,A

SHe+W+g+51X,A S1f+W+A+5Wf,A S1e+e+g+5+f,A S1e+W2AG5+f,A S1e+W+B+5+p,A O5W1+YC251X,A H4Y8G81Xc41,E 5CAY4H114G1,A

SHe+W+g+5+f,A S1f+W+A+5WZ,A S1e+e+g+5+Z,A S1e+W2AG5+Z,A S5e+W+B+44f,A O5W1+YC25+f,A +O1XGe24MK1,B 5CAY4H11411,A

SHe+W+g+5+Z,A S1f+W+A+52f,A S1e+e+AGD+X,A S1e+W2A+LGX,A S5e+W+B+44Z,A O5W1+YC25+Z,A +O1XGe24M51,B 5CAY4H114+9,A

SHe+W+AGD+X,A S1f+W+A+52Z,A S1e+e+AG5GX,A S1e+W2A+L1X,A S1eGW+B+44f,A O1W12YC25GX,B WG+a819+Wpo,I 5CAY4H114+3,A

SHe+W+AG5GX,A S1f+W+A+5+p,A S1e+e+AG51X,A S1e+W2A+L+f,A S1eGW+B+44Z,A O1W14YC24XI,E O5W1+WD25+f,A 4I8ef5O+4+K,Q

SHe+W+AG51X,A S5f+W+A+44f,A S1e+e+AG5+f,A S1e+W2A+L+Z,A S1e+Y+B+44f,A O1W12YC25+f,B O5W1+WD25+Z,A 58AY6H194+1,A

SHe+W+AG5+f,A S5f+W+A+44Z,A S1e+e+AG5+Z,A S1e+W2A+5XX,A S1e+Y+B+44Z,A O1W12YC25+Z,B O1W12WD25+f,B 58AY6H11C+1,A

SHe+W+AG5+Z,A G2W8411OTXW,G S1e+e+A+LGX,A S1e+W2A+5Wf,A S1e+W+h+44f,A +6+Q1GH16MW,D O1W12WD25+Z,B 58AY6H114G1,A

SHe+W+A+LGX,A S1fGW+A+44f,A S1e+e+A+L1X,A S1e+W2A+5WZ,A S1e+W+h+44Z,A O1W1+Yi251X,B O1W1+Wj25+f,B 58AY6H11411,A

SHe+W+A+L1X,A S1fGW+A+44Z,A S1e+e+A+L+f,A S1e+W2A+52f,A H+a+411OTXW,G O1W1+Yi25+f,B O1W1+Wj25+Z,B 58AY6H114+9,A

SHe+W+A+L+f,A S1f+Y+A844X,A S1e+e+A+L+Z,A S1e+W2A+52Z,A S1e+W+BG44f,A O1W1+Yi25+Z,B +6+QWO116MW,D 58AY6H114+3,A

SHe+W+A+L+Z,A S1f+Y+A+C4X,A S1e+e+A+5XX,A S1e+W2A+5+p,A S1e+W+BG44Z,A O1W1+YCID+X,B O1W1+WDI51X,B 54AI2GX8i+W,K

SHe+W+A+5XX,A S1f+Y+A+4KX,A S1e+e+A+5Wf,A S5e+W2A+44f,A S1e+W+B+KKX,A O1W1+YCI5GX,B O1W1+WDI5+f,B 58AY4H1H4G1,A

SHe+W+A+5Wf,A S1f+Y+A+45X,A S1e+e+A+5WZ,A S5e+W2A+44Z,A S1e+W+B+K5X,A O1W1+YCI51X,B O1W1+WDI5+Z,B 58AY4H1H411,A

Page 10: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 26

SHe+W+A+5WZ,A S1f+Y+A+44f,A S1e+e+A+52f,A S1eGW2A+44f,A S1e+W+B+K4f,A O1W1+YCI5+f,B O1W1+WD2LGX,B 58AY4H1H4+9,A

SHe+W+A+52f,A S1f+Y+A+44Z,A S1e+e+A+52Z,A S1eGW2A+44Z,A S1e+W+B+K4Z,A O1W1+YCI5+Z,B O1W1+WD2aXI,E 58AY4H1H4+3,A

SHe+W+A+52Z,A S1f+W+g844X,A S1e+e+A+5+p,A S1e+Y2A+44f,A S1e+W+B+4bX,A O1W1+YC2LGX,B O1W1+WD2L+f,B 54AI2GW8E4W,K

SHe+W+A+5+p,A S1f+W+g+C4X,A S5e+e+A+44f,A S1e+Y2A+44Z,A S1e+W+B+4af,A O1W1+YC2L1X,B O1W1+WD2L+Z,B 58AY4H114W9,A

G4WG411OTXW,G S1f+W+g+4KX,A S5e+e+A+44Z,A I+e+411OTXW,G S1e+W+B+4aZ,A O1W1+YC2L+f,B O1W1+WD25XX,B 58AY4H114W3,A

SLe+W+A+44f,A S1f+W+g+45X,A S1eGe+A+44f,A S1e+W2g+44f,A S1e+W+B+46f,A O1W1+YC2L+Z,B O1W1+WD25Wf,B 58AY4H114+J,L

SLe+W+A+44Z,A S1f+W+g+44f,A S1eGe+A+44Z,A S1e+W2g+44Z,A S1e+W+B+46Z,A O1W1+YC25XX,B O1W1+WD25WZ,B 34C2Wg2g++X,A

SHeGW+A+4KX,A S1f+W+g+44Z,A K+m+411OTXW,G S1e+W2AGC4X,A S1e+W+B+44p,A O1W1+YC25Wf,B O1W1+WD252f,B 2aKH2WX8g4+,K

SHeGW+A+45X,A S1f+W+AGC4X,A S1e+g+A+44f,A S1e+W2AG4KX,A S5e+W+A15+f,A O1W1+YC25WZ,B O1W1+WD252Z,B 34C2Wg2Y+GX,A

SHeGW+A+44f,A S1f+W+AG4KX,A S1e+g+A+44Z,A S1e+W2AG45X,A S5e+W+A15+Z,A O1W1+YC252f,B O1W1+WD25+p,B 34C2Wg2Y+1X,A

SHeGW+A+44Z,A S1f+W+AG45X,A S1e+e+g844X,A S1e+W2AG44f,A S1eGW+A15+f,A O1W1+YC252Z,B O5W1+WD244f,A 34C2Wg2Y++f,A

SHe+Y+A844X,A S1f+W+AG44f,A S1e+e+g+C4X,A S1e+W2AG44Z,A S1eGW+A15+Z,A O1W1+YC25+p , O5W1+WD244Z,A 34C2Wg2Y++Z,A

SHe+Y+A+C4X,A S1f+W+AG44Z,A S1e+e+g+4KX,A S1e+W2A+KKX,A S1e+Y+A15+f,A O5W1+YC24KX,A O1W12WD244f,B +I19AYa2+Y6,L

SHe+Y+A+4KX,A S1f+W+A+KKX,A S1e+e+g+45X,A S1e+W2A+K5X,A S1e+Y+A15+Z,A O5W1+YC245X,A O1W12WD244Z,B 3+C2Yg2Y8+X,B

SHe+Y+A+45X,A S1f+W+A+K5X,A S1e+e+g+44f,A S1e+W2A+K4f,A S1e+W+g15+f,A O5W1+YC244f,A O1W1+Wj244f,B 3+C2Yg2Y+GX,B

SHe+Y+A+44f,A S1f+W+A+K4f,A S1e+e+g+44Z,A S1e+W2A+K4Z,A S1e+W+g15+Z,A O5W1+YC244Z,A O1W1+Wj244Z,B 3+C2Yg2Y+1X,B

SHe+Y+A+44Z,A S1f+W+A+K4Z,A S1e+e+AGC4X,A S1e+W2A+4bX,A S1e+W+AH5+f,A O1W14YC24II,E +6+QWO+WcMW,D 3+C2Yg2Y++f,B

SHe+W+g844X,A S1f+W+A+4bX,A S1e+e+AG4KX,A S1e+W2A+4af,A S1e+W+AH5+Z,A O1W12YC244f,B O1W1+WDI44f,B 3+C2Yg2Y++Z,B

SHe+W+g+C4X,A S1f+W+A+4af,A S1e+e+AG45X,A S1e+W2A+4aZ,A GWY+821OTXW,G O1W12YC244Z,B O1W1+WDI44Z,B +m321GK41qO,D

SHe+W+g+4KX,A S1f+W+A+4aZ,A S1e+e+AG44f,A S1e+W2A+46f,A S1e+W+A1L1X,A +6+Q1GGWcMW,D O1W1+WD2aII,E 3+C2WgYY8+X,B

SHe+W+g+45X,A S1f+W+A+46f,A S1e+e+AG44Z,A S1e+W2A+46Z,A S1e+W+A1L+f,A O1W1+Yi244f,B O1W1+WD2K4f,B 3+C2WgYY+GX,B

SHe+W+g+44f,A S1f+W+A+46Z,A S1e+e+A+KKX,A S1e+W2A+44p,A S1e+W+A1L+Z,A O1W1+Yi244Z,B O1W1+WD2K4Z,B 3+C2WgYY+1X,B

SHe+W+g+44Z,A S1f+W+A+44p,A S1e+e+A+K5X,A S5e+W+B+a+f,A S1e+W+A15XX,A O1W1+YCIC4X,B O1W1+WD24bX,B 3+C2WgYY++f,B

SHe+W+AGC4X,A K2e8G48+1iJ,D S1e+e+A+K4f,A S5e+W+B+a+Z,A S1e+W+A15Wf,A O1W1+YCI4KX,B O1W1+WD24af,B 3+C2WgYY++Z,B

SHe+W+AG4KX,A K4m+X81Xc41,A S1e+e+A+K4Z,A S1eGW+B+a+f,A S1e+W+A15WZ,A O1W1+YCI45X,B O1W1+WD24aZ,B 3+C2Wg2o8+X,B

SHe+W+AG45X,A K4m+W8HXc41,A S1e+e+A+4bX,A S1eGW+B+a+Z,A S1e+W+A152f,A O1W1+YCI44f,B O1W1+WD246f,B 3+C2Wg2o+GX,B

SHe+W+AG44f,A K4m+W81fc41,A S1e+e+A+4af,A S1e+Y+B+a+f,A S1e+W+A152Z,A O1W1+YCI44Z,B O1W1+WD246Z,B 3+C2Wg2o+1X,B

SHe+W+AG44Z,A K4m+W81Xk41,A S1e+e+A+4aZ,A S1e+Y+B+a+Z,A S1e+W+A15+p,A O1W1+YC2KKX,B O1W1+WD244p,B 3+C2Wg2o++f,B

SHe+W+A+KKX,A K4m+W81XcK1,A S1e+e+A+46f,A S1e+W+h+a+f,A S5e+W+A144f,A O1W1+YC2K5X,B O1W1+Wi264f,B 3+C2Wg2o++Z,B

SHe+W+A+K5X,A K4m+W81Xc51,A S1e+e+A+46Z,A S1e+W+h+a+Z,A S5e+W+A144Z,A O1W1+YC2K4f,B O1W1+Wi264Z,B 3+C2Wg2YGGX,B

SHe+W+A+K4f,A G2WAGK8+1iJ,D S1e+e+A+44p,A H+a+G41OTXW,G S1eGW+A144f,A O1W1+YC2K4Z,B S1e+2+C264f,A 3+C2Wg2YG1X,B

SHe+W+A+K4Z,A K+m+Y81fc41,A GSXY+GK4581,A S1e+W+BGaGX,A S1eGW+A144Z,A O1W1+YC24bX,B O1W1+WCI64f,B 3+C2Wg2YG+f,B

SHe+W+A+4bX,A K+m+Y81Xk41,A GSXY+G44D81,A S1e+W+BGa1X,A S1e+Y+A144f,A O1W1+YC24af,B O1W1+WCI64Z,B 3+C2Wg2YG+Z,B

SHe+W+A+4af,A K+m+Y81XcK1,A GCWoWK+8C+f,L S1e+W+BGa+f,A S1e+Y+A144Z,A O1W1+YC24aZ,B WG+a81+OUbW,H 3+C2Wg2Y+XX,B

SHe+W+A+4aZ,A K+m+Y81Xc51,A GOXY2G4C581,A S1e+W+BGa+Z,A S1e+W+g144f,A O1W1+YC246f,B O1W1+WC26af,B 3+C2Wg2Y+Wf,B

SHe+W+A+46f,A 9+K1W211+po,P GOXY2G44D81,A S1e+W+B+qGX,A S1e+W+g144Z,A O1W1+YC246Z,B O1W1+WC26aZ,B 3+C2Wg2Y+WZ,B

SHe+W+A+46Z,A K+m+W81nc51,G GOXY2G445O1,A S1e+W+B+q1X,A S1e+W+AH44f,A O1W1+YC244p , S1e+++C264p,E 3+C2Wg2Y+2f,B

SHe+W+A+44p,A K+m+W81XsK1,G GOXY2G44591,A S1e+W+B+q+f,A S1e+W+AH44Z,A S5e+8+C25+f,A X+24W41XXLH,O 3+C2Wg2Y+2Z,B

S5f+W+A+5+f,A K+m+W81Xs51,G GCWo+G4AC+f,L S1e+W+B+q+Z,A GWY+411OTXW,G S5e+8+C25+Z,A 4iAWnC8+2+X,A 3+C2Wg2Y++p,B

S5f+W+A+5+Z,A K+m+W81Xcb1,G GOXY+G4K5O1,A S1e+W+B+aXX,A S1e+W+A1K4f,A S1eG8+C25+f,A 1W61Kbe82+X,B 2aKH2WWfA4+,K

G2W8821OTXW,G G6WSe54IG+W,K GOXY+G4K591,A S1e+W+B+aWf,A S1e+W+A1K4Z,A S1eG8+C25+Z,A 1W61Kbe+A+X,B 34C2Wg22WGX,A

S1fGW+A+51X,A GOXaY44gW+1,A GOXY+G445f1,D S1e+W+B+aWZ,A S1e+W+A14bX,A K+m+82+OUbW,G 1W61Kbe+2GX,B 34C2Wg22W1X,A

S1fGW+A+5+f,A GOXaY44Ye+1,A S1e+Y49+Y51,A S1e+W+B+a2f,A S1e+W+A14af,A G6WU+G9+Yc+,K 1W61Kbe+21X,B 34C2Wg22W+f,A

S1fGW+A+5+Z,A GOXaY44YWG1,A S1e+Y49+Y43,A S1e+W+B+a2Z,A S1e+W+A14aZ,A S1e+A+C25+f,A 1W61Kbe+2+f,B 34C2Wg22W+Z,A

S1f+Y+A85+X,A GOXaY44YW11,A S1e+W49Gg41,E S1e+W+B+a+p,A S1e+W+A146f,A S1e+A+C25+Z,A 1W61Kbe+2+Z,B +I19AYa2+H6,L

S1f+Y+A+D+X,A GOXaY44YW+9,A S1e+W49GYK1,A S5e+W+B+5+f,A S1e+W+A146Z,A G6WQ+G116MW,D 4C8mg6e+4+A,Q 3+C2Yg22WGX,B

S1f+Y+A+5GX,A G6WSW45Im+W,K S1e+W49GY51,A S5e+W+B+5+Z,A S1e+W+A144p,A S1e+81C24XI,E 4eAWoC882+X,A 3+C2Yg22W1X,B

============================ CHAIN NUMBERS 3201 – 3840 =================

3+C2Yg22W+f,B 44GH2GaAE4W,M MKu+K4+441X,A MGu+G5+44+p,A MKu+G4+451X,A H8aY8I8G491,A M+u+O4W45+Z,A M+u+I41444f,A

3+C2Yg22W+Z,B 48GX4H534W9,G MKu+K4+44+f,A G4WGW8+mexW,G MKu+G4+45+f,A H8aY8I8G489,A M+u+O4+KD+X,A M+u+I41444Z,A

+m321GI21qO,D 48GX4H534W3,G MKu+K4+44+Z,A MKu+G4+aC+X,A MKu+G4+45+Z,A H8aY8I8G483,A M+u+O4+K5GX,A G6WO414IH4e,L

3+C2WgY2WGX,B 48GX4H534+J,O MGuGL4+44+X,A MKu+G4+a4GX,A K6eO414228e,L H8aY8I8+4f1,D M+u+O4+K51X,A M+u+G41K44f,G

3+C2WgY2W1X,B 3+C2WeZ21+f,B K6eOa542++e,L MKu+G4+a41X,A MGuGG4+451X,A H8aY8I8+4e9,D M+u+O4+K5+f,A M+u+G41K44Z,G

3+C2WgY2W+f,B 3+C2WeZ21+Z,B MGuGK4+C4+X,A MKu+G4+a4+f,A MGuGG4+45+f,A H8aY8I8+4e3,D M+u+O4+K5+Z,A M+u+G414KKX,G

3+C2WgY2W+Z,B 5+K1YO321+f,B MGuGK4+4C+X,A MKu+G4+a4+Z,A MGuGG4+45+Z,A H8aY8I8+4A9,D M+u+O4+4LGX,A M+u+G414K5X,G

3+C2Wg2Ie+X,B 5+K1YO321+Z,B MGuGK4+44GX,A K6eO4142+Ye,L MGu+I4G45+X,A H8aY8I8+4A3,D M+u+O4+4L1X,A M+u+G414K4f,G

3+C2Wg2IWGX,B +K1G92KII86,L MGuGK4+441X,A MGuGG4+aC+X,A MGu+I4+C5+X,A H8aY8I8+48J,D M+u+O4+4L+f,A M+u+G414K4Z,G

3+C2Wg2IW1X,B 5+K1WO3I11X,G MGuGK4+44+f,A MGuGG4+a4GX,A MGu+I4+4D+X,A M4u+O4+a4+f,A M+u+O4+4L+Z,A M+u+G4144bX,G

3+C2Wg2IW+f,B 5+K1WO3I1+f,G MGuGK4+44+Z,A MGuGG4+a41X,A MGu+I4+45GX,A M4u+O4+a4+Z,A M+u+O4+45XX,A M+u+G4144af,G

3+C2Wg2IW+Z,B 5+K1WO3I1+Z,G MGu+M4G44+X,A MGuGG4+a4+f,A MGu+I4+451X,A M+uGO4+a4+f,A M+u+O4+45Wf,A M+u+G4144aZ,G

3+C2Wg22mGX,B 44GH2GaAA4K,M MGu+M4+C4+X,A MGuGG4+a4+Z,A MGu+I4+45+f,A M+uGO4+a4+Z,A M+u+O4+45WZ,A M+u+G41446f,G

3+C2Wg22m1X,B 5+K1WO32H1X,G MGu+M4+4C+X,A MGu+I4Ga4+X,A MGu+I4+45+Z,A K+m+W8+mexW,G M+u+O4+452f,A M+u+G41446Z,G

3+C2Wg22m+f,B 5+K1WO32H+f,G MGu+M4+44GX,A MGu+I4+i4+X,A MGu+G4WC5+X,A M+u+Q4+aC+X,A M+u+O4+452Z,A M+u+G41444p,G

3+C2Wg22m+Z,B 5+K1WO32H+Z,G MGu+M4+441X,A MGu+I4+aC+X,A MGu+G4W4D+X,A M+u+Q4+a4GX,A M+u+O4+45+p,A M4u+G4+55+f,A

3+C2Wg22WXX,B 5+K1WO321XX,G MGu+M4+44+f,A MGu+I4+a4GX,A MGu+G4W45GX,A M+u+Q4+a41X,A M4u+O4+444f,A M4u+G4+55+Z,A

3+C2Wg22WWf,B 5+K1WO321Wf,G MGu+M4+44+Z,A MGu+I4+a41X,A MGu+G4W451X,A M+u+Q4+a4+f,A M4u+O4+444Z,A M+u+I4+55+f,A

3+C2Wg22WWZ,B 5+K1WO321WZ,G MGu+K4WC4+X,A MGu+I4+a4+f,A MGu+G4W45+f,A M+u+Q4+a4+Z,A M+uGO4+444f,A M+u+I4+55+Z,A

3+C2Wg22W2f,B 5+K1WO3212f,G MGu+K4W4C+X,A MGu+I4+a4+Z,A MGu+G4W45+Z,A G6WQ4H42+Ye,L M+uGO4+444Z,A M+u+G4+L5+f,G

3+C2Wg22W2Z,B 5+K1WO3212Z,G MGu+K4W44GX,A MGu+G4Wi4+X,A MGu+G4+KD+X,A M+u+O4WaC+X,A K+m+41+mexW,G M+u+G4+L5+Z,G

3+C2Wg22W+p,B 5+K1WO321+p,G MGu+K4W441X,A MGu+G4WaC+X,A MGu+G4+K5GX,A 8n2J+m+a4GX,B M+u+Q4+444f,A G6WO414AA8e,L

2aKH2WW8A4K,K 3+C2WeZ2+4f,B MGu+K4W44+f,A MGu+G4Wa4GX,A MGu+G4+K51X,A M+u+O4Wa41X,A M+u+Q4+444Z,A M+u+G4+5L1X,G

34C2Wg2211X,A 3+C2WeZ2+4Z,B MGu+K4W44+Z,A MGu+G4Wa41X,A MGu+G4+K5+f,A M+u+O4Wa4+f,A G6WQ4H4214e,L M+u+G4+5L+f,G

34C2Wg221+f,A 5+K1YO32+4f,B MGu+K4+KC+X,A MGu+G4Wa4+f,A MGu+G4+K5+Z,A M+u+O4Wa4+Z,A M+u+O4W444f,A M+u+G4+5L+Z,G

34C2Wg221+Z,A 5+K1YO32+4Z,B MGu+K4+K4GX,A MGu+G4Wa4+Z,A MGu+G4+4LGX,A M+u+O4+qC+X,A M+u+O4W444Z,A M+u+G4+55XX,G

+I19AYa2286,L +K1G92KIH46,L MGu+K4+K41X,A MGu+G4+qC+X,A MGu+G4+4L1X,A M+u+O4+q4GX,A M+u+O4+KC4X,A M+u+G4+55Wf,G

3+C2Yg2211X,B 5+K1WO3I+4f,G MGu+K4+K4+f,A MGu+G4+q4GX,A MGu+G4+4L+f,A M+u+O4+q41X,A M+u+O4+K4KX,A M+u+G4+55WZ,G

3+C2Yg221+f,B 5+K1WO3I+4Z,G MGu+K4+K4+Z,A MGu+G4+q41X,A MGu+G4+4L+Z,A M+u+O4+q4+f,A M+u+O4+K45X,A M+u+G4+552f,G

3+C2Yg221+Z,B 44GH2GaAA4A,M MGu+K4+4KGX,A MGu+G4+q4+f,A MGu+G4+45XX,A M+u+O4+q4+Z,A M+u+O4+K44f,A M+u+G4+552Z,G

+m321GH11qO,D 5+K1WO32G4f,G MGu+K4+4K1X,A MGu+G4+q4+Z,A MGu+G4+45Wf,A M+u+O4+aKGX,A M+u+O4+K44Z,A M+u+G4+55+p,G

3+C2WgY211X,B 5+K1WO32G4Z,G MGu+K4+4K+f,A MGu+G4+aKGX,A MGu+G4+45WZ,A M+u+O4+aK1X,A M+u+O4+4KKX,A M4u+G4+544f,A

3+C2WgY21+f,B 5+K1WO32+bX,G MGu+K4+4K+Z,A MGu+G4+aK1X,A MGu+G4+452f,A M+u+O4+aK+f,A M+u+O4+4K5X,A M4u+G4+544Z,A

3+C2WgY21+Z,B 5+K1WO32+af,G MGu+K4+44XX,A MGu+G4+aK+f,A MGu+G4+452Z,A M+u+O4+aK+Z,A M+u+O4+4K4f,A M+u+I4+544f,A

3+C2Wg2I9+X,B 5+K1WO32+aZ,G MGu+K4+44Wf,A MGu+G4+aK+Z,A MGu+G4+45+p,A M+u+O4+a4XX,A M+u+O4+4K4Z,A M+u+I4+544Z,A

3+C2Wg2I1GX,B 5+K1WO32+6f,G MGu+K4+44WZ,A MGu+G4+a4XX,A G4WG41+mexW,G M+u+O4+a4Wf,A M+u+O4+44bX,A M+u+G4+L44f,G

3+C2Wg2I11X,B 5+K1WO32+6Z,G MGu+K4+442f,A MGu+G4+a4Wf,A MKu+G4+444f,A M+u+O4+a4WZ,A M+u+O4+44af,A M+u+G4+L44Z,G

3+C2Wg2I1+f,B 5+K1WO32+4p,G MGu+K4+442Z,A MGu+G4+a4WZ,A MKu+G4+444Z,A M+u+O4+a42f,A M+u+O4+44aZ,A G6WO414A94e,L

3+C2Wg2I1+Z,B 3+C2WeY224f,B MGu+K4+44+p,A MGu+G4+a42f,A K6eO414214e,L M+u+O4+a42Z,A M+u+O4+446f,A M+u+G4+5K4f,G

3+C2Wg22HGX,B 3+C2WeY224Z,B G4WH+G+mexW,G MGu+G4+a42Z,A MGuGG4+444f,A M+u+O4+a4+p,A M+u+O4+446Z,A M+u+G4+5K4Z,G

3+C2Wg22H1X,B 5+K1WO2I24f,G MKu+G5+C4+X,A MGu+G4+a4+p,A MGuGG4+444Z,A M4u+O4+4a+f,A M+u+O4+444p,A M+u+G4+54bX,G

3+C2Wg22H+f,B 5+K1WO2I24Z,G MKu+G5+4C+X,A G4WGG4+mexW,G MGu+I4G444X,A M4u+O4+4a+Z,A M4u+G414a+f,A M+u+G4+54af,G

Page 11: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 27

3+C2Wg22H+Z,B 44GH2GW8AcA,M MKu+G5+44GX,A MKu+G4+4aGX,A MGu+I4+C44X,A M+uGO4+4a+f,A M4u+G414a+Z,A M+u+G4+54aZ,G

3+C2Wg221XX,B 5+K1WO222af,S MKu+G5+441X,A MKu+G4+4a1X,A MGu+I4+4C4X,A M+uGO4+4a+Z,A M+u+I414a+f,A M+u+G4+546f,G

3+C2Wg221Wf,B 5+K1WO222aZ,S MKu+G5+44+f,A MKu+G4+4a+f,A MGu+I4+44KX,A K+m+G4+mexW,G M+u+I414a+Z,A M+u+G4+546Z,G

3+C2Wg221WZ,B 5+K1WO2226f,S MKu+G5+44+Z,A MKu+G4+4a+Z,A MGu+I4+445X,A M+u+Q4+4aGX,A G6WO414IGHe,L M+u+G4+544p,G

3+C2Wg2212f,B 5+K1WO2226Z,S K6eOK942++e,L K6eO4142+He,L MGu+I4+444f,A M+u+Q4+4a1X,A M+u+G41KaGX,G M4u+G4+464f,A

3+C2Wg2212Z,B 5+K1WO2224p,S MGuGG5+C4+X,A MGuGG4+4aGX,A MGu+I4+444Z,A M+u+Q4+4a+f,A M+u+G41Ka1X,G M4u+G4+464Z,A

3+C2Wg221+p,B X+24W44IIPa,O MGuGG5+4C+X,A MGuGG4+4a1X,A MGu+G4WC44X,A M+u+Q4+4a+Z,A M+u+G41Ka+f,G M+u+I4+464f,A

2aKH2WW8A4A,K LCiW928+481,A MGuGG5+44GX,A MGuGG4+4a+f,A MGu+G4W4C4X,A G6WQ4H42+He,L M+u+G41Ka+Z,G M+u+I4+464Z,A

34C2Wg22+4f,A LCiW82O+481,A MGuGG5+441X,A MGuGG4+4a+Z,A MGu+G4W44KX,A M+u+O4W4aGX,A M+u+G414qGX,G M+u+G4+K64f,G

34C2Wg22+4Z,A LCiW8288481,A MGuGG5+44+f,A MGu+I4G4a+X,A MGu+G4W445X,A M+u+O4W4a1X,A M+u+G414q1X,G M+u+G4+K64Z,G

+I19AYa2146,L LCiW828+C81,A MGuGG5+44+Z,A MGu+I4+Ca+X,A MGu+G4W444f,A M+u+O4W4a+f,A M+u+G414q+f,G M+u+G4+4M4f,G

3+C2Yg22+4f,B LCiW828+4O1,A MGu+I5G44+X,A MGu+I4+4i+X,A MGu+G4W444Z,A M+u+O4W4a+Z,A M+u+G414q+Z,G M+u+G4+4M4Z,G

3+C2Yg22+4Z,B LCiW828+491,A MGu+I5+C4+X,A MGu+I4+4aGX,A MGu+G4+KC4X,A M+u+O4+Ki+X,A M+u+G414aXX,G G6WO415314e,L

+m321GGWXqO,D LCiW828+489,A MGu+I5+4C+X,A MGu+I4+4a1X,A MGu+G4+K4KX,A M+u+O4+KaGX,A M+u+G414aWf,G M+u+G4+46af,G

3+C2WgY2+4f,B LCiW828+483,A MGu+I5+44GX,A MGu+I4+4a+f,A MGu+G4+K45X,A M+u+O4+Ka1X,A M+u+G414aWZ,G M+u+G4+46aZ,G

3+C2WgY2+4Z,B K6eOa58+4+e,L MGu+I5+441X,A MGu+I4+4a+Z,A MGu+G4+K44f,A M+u+O4+Ka+f,A M+u+G414a2f,G M+u+G4+466f,G

3+C2Wg2I84X,B L8iWA288481,A MGu+I5+44+f,A MGu+G4WCa+X,A MGu+G4+K44Z,A M+u+O4+Ka+Z,A M+u+G414a2Z,G M+u+G4+466Z,G

3+C2Wg2I+KX,B L8iWA28+C81,A MGu+I5+44+Z,A MGu+G4W4i+X,A MGu+G4+4KKX,A M+u+O4+4qGX,A M+u+G414a+p,G M+u+G4+464p,G

3+C2Wg2I+5X,B L8iWA28+4O1,A MGu+G5WC4+X,A MGu+G4W4aGX,A MGu+G4+4K5X,A M+u+O4+4q1X,A M4u+G4145+f,A W4+C2+Hnep+,H

3+C2Wg2I+4f,B L8iWA28+491,A MGu+G5W4C+X,A MGu+G4W4a1X,A MGu+G4+4K4f,A M+u+O4+4q+f,A M4u+G4145+Z,A 1W63+m4A2aX,G

3+C2Wg2I+4Z,B L8iWA28+489,A MGu+G5W44GX,A MGu+G4W4a+f,A MGu+G4+4K4Z,A M+u+O4+4q+Z,A M+u+I4145+f,A 1W63+m42AaX,G

3+C2Wg22GKX,B L8iWA28+483,A MGu+G5W441X,A MGu+G4W4a+Z,A MGu+G4+44bX,A M+u+O4+4aXX,A M+u+I4145+Z,A C+m3a4+2CAX,B

3+C2Wg22G5X,B K6eO41C24+e,L MGu+G5W44+f,A MGu+G4+Ki+X,A MGu+G4+44af,A M+u+O4+4aWf,A G6WO414II8e,L I1824S61GGX,B

3+C2Wg22G4f,B L8iW828G4O1,A MGu+G5W44+Z,A MGu+G4+KaGX,A MGu+G4+44aZ,A M+u+O4+4aWZ,A M+u+G41K51X,G 1W63+m422af,G

3+C2Wg22G4Z,B L8iW828G491,A MGu+G5+KC+X,A MGu+G4+Ka1X,A MGu+G4+446f,A M+u+O4+4a2f,A M+u+G41K5+f,G 1W63+m422aZ,G

3+C2Wg22+bX,B L8iW828G489,A MGu+G5+K4GX,A MGu+G4+Ka+f,A MGu+G4+446Z,A M+u+O4+4a2Z,A M+u+G41K5+Z,G MGuWoCG+++X,J

3+C2Wg22+af,B L8iW828G483,A MGu+G5+K41X,A MGu+G4+Ka+Z,A MGu+G4+444p,A M+u+O4+4a+p,A M+u+G414LGX,G C+m3a4W2C8X,B

3+C2Wg22+aZ,B L8iW828+4f1,D MGu+G5+K4+f,A MGu+G4+4qGX,A HCaY8I88481,A M4u+O4+45+f,A M+u+G414L1X,G I1824Sc1+GX,B

3+C2Wg22+6f,B L8iW828+4e9,D MGu+G5+K4+Z,A MGu+G4+4q1X,A HCaY8I8+C81,A M4u+O4+45+Z,A M+u+G414L+f,G 1W63+m4I24f,G

3+C2Wg22+6Z,B L8iW828+4e3,D MGu+G5+4KGX,A MGu+G4+4q+f,A a+86+G4IIPa,O M+uGO4+45+f,A M+u+G414L+Z,G 1W63+m4I24Z,G

3+C2Wg22+4p,B L8iW828+4A9,D MGu+G5+4K1X,A MGu+G4+4q+Z,A H8aYAI88481,A M+uGO4+45+Z,A M+u+G4145XX,G MGuWmC+G8+X,E

288Y4Xb34G1,B L8iW828+4A3,D MGu+G5+4K+f,A MGu+G4+4aXX,A H8aYAI8+C81,A K+m+82+mexW,G M+u+G4145Wf,G L8iWO68++15,D

288Y4Xb3411,B L8iW828+48J,D MGu+G5+4K+Z,A MGu+G4+4aWf,A H8aYAI8+4O1,A M+u+Q4+451X,A M+u+G4145WZ,G C+m3a4+2K8f,B

+I1851P+c4K,Q G4WI+W+mexW,G MGu+G5+44XX,A MGu+G4+4aWZ,A H8aYAI8+491,A M+u+Q4+45+f,A M+u+G41452f,G MGuWmC+++XX,E

48GX4H5J4G1,G MKu+K4G44+X,A MGu+G5+44Wf,A MGu+G4+4a2f,A H8aYAI8+489,A M+u+Q4+45+Z,A M+u+G41452Z,G I1824S61+Wf,B

48GX4H5J411,G MKu+K4+C4+X,A MGu+G5+44WZ,A MGu+G4+4a2Z,A H8aYAI8+483,A G6WQ4H4228e,L M+u+G4145+p,G MGuWmC++++p,E

48GX4H5J4+9,G MKu+K4+4C+X,A MGu+G5+442f,A MGu+G4+4a+p,A G6WQ4HC24+e,L M+u+O4W451X,A M4u+G41444f,A 4YA8eA8++SK,D

48GX4H5J4+3,G MKu+K4+44GX,A MGu+G5+442Z,A G4WG82+mexW,G H8aY8I8G4O1,A M+u+O4W45+f,A M4u+G41444Z,A 54AAWK8+64X,E

============================ CHAIN NUMBERS 3841 – 4480 =================

2WA2Wee864X,B I182+S611Wf,B CnA2YO+W++Z,A +q31Gn444+f,A Z+IM4G8+2OX,A +m338H44945,B K4eG91M6++X,K O1W1GeeW29X,B

2WA2Wee+E4X,B I182+S611WZ,B CnA2WOWe++X,A +q31Gn444+Z,A Z+IM4G8+29X,A +m338H441K5,B 3+C2a6X284X,B O1W1GeeW28f,B

2WA2Wee+6KX,B I182+S6112f,B amCbGe+G8+I,E +m31InK44+X,B Z+IM4G8+28f,A +m338H44155,B 3+C2a6X2+KX,B O1W1GeeW28Z,B

2WA2Wee+65X,B I182+S6112Z,B p+o+91GGI41,K +m31In4C4+X,B Z+IM4G8+28Z,A +m338H4414D,B K8eWA266+GX,A O1W1Ge8mA8X,B

2WA2Wee+64f,B I182+S611+p,B CnA2WOWW+1X,A +m31In44C+X,B Z+I66GO+28X,A J4o2+G8+3C9,A 3+C2a6X2+4f,B O1W1Ge8m2OX,B

2WA2Wee+64Z,B C+m3W4+352f,B CnA2WOWW++f,A +m31In444GX,B Z+I66G8828X,A J+o22GO+3C1,E 3+C2a6X2+4Z,B O1W1Ge8m29X,B

5+K1GK8GE4X,J C+m3W4W35+f,B CnA2WOWW++Z,A +m31In4441X,B Z+I66G8+A8X,A +m338Ha4941,B K4eG1+N6W+X,K O1W1Ge8m28f,B

5+K1GK8G65X,G X+24W41nep+,H CnA2WO+m8+X,A +m31In444+f,B Z+I66G8+2OX,A +m338Ha41K1,B K8eW826M+GX,A O1W1Ge8m28Z,B

5+K1GK8G64f,G M+u+mC1GWGX,G CnA2WO+m+GX,A +m31In444+Z,B Z+I66G8+29X,A +m338Ha4151,B 3+C2a612G4f,B O1W1Ge8WIOX,B

5+K1GK8G64Z,G HWc3+m++1Af,D CnA2WO+m+1X,A +m31GnaC4+X,B Z+I66G8+28f,A +m338Ha4149,B 3+C2a612G4Z,B O1W1Ge8WI9X,B

+K1G51P+c4X,C HWc3+m++1AZ,D CnA2WO+m++f,A +m31Gna4C+X,B Z+I66G8+28Z,A J+o22G8+3C9,A K4eG1+M624X,K O1W1Ge8WI8f,B

5+K1GK8+6af,G M+u+mC1+WXX,J CnA2WO+m++Z,A +m31Gna44GX,B Z+I64Ge828X,A J+o2+G8GBC1,E K8eW8266+Wf,D O1W1Ge8WI8Z,B

5+K1GK8+6aZ,G M+u+mC1+WWf,G CnA2WO+WGGX,A +m31Gna441X,B Z+I64Ge+A8X,A +m338H44H51,B K8eW8266+WZ,D O1W1Ge8W2fX,B

5+K1GK8+64p,H M+u+mC1+W+p,E CnA2WO+WG1X,A +m31Gna44+f,B Z+I64Ge+2OX,A +m338H44H49,B K8eW8266++p,L O1W1Ge8W2ef,B

4YA8eA8+44S,D L4q1GK1+W+f,A CnA2WO+WG+f,A +m31Gna44+Z,B Z+I64Ge+29X,A J+o2+G8G3C9,A 4eAWC38+2X5,D O1W1Ge8W2eZ,B

54AAWK2424X,E L4q1GK1+W+Z,A CnA2WO+WG+Z,A +m31Gn4KC+X,B Z+I64Ge+28f,A J+o2+G8+3j1,E 1I2eX4KIG+X,K O1W1Ge8W2Af,B

2WA2WeYC24X,B GKXG51OGCX+,C CnA2WO+W+XX,A +m31Gn4K4GX,B Z+I64Ge+28Z,A J+o2+G8+3i9,A +m3+eAagW+X,B O1W1Ge8W2AZ,B

2WA2WeY4A4X,B G6WR+m1+Yc+,K CnA2WO+W+Wf,A +m31Gn4K41X,B Z+I64G8GA8X,A J+o2+G8+3CJ,E +m3+eAaYe+X,B O1W1Ge8W28p,B

2WA2WeY42KX,B L+q1GK1GW+f,G CnA2WO+W+WZ,A +m31Gn4K4+f,B Z+I64G8G2OX,A L2g882+Wa+D,L +m3+eAaYWGX,B T5e88+8W4C1,A

2WA2WeY425X,B L+q1GK1GW+Z,G CnA2WO+W+2f,A +m31Gn4K4+Z,B Z+I64G8G29X,A L4i+H4115+X,A +m3+eAaYW1X,B T5e+9+8W4C1,A

2WA2WeY424f,B L+q1GK1+WXX,J CnA2WO+W+2Z,A +m31Gn44KGX,B Z+I64G8G28f,A L4i+G4H15+X,A +m3+eAaYW+f,B T5e+8+OW4C1,A

2WA2WeY424Z,B L+q1GK1+WWf,G CnA2WO+W++p,A +m31Gn44K1X,B Z+I64G8G28Z,A L4i+G4195+X,A +m3+eAaYW+Z,B T5e+8+8e4C1,A

5+K1GK2KA4X,J L+q1GK1+WWZ,G G4WGG45BGX6,G +m31Gn44K+f,B Z+I64G8+IOX,A L4i+G411D+X,A 1248H4LIm+X,M T5e+8+8WCC1,A

5+K1GK2K24f,G L+q1GK1+W+p,H i18+2+X8gc1,K +m31Gn44K+Z,B Z+I64G8+I9X,A L4i+G4115GX,A 1G5+O64oWGX,G T5e+8+8W4S1,A

5+K1GK2K24Z,G WG+a814hA4K,M CrA2WO++W+f,A +m31Gn444XX,B Z+I64G8+I8f,A L4i+G41151X,A 1G5+O64oW1X,G T5e+8+8W4D1,A

+K1G51P+c4C,C iH8W2+W8Ac1,K CrA2WO++W+Z,A +m31Gn444Wf,B Z+I64G8+I8Z,A L4i+G4115+f,A 1G5+O64oW+f,G T5e+8+8W4C9,A

5+K1GK242af,G DLB24HG+4+1,A D3AA2GWX24+,K +m31Gn444WZ,B Z+I64G8+2fX,A L4i+G4115+Z,A 1G5+O64oW+Z,G T5e+8+8W4C3,A

5+K1GK242aZ,G DLB24H+84+1,A CnAIWO++WGX,A +m31Gn4442f,B Z+I64G8+2ef,A K2e8e6+Wa+D,L 1248H4KII4X,M T1eG9+8W4C1,A

5+K1GK2424p,H DLB24H++C+1,A CnAIWO++W+f,A +m31Gn4442Z,B Z+I64G8+2eZ,A L+i+I4195+X,A 1G5+O64YWWf,G T1eG8+OW4C1,A

M+u4++1+Ava,G DLB24H++4G1,A CnAIWO++W+Z,A +m31Gn444+p,B Z+I64G8+2Af,A L+i+I411D+X,A 1G5+O64YWWZ,G T1eG8+8e4C1,A

C4m3X4+2a8X,A DLB24H++411,A B3I92WW+24K,K GOXa++C2KOC,G Z+I64G8+2AZ,A L+i+I4115GX,A 1G5+O64YW+p,O T1eG8+8WCC1,A

32IHWa8+58I,E DLB24H++4+9,A CnA2YO++W+f,A +q31Hm4a4+X,A Z+I64G8+28p,A L+i+I41151X,A 4I9851O+4Q4,D T1eG8+8W4S1,A

32IHWa4218I,E DLB24H++4+3,A CnA2YO++W+Z,A +q31GmKa4+X,A J4oA+G8W28X,A L+i+I4115+f,A 4aI29Y845+X,A T1eG8+8W4D1,A

C4m3W4+2i8X,A CL8mf5O+4++,C amCbGe+8G+I,E +q31Gm4i4+X,A J4o21G8W28X,A L+i+I4115+Z,A 4GH2GaeC5+X,B T1eG8+8W4C9,A

C4m3W4+2aOX,A DHB26H+84+1,A p+o+1+HGo41,K +q31Gm4aC+X,A J4o2+GOW28X,A K2e8824Ya+D,L 4GH2Gae4D+X,B T1eG8+8W4C3,A

C4m3W4+2a9X,A DHB26H++C+1,A CnA2WOW+W+f,A +q31Gm4a4GX,A J4o2+G8e28X,A L+i+G41H5GX,A 4GH2Gae45GX,B T1e+A+OW4C1,A

C4m3W4+2a8f,A DHB26H++4G1,A CnA2WOW+W+Z,A +q31Gm4a41X,A J4o2+G8WA8X,A L+i+G41H51X,A 4GH2Gae451X,B T1e+A+8e4C1,A

C4m3W4+2a8Z,A DHB26H++411,A CnA2WO+Ge+X,A +q31Gm4a4+f,A J4o2+G8W2OX,A L+i+G41H5+f,A 4GH2Gae45+f,B T1e+A+8WCC1,A

6+O1Jem+24K,K DHB26H++4+9,A CnA2WO+GWGX,A +q31Gm4a4+Z,A J4o2+G8W29X,A L+i+G41H5+Z,A 4GH2Gae45+Z,B T1e+A+8W4S1,A

6+O1qk+++XI,E DHB26H++4+3,A CnA2WO+GW1X,A +m31ImKa4+X,B J4o2+G8W28f,A L+i+G4115XX,D +I1A5HO+4Q4,D T1e+A+8W4D1,A

C+m3Y4+2a8f,B D3AA2GX+a+W,K CnA2WO+GW+f,A +m31Im4i4+X,B J4o2+G8W28Z,A L+i+G4115Wf,D 4WI2AY8C5+X,B T1e+A+8W4C9,A

C+m3Y4+2a8Z,B DHB24H+G4G1,A CnA2WO+GW+Z,A +m31Im4aC+X,B J+oI1G8W28X,A L+i+G4115WZ,D 4WI2AY84D+X,B T1e+A+8W4C3,A

C+m3W4W2i8X,B DHB24H+G411,A CnA2WO++mGX,A +m31Im4a4GX,B J+oI+GOW28X,A L+i+G41152f,D 4WI2AY845GX,B T1e+8+ee4C1,A

C+m3W4W2aOX,B DHB24H+G4+9,A CnA2WO++m1X,A +m31Im4a41X,B J+oI+G8e28X,A L+i+G41152Z,D 4WI2AY8451X,B T1e+8+eWCC1,A

C+m3W4W2a8f,B DHB24H+G4+3,A CnA2WO++m+f,A +m31Im4a4+f,B J+oI+G8WA8X,A L+i+G4115+p,D 4WI2AY845+f,B T1e+8+eW4S1,A

C+m3W4W2a8Z,B D3AA2GW+64W,K CnA2WO++m+Z,A +m31Im4a4+Z,B J+oI+G8W2OX,A L2g882+Wa+S,L 4WI2AY845+Z,B T1e+8+eW4D1,A

C+m3W4+Ii8X,B DHB24H++4W9,A CnA2WO++WXX,A +m31Gmai4+X,B J+oI+G8W29X,A L4i+H41144X,A 4WI28Y8KD+X,G T1e+8+eW4C9,A

C+m3W4+IaOX,B DHB24H++4W3,A CnA2WO++WWf,A +m31GmaaC+X,B J+oI+G8W28f,A L4i+G4H144X,A 4WI28Y8K5GX,G T1e+8+eW4C3,A

C+m3W4+Ia8f,B DHB24H++4+J,L CnA2WO++WWZ,A +m31Gmaa4GX,B J+oI+G8W28Z,A L4i+G41944X,A 4WI28Y8K51X,G T1e+8+8mCC1,A

C+m3W4+Ia8Z,B 34I9Ge8+64X,E CnA2WO++W2f,A +m31Gmaa41X,B J+o22GOW28X,A L4i+G411C4X,A 4WI28Y8K5+f,G T1e+8+8m4S1,A

C+m3W4+2qOX,B 4K8n1WS24+X,K CnA2WO++W2Z,A +m31Gmaa4+f,B J+o22G8e28X,A L4i+G4114KX,A 4WI28Y8K5+Z,G T1e+8+8m4D1,A

Page 12: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 28

124A4H22+co,D 32IA8I8+4+U,L CnA2WO++W+p,A +m31Gmaa4+Z,B J+o22G8WA8X,A L4i+G41145X,A 4WI28Y84LGX,G T1e+8+8m4C9,A

C+m3W4+2q8f,B 34I1Ge8864X,A CbA2WO1+W+f,A +m31Gm4qC+X,B J+o22G8W2OX,A L4i+G41144f,A 4WI28Y84L1X,G T1e+8+8m4C3,A

C+m3W4+2q8Z,B 34I1Ge8+E4X,A CbA2WO1+W+Z,A +m31Gm4q4GX,B J+o22G8W29X,A L4i+G41144Z,A 4WI28Y84L+f,G T1e+8+8WKS1,A

+6+Oi74YW+C,L 34I1Ge8+6KX,A 8D+eA2OGCX+,C +m31Gm4q41X,B J+o22G8W28f,A K2e8e6+Wa+S,L 4WI28Y84L+Z,G T1e+8+8WKD1,A

C+m3W4+2aef,B 34I1Ge8+65X,A CXA2WO1GWGX,A +m31Gm4q4+f,B J+o22G8W28Z,A L+i+I41944X,A 4WI28Y845XX,G T1e+8+8WKC9,A

C+m3W4+2aeZ,B 34I1Ge8+64f,A AXI1We++1Af,D +m31Gm4q4+Z,B J+o2+Gee28X,A L+i+I411C4X,A 4WI28Y845Wf,G T1e+8+8WKC3,A

C+m3W4+2aAf,B 34I1Ge8+64Z,A AXI1We++1AZ,D +m31Gm4aKGX,B J+o2+GeWA8X,A L+i+I4114KX,A 4WI28Y845WZ,G T1e+8+8W4j1,A

C+m3W4+2aAZ,B 3+I1Ge8GE4X,J CXA2WO1+WXX,J +m31Gm4aK1X,B J+o2+GeW2OX,A L+i+I41145X,A 4WI28Y8452f,G T1e+8+8W4i9,A

C+m3W4+2a8p,B 3+I1Ge8G64f,A CXA2WO1+WWf,A +m31Gm4aK+f,B J+o2+GeW29X,A L+i+I41144f,A 4WI28Y8452Z,G T1e+8+8W4i3,A

H2aC++73924,G +I+m52f+c4X,C CXA2WO1+W+p,H +m31Gm4aK+Z,B J+o2+GeW28f,A L+i+I41144Z,A 4WI28Y845+p,G T1e+8+8W4E9,A

4YCIGO8+58I,E 3+K2GK8+6af,D o4m+e6+WaGX,A +m31Gm4a4XX,B J+o2+GeW28Z,A K2e8824Ya+S,L K2mC++A4GKi,G T1e+8+8W4E3,A

4YCIGO4218I,E 3+K2GK8+6aZ,D o4m+e6+Wa1X,A +m31Gm4a4Wf,B J+o2+G8mA8X,A L+i+G41H4KX,A O5W1He8W28X,A T1e+8+8W4CJ,A

I582+S611GX,A 3+I1Ge8+64p,H a+86+G1GnPX,M +m31Gm4a4WZ,B J+o2+G8m2OX,A L+i+G41H45X,A O5W1GeOW28X,A T5e88+8+aC1,A

I582+S6111X,A G4WGW85BGX6,G I4mI1GH+Yc+,K +m31Gm4a42f,B J+o2+G8m29X,A L+i+G41H44f,A O5W1Ge8e28X,A T5e+9+8+aC1,A

I582+S611+f,A CrA2WO+W8+X,A o+m+g6+WaGX,A +m31Gm4a42Z,B J+o2+G8m28f,A L+i+G41H44Z,A O5W1Ge8WA8X,A T5e+8+O+aC1,A

I582+S611+Z,A CrA2WO+W+GX,A o+m+g6+Wa1X,A +m31Gm4a4+p,B J+o2+G8m28Z,A L+i+G4114bX,D O5W1Ge8W2OX,A T5e+8+88aC1,A

O1W1Ge+OQ4K,K i18+A1W8Ac1,K 4K8mb6O+4+X,C Z4IE4G8+28X,A J+o2+G8WIOX,A L+i+G4114af,D O5W1Ge8W29X,A T5e+8+8+iC1,A

O1W14Y66+XI,E CrA2WO+W++f,A o+m+e6+maGX,A Z4I65G8+28X,A J+o2+G8WI9X,A L+i+G4114aZ,D O5W1Ge8W28f,A T5e+8+8+aS1,A

I1822S611+f,B CrA2WO+W++Z,A o+m+e6+ma1X,A Z4I64GO+28X,A J+o2+G8WI8f,A L+i+G41146f,D O5W1Ge8W28Z,A T5e+8+8+aD1,A

I1822S611+Z,B CnAIWO+e++X,A o+m+X4GGM4X,K Z4I64G8828X,A J+o2+G8WI8Z,A L+i+G41146Z,D O1W1IeOW28X,B T5e+8+8+aC9,A

I182+Sc11+f,B D3AA2GX+Y4+,K o+m+e6+WaWf,A Z4I64G8+A8X,A J+o2+G8W2fX,A L+i+G41144p,D O1W1Ie8e28X,B T5e+8+8+aC3,A

I182+Sc11+Z,B CnAIWO+W+GX,A o+m+e6+WaWZ,A Z4I64G8+2OX,A J+o2+G8W2ef,A KKem1+M6++X,K O1W1Ie8WA8X,B T1eG9+8+aC1,A

I182+S6H1+f,B CnAIWO+W+1X,A GOXa++CI4OC,G Z4I64G8+29X,A J+o2+G8W2eZ,A 3+C2a6H2+6X,B O1W1Ie8W2OX,B T1eG8+O+aC1,A

I182+S6H1+Z,B CnAIWO+W++f,A +q31Hn444+X,A Z4I64G8+28f,A J+o2+G8W2Af,A 3+C2a61A+6X,B O1W1Ie8W29X,B T1eG8+88aC1,A

+a2IGK113XA,D CnAIWO+W++Z,A +q31GnK44+X,A Z4I64G8+28Z,A J+o2+G8W2AZ,A 3+C2a61286X,B O1W1Ie8W28f,B T1eG8+8+iC1,A

+O1WZ4r3++I,L B3I92WW+24A,K +q31Gn4C4+X,A Z+IM5G8+28X,A J+o2+G8W28p,A 3+C2a612+MX,B O1W1Ie8W28Z,B T1eG8+8+aS1,A

I182+S61H+f,B CnA2YO+W8+X,A +q31Gn44C+X,A Z+IM4GO+28X,A J4oA+G8+3C1,E KCeW8266+GX,A O1W1Geee28X,B T1eG8+8+aD1,A

I182+S61H+Z,B CnA2YO+W+1X,A +q31Gn444GX,A Z+IM4G8828X,A +m338HK4145,B 3+C2a612+6f,B O1W1GeeWA8X,B T1eG8+8+aC9,A

I182+S611XX,B CnA2YO+W++f,A +q31Gn4441X,A Z+IM4G8+A8X,A +m338H4C145,B 3+C2a612+6Z,B O1W1GeeW2OX,B T1eG8+8+aC3,A

============================ CHAIN NUMBERS 4481 – 5120 =================

T1e+A+O+aC1,A O1W1+e9+aE3,B 4GH+K5AK3+9,G H8aa++1OSXW,G +e2cW6XDW+1,B 184WO61XaW9,D i584W41114f,A i5848+Ka48X,A

T1e+A+88aC1,A O1W1+e9+aCJ,B 4GH+K5AK3+3,G 2K96X5+aW81,A +e2cW6X5e+1,B 184WO61XaW3,D i584W41114Z,A i5848+4i48X,A

T1e+A+8+iC1,A 4A8eA2e+4q8,D 4GH+K5A4JG1,G 2K96W5GaW81,A +e2cW6X5WG1,B 184WO61Xa+J,H i184W418eYX,K i5848+4aC8X,A

T1e+A+8+aS1,A 4KH+L5A4Y+1,A 4GH+K5A4J11,G 2K96W5+iW81,A +e2cW6X5W11,B iL8C4+444C1,A S1e+W41Gg4X,E i5848+4a4OX,A

T1e+A+8+aD1,A +e2Y8YgCY+1,B 4GH+K5A4J+9,G 2K96W5+ae81,A +e2cW6X5W+9,B iL845+444C1,A q+e4W41Gg4X,E i5848+4a49X,A

T1e+A+8+aC9,A +e2Y8Yg4g+1,B 4GH+K5A4J+3,G 2K96W5+aWO1,A +e2cW6X5W+3,B iL844+K44C1,A i184W41H14f,A i5848+4a48f,A

T1e+A+8+aC3,A +e2Y8Yg4YG1,B 4GH+K5A43X1,G 2K96W5+aW91,A +e2cW61Le+1,B iL844+4C4C1,A i184W41H14Z,A i5848+4a48Z,A

T1e+8+e8aC1,A +e2Y8Yg4Y11,B 4GH+K5A43W9,G 2K96W5+aW89,A +e2cW61LWG1,B iL844+44CC1,A i184W41114p,C i18K9+4a48X,A

T1e+8+e+iC1,A +e2Y8Yg4Y+9,B 4GH+K5A43W3,G 2K96W5+aW83,A +e2cW61LW11,B iL844+444S1,A nGYY1GKIG+W,K i18K8+Ka48X,A

T1e+8+e+aS1,A +e2Y8Yg4Y+3,B 4GH+K5A4329,G 2G96Y5GaW81,B +e2cW61LW+9,B iL844+444D1,A n4Y29I4YW+1,A i18K8+4i48X,A

T1e+8+e+aD1,A +A+gAIe+4q8,D 4GH+K5A4323,G 2G96Y5+iW81,B +e2cW61LW+3,B iL844+444C9,A n4Y28IKYW+1,A i18K8+4aC8X,A

T1e+8+e+aC9,A 4GH+M5ACY+1,B 4GH+K5A43+J,G 2G96Y5+ae81,B +e2cW615mG1,B iL844+444C3,A n4Y28I4gW+1,A i18K8+4a4OX,A

T1e+8+e+aC3,A 4GH+M5A4g+1,B GeYa++CGE1C,G 2G96Y5+aWO1,B +e2cW615m11,B iH8K5+444C1,A n4Y28I4Ye+1,A i18K8+4a49X,A

T1e+8+8GiC1,A 4GH+M5A4YG1,B 1K52nn+6++X,A 2G96Y5+aW91,B +e2cW615m+9,B iH8K4+K44C1,A n4Y28I4YWG1,A i18K8+4a48f,A

T1e+8+8GaS1,A 4GH+M5A4Y11,B 1K52mnG6++X,A 2G96Y5+aW89,B +e2cW615m+3,B iH8K4+4C4C1,A n4Y28I4YW11,A i18K8+4a48Z,A

T1e+8+8GaD1,A 4GH+M5A4Y+9,B 1K52mn+E++X,A 2G96Y5+aW83,B +e2cW615WX1,B iH8K4+44CC1,A n4Y28I4YW+9,A i184A+Ka48X,A

T1e+8+8GaC9,A 4GH+M5A4Y+3,B 1K52mn+68+X,A 2G96W5WiW81,B +e2cW615WW9,B iH8K4+444S1,A n4Y28I4YW+3,A i184A+4i48X,A

T1e+8+8GaC3,A 4GH+K5AKg+1,G 1K52mn+6+GX,A 2G96W5Wae81,B +e2cW615WW3,B iH8K4+444D1,A n+Y29HKIG+W,K i184A+4aC8X,A

T1e+8+8+qS1,A 4GH+K5AKYG1,G 1K52mn+6+1X,A 2G96W5WaWO1,B +e2cW615W29,B iH8K4+444C9,A n+Y2AI4gW+1,A i184A+4a4OX,A

T1e+8+8+qD1,A 4GH+K5AKY11,G 1K52mn+6++f,A 2G96W5WaW91,B +e2cW615W23,B iH8K4+444C3,A n+Y2AI4Ye+1,A i184A+4a49X,A

T1e+8+8+qC9,A 4GH+K5AKY+9,G 1K52mn+6++Z,A 2G96W5WaW89,B +e2cW615W+J,B iH846+K44C1,A n+Y2AI4YWG1,A i184A+4a48f,A

T1e+8+8+qC3,A 4GH+K5AKY+3,G 1G52onG6++X,B 2G96W5WaW83,B 6KOeuD++++X,E iH846+4C4C1,A n+Y2AI4YW11,A i184A+4a48Z,A

T1e+8+8+aj1,A 4GH+K5A4oG1,G 1G52on+E++X,B 2G96W5+qe81,B 5+K1GK+GILX,M iH846+44CC1,A n+Y2AI4YW+9,A i1848+ai48X,A

T1e+8+8+ai9,A 4GH+K5A4o11,G 1G52on+68+X,B 2G96W5+qWO1,B 5+K1GK+X2bX,H iH846+444S1,A n+Y2AI4YW+3,A i1848+aaC8X,A

T1e+8+8+ai3,A 4GH+K5A4o+9,G 1G52on+6+GX,B 2G96W5+qW91,B C+m1a2+YCAX,B iH846+444D1,A n+Y21GLIm+W,K i1848+aa4OX,A

T1e+8+8+aE9,A 4GH+K5A4o+3,G 1G52on+6+1X,B 2G96W5+qW89,B I18+4E6XGGX,B iH846+444C9,A n+Y28I4oWG1,A i1848+aa49X,A

T1e+8+8+aE3,A 4GH+K5A4YX1,G 1G52on+6++f,B 2G96W5+qW83,B 1W63+m1+Yaf,G iH846+444C3,A n+Y28I4oW11,A i1848+aa48f,A

T1e+8+8+aCJ,A 4GH+K5A4YW9,G 1G52on+6++Z,B 2G96W5+amO1,B 1W63+m1+YaZ,G iH844+aC4C1,A n+Y28I4oW+9,A i1848+aa48Z,A

4YA8eA8++gY,D 4GH+K5A4YW3,G 1G52mnWE++X,B 2G96W5+am91,B 6GOWuD+G8+X,E iH844+a4CC1,A n+Y28I4oW+3,A i1848+4qC8X,A

54AAWK1+b81,E 4GH+K5A4Y29,G 1G52mnW68+X,B 2G96W5+am89,B 5GKXOL+G8+X,H iH844+a44S1,A n+Y21GKII4W,K i1848+4q4OX,A

2WA2WeX8b81,B 4GH+K5A4Y23,G 1G52mnW6+GX,B 2G96W5+am83,B C+m1a2+YK8f,B iH844+a44D1,A n+Y28I4YWW9,A i1848+4q49X,A

2WA2WeX+j81,B 4GH+K5A4Y+J,G 1G52mnW6+1X,B 2G96W5+aWf1,B 6GOWuD++++p,C iH844+a44C9,A n+Y28I4YWW3,A i1848+4q48f,A

2WA2WeX+bO1,B 468OK58+4Ie,D 1G52mnW6++f,B 2G96W5+aWe9,B I8ea++4Y2Q3,G iH844+a44C3,A n+Y28I4YW+J,L i1848+4q48Z,A

2WA2WeX+b91,B 4CGWfAA4181,A 1G52mnW6++Z,B 2G96W5+aWe3,B 4KH1DI425+1,A iH844+4KCC1,A i58C8+44aC1,A i1848+4aKOX,A

2WA2WeX+b89,B 1G524XgC181,B 1G52mn+M8+X,B 2G96W5+aWA9,B 4KH1CIK25+1,A iH844+4K4S1,A i5849+44aC1,A i1848+4aK9X,A

2WA2WeX+b83,B 1G524Xg4981,B 1G52mn+M+GX,B 2G96W5+aWA3,B 4KH1CI4A5+1,A iH844+4K4D1,A i5848+K4aC1,A i1848+4aK8f,A

5+K1GK1Gj81,H 1G524Xg41O1,B 1G52mn+M+1X,B 2G96W5+aW8J,B 4KH1CI42D+1,A iH844+4K4C9,A i5848+4CaC1,A i1848+4aK8Z,A

5+K1GK1GbO1,G 1G524Xg4191,B 1G52mn+M++f,B H6YU+G+Wa+e,L 4KH1CI425G1,A iH844+4K4C3,A i5848+44iC1,A i1848+4a4fX,A

5+K1GK1Gb91,G 1G524Xg4189,B 1G52mn+M++Z,B HCac1G11481,A 4KH1CI42511,A iH844+44KS1,A i5848+44aS1,A i1848+4a4ef,A

5+K1GK1Gb89,G 1G524Xg4183,B 1G52mn+6GGX,B HCac+GH1481 , 4KH1CI425+9,A iH844+44KD1,A i5848+44aD1,A i1848+4a4eZ,A

5+K1GK1Gb83,G +6+QKL8+4Ie,D 1G52mn+6G1X,B HCac+G19481,A 4KH1CI425+3,A iH844+44KC9,A i5848+44aC9,A i1848+4a4Af,A

5+K1GK1+bf1,H 48GWgAAC181,B 1G52mn+6G+f,B HCac+G11C81,A 4GH1EIK25+1,B iH844+44KC3,A i5848+44aC3,A i1848+4a4AZ,A

5+K1GK1+be9,G 48GWgAA4981,B 1G52mn+6G+Z,B HCac+G114O1,A 4GH1EI4A5+1,B iH844+444j1,A i18K9+44aC1,A i1848+4a48p,A

5+K1GK1+be3,G 48GWgAA41O1,B 1G52mn+6+XX,B HCac+G11491,A 4GH1EI42D+1,B iH844+444i9,A i18K8+K4aC1,A i58C8+44a8X,A

5+K1GK1+b8J,H 48GWgAA4191,B 1G52mn+6+Wf,B HCac+G11489,A 4GH1EI425G1,B iH844+444i3,A i18K8+4CaC1,A i5849+44a8X,A

K2mC++A4Wum,G 48GWgAA4189,B 1G52mn+6+WZ,B HCac+G11483,A 4GH1EI42511,B iH844+444E9,A i18K8+44iC1,A i5848+K4a8X,A

O5W11e9+aC1,A 48GWgAA4183,B 1G52mn+6+2f,B G6WUWK+Wa+e,L 4GH1EI425+9,B iH844+444E3,A i18K8+44aS1,A i5848+4Ca8X,A

O5W1+eP+aC1,A 48GWeAAK981,G 1G52mn+6+2Z,B H8ac2G19481,A 4GH1EI425+3,B iH844+444CJ,A i18K8+44aD1,A i5848+44i8X,A

O5W1+e98aC1,A 48GWeAAK1O1,G 1G52mn+6++p,B H8ac2G11C81,A 4GH1CIaA5+1,B 4M8uY4a24+W,K i18K8+44aC9,A i5848+44aOX,A

O5W1+e9+iC1,A 48GWeAAK191,G KIf8418+4u4,D H8ac2G114O1,A 4GH1CIa2D+1,B 4S9Wb5424+1,A i18K8+44aC3,A i5848+44a9X,A

O5W1+e9+aS1,A 48GWeAAK189,G Kao+9284a+X,A H8ac2G11491,A 4GH1CIa25G1,B 4S9Wa5K24+1,A i184A+K4aC1,A i5848+44a8f,A

O5W1+e9+aD1,A 48GWeAAK183,G Kao+82O4a+X,A H8ac2G11489,A 4GH1CIa2511,B 4S9Wa54A4+1,A i184A+4CaC1,A i5848+44a8Z,A

O5W1+e9+aC9,A 48GWeAA4HO1,G Kao+828Ca+X,A H8ac2G11483,A 4GH1CIa25+9,B 4S9Wa542C+1,A i184A+44iC1,A i18K9+44a8X,A

O5W1+e9+aC3,A 48GWeAA4H91,G Kao+8284i+X,A G6WU+G4Ya+e,L 4GH1CIa25+3,B 4S9Wa5424G1,A i184A+44aS1,A i18K8+K4a8X,A

O1W12eP+aC1,B 48GWeAA4H89,G Kao+8284aGX,A H8ac+G1H4O1,A 4GH1CI4ID+1,B 4S9Wa542411,A i184A+44aD1,A i18K8+4Ca8X,A

O1W12e98aC1,B 48GWeAA4H83,G Kao+8284a1X,A H8ac+G1H491,A 4GH1CI4I5G1,B 4S9Wa5424+9,A i184A+44aC9,A i18K8+44i8X,A

O1W12e9+iC1,B 48GWeAA41f1,G Kao+8284a+f,A H8ac+G1H489,A 4GH1CI4I511,B 4S9Wa5424+3,A i184A+44aC3,A i18K8+44aOX,A

O1W12e9+aS1,B 48GWeAA41e9,G Kao+8284a+Z,A H8ac+G1H483,A 4GH1CI4I5+9,B 468Og5a24+W,K i1848+aCaC1,A i18K8+44a9X,A

O1W12e9+aD1,B 48GWeAA41e3,G GIXA4H8+4u4,D H8ac+G114f1,D 4GH1CI4I5+3,B 4O9Wc54A4+1,A i1848+a4iC1,A i18K8+44a8f,A

O1W12e9+aC9,B 48GWeAA41A9,G KWo+A28Ca+X,A H8ac+G114e9,D 4GH1CI42LG1,B 4O9Wc542C+1,A i1848+a4aS1,A i18K8+44a8Z,A

Page 13: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 29

O1W12e9+aC3,B 48GWeAA41A3,G KWo+A284i+X,A H8ac+G114e3,D 4GH1CI42L11,B 4O9Wc5424G1,A i1848+a4aD1,A i184A+K4a8X,A

O1W1+ef8aC1,B 48GWeAA418J,G KWo+A284aGX,A H8ac+G114A9,D 4GH1CI42L+9,B 4O9Wc542411,A i1848+a4aC9,A i184A+4Ca8X,A

O1W1+ef+iC1,B 4A8eA2e+4M8,D KWo+A284a1X,A H8ac+G114A3,D 4GH1CI42L+3,B 4O9Wc5424+9,A i1848+a4aC3,A i184A+44i8X,A

O1W1+ef+aS1,B 4KH+L5A43+1,A KWo+A284a+f,A H8ac+G1148J,D 4GH1CI425X1,B 4O9Wc5424+3,A i1848+4KiC1,A i184A+44aOX,A

O1W1+ef+aD1,B +e2Y8YgC3+1,B KWo+A284a+Z,A GKXK++1ejX+,G 4GH1CI425W9,B 468OY4b2a+W,K i1848+4KaS1,A i184A+44a9X,A

O1W1+ef+aC9,B +e2Y8Yg4B+1,B KWo+828Ki+X,G +i2cX615W+1,A 4GH1CI425W3,B 4O9Wa54I4G1,A i1848+4KaD1,A i184A+44a8f,A

O1W1+ef+aC3,B +e2Y8Yg43G1,B KWo+828KaGX,G +i2cW6H5W+1,A 4GH1CI42529,B 4O9Wa54I411,A i1848+4KaC9,A i184A+44a8Z,A

O1W1+e9GiC1,B +e2Y8Yg4311,B KWo+828Ka1X,G +i2cW61DW+1,A 4GH1CI42523,B 4O9Wa54I4+9,A i1848+4KaC3,A i1848+aCa8X,A

O1W1+e9GaS1,B +e2Y8Yg43+9,B KWo+828Ka+f,G +i2cW615e+1,A 4GH1CI425+J,B 4O9Wa54I4+3,A i1848+44qS1,A i1848+a4i8X,A

O1W1+e9GaD1,B +e2Y8Yg43+3,B KWo+828Ka+Z,G +i2cW615WG1,A 162OC3+mq+8,L 468OY4a264W,K i1848+44qD1,A i1848+a4aOX,A

O1W1+e9GaC9,B +A+gAIe+4M8,D KWo+8284qGX,G +i2cW615W11,A 1C38a61Xa+1,E 4O9Wa5424W9,A i1848+44qC9,A i1848+a4a9X,A

O1W1+e9GaC3,B 4GH+M5AC3+1,B KWo+8284q1X,G +i2cW615W+9,A +m3+a9Xfa+1,B 4O9Wa5424W3,A i1848+44qC3,A i1848+a4a8f,A

O1W1+e9+qS1,B 4GH+M5A4B+1,B KWo+8284q+f,G +i2cW615W+3,A +m3+C34qaG1,G 4O9Wa5424+J,L i1848+44aj1,A i1848+a4a8Z,A

O1W1+e9+qD1,B 4GH+M5A43G1,B KWo+8284q+Z,G +e2cY6H5W+1,B +m3+C34qa11,G iH8aW4+88YX,K i1848+44ai9,A i1848+4Ki8X,A

O1W1+e9+qC9,B 4GH+M5A4311,B KWo+8284aXX,G +e2cY61DW+1,B +m3+C34qa+9,G S5e8W41+Y4X,E i1848+44ai3,A i1848+4KaOX,A

O1W1+e9+qC3,B 4GH+M5A43+9,B KWo+8284aWf,G +e2cY615e+1,B +m3+C34qa+3,G q4eCW41+Y4X,E i1848+44aE9,A i1848+4Ka9X,A

O1W1+e9+aj1,B 4GH+M5A43+3,B KWo+8284aWZ,G +e2cY615WG1,B 184WO61ni+1,H i584W41914X,A i1848+44aE3,A i1848+4Ka8f,A

O1W1+e9+ai9,B 4GH+K5AKB+1,G KWo+8284a2f,G +e2cY615W11,B 184WO61naG1,G i584W41194X,A i1848+44aCJ,A i1848+4Ka8Z,A

O1W1+e9+ai3,B 4GH+K5AK3G1,G KWo+8284a2Z,G +e2cY615W+9,B 184WO61na+9,G i584W4111KX,A i58C8+4a48X,A i1848+44qOX,A

O1W1+e9+aE9,B 4GH+K5AK311,G KWo+8284a+p,G +e2cY615W+3,B 184WO61XaX1,H i584W41115X,A i5849+4a48X,A i1848+44q9X,A

============================ CHAIN NUMBERS 5121 – 5760 =================

i1848+44q8f,A i184A+64eC1,A O1W12Y44a9X,B H8aWG455+f1,D GGX2WO221E9,D 3KKYOL+8++X,A L+i+O48+KGc,A K8mW2+g5189,G

i1848+44q8Z,A i184A+64WS1,A O1W12Y44a8f,B H8aWG455+e9,D GGX2WO221E3,D 3KKYOL++8+X,A L+i+O48+K1c,A OHW12eA+4Gc,A

i1848+44afX,A i184A+64WD1,A O1W12Y44a8Z,B H8aWG455+e3,D GGX2WO221CJ,D I8mWG4442ef,D +A+gm3X4GQ+,B OHW12eA+41c,A

i1848+44aef,A i184A+64WC9,A O1W1+YaCa8X,B H8aWG455+A9,D 9J2g2Ga24+W,K I8mWG4442eZ,D 248Im314WS1,B OHW1+eg+4Gc,A

i1848+44aeZ,A i184A+64WC3,A O1W1+Ya4i8X,B H8aWG455+A3,D 9L325H424+1,A 3GKYOL+G8+X,H 248Im314WD1,B OHW1+eg+41c,A

i1848+44aAf,A i1848+cCWC1,A O1W1+Ya4aOX,B H8aWG455+8J,D 9L324HK24+1,A C98WX4H14+L,L 248Im314WC9,B OHW1+eAG4Gc,A

i1848+44aAZ,A i1848+c4eC1,A O1W1+Ya4a9X,B HAYe821HK+1,L 9L324H4A4+1,A 3GKYOL+G++f,A K8eW82C2+Yf,L OHW1+eAG41c,A

i1848+44a8p,A i1848+c4WS1,A O1W1+Ya4a8f,B +e2YeKI5H+1,B 9L324H42C+1,A 3GKYOL++++p,C K8eW82C2+YZ,L OHW1+eA+KGc,A

GKXK++8OZ92,G i1848+c4WD1,A O1W1+Ya4a8Z,B +e2YeK2DH+1,B 9L324H424G1,A fH26+G8G4Gc,A K4eG1+S23C1,K OHW1+eA+K1c,A

+i2afX134+1,A i1848+c4WC9,A O1W1+Y4Ki8X,B HKb+G42gX+1,A 9L324H42411,A fH26+G8G41c,A +a2Im2H4e94,B +a2M+8QD+86,B

+i2aeXH34+1,A i1848+c4WC3,A O1W1+Y4KaOX,B +e2YeK25HG1,B 9L324H424+9,A fH26+G8+KGc,A L+i+G49+4Xc,A OHW1+eA+4Xc,A

+i2aeX1B4+1,A i1848+6KeC1,A O1W1+Y4Ka9X,B +e2YeK25H11,B 9L324H424+3,A fH26+G8+K1c,A +A+gm2X4mB+,B +A+k+8gL+94,B

+i2aeX13C+1,A i1848+6KWS1,A O1W1+Y4Ka8f,B +e2YeK25H+9,B 932AAHa24+W,K 248KCm4a+D1,B +K1Im2H4e94,B +K1M+8QD+86,B

+i2aeX134G1,A i1848+6KWD1,A O1W1+Y4Ka8Z,B +e2YeK25H+3,B 9H326H4A4+1,A 248KCm4a+C9,B +A+gm2X4mA8,B +A+k+8gL+8C,B

+i2aeX13411,A i1848+6KWC9,A O1W1+Y44qOX,B GAWee61HK+1,L 9H326H42C+1,A f126+G9+aGL,A ZGG62GA+4Gc,A 48GW61g5191,G

+i2aeX134+9,A i1848+6KWC3,A O1W1+Y44q9X,B HGb+I42gX+1,A 9H326H424G1,A Q1m+G852W+U,E ZGG62GA+41c,A 48GW61g5189,G

+i2aeX134+3,A i1848+64mS1,A O1W1+Y44q8f,B +e2YeKY51G1,B 9H326H42411,A mWa5+W52W+U,E ZGG6+Gg+4Gc,A O1W18eg+4Gc,B

+e2agXH34+1,B i1848+64mD1,A O1W1+Y44q8Z,B +e2YeKY5111,B 9H326H424+9,A +C+p8H441D1,B ZGG6+Gg+41c,A O1W18eg+41c,B

+e2agX1B4+1,B i1848+64mC9,A O1W1+Y44afX,B +e2YeKY51+9,B 9H326H424+3,A +C+p8H441C9,B Z+H62GA+4Gc,A O1W18eAG4Gc,B

+e2agX13C+1,B i1848+64mC3,A O1W1+Y44aef,B +e2YeKY51+3,B 932A2Gb2a+W,K JGoY+G8+4GL,A Z+H62GA+41c,A O1W18eAG41c,B

+e2agX134G1,B i1848+64Wj1,A O1W1+Y44aeZ,B GAWe825JK+1,L 9H324H4I4G1,A JGo22G8+4Gc,A Z+H6+Gg+4Gc,A O1W18eA+KGc,B

+e2agX13411,B i1848+64Wi9,A O1W1+Y44aAf,B HGb+G42oXG1,G 9H324H4I411,A JGo22G8+41c,A Z+H6+Gg+41c,A O1W18eA+K1c,B

+e2agX134+9,B i1848+64Wi3,A O1W1+Y44aAZ,B HGb+G42oX11,G 9H324H4I4+9,A JGo2+Ge+4Gc,A 84WH4m451D1,B 42G8I4g5+O6,G

+e2agX134+3,B i1848+64WE9,A O1W1+Y44a8p,B HGb+G42oX+9,G 9H324H4I4+3,A JGo2+Ge+41c,A 84WH4m451C9,B O1W18eA+4Xc,B

+e2aeXXB4+1,B i1848+64WE3,A XK2geL+X++1,E HGb+G42oX+3,G 932A2Ga264W,K JGo2+G8G4Gc,A Z+G68Gg+4Gc,A 44GG51Q5+f4,G

+e2aeXX3C+1,B i1848+64WCJ,A XK2YfL+X++1,A HGb+G42YXX1,D 9H324H424W9,A JGo2+G8G41c,A Z+G68Gg+41c,A 42G8A2g5+O6,G

+e2aeXX34G1,B HAYg2GX14+8,L XK2YeLGX++1,A HGb+G42YXW9,D 9H324H424W3,A JGo2+G8+KGc,A Z+G68GAG4Gc,A 44GG51Q5+eC,G

+e2aeXX3411,B HKb25H224+1,A XK2YeL+f++1,A HGb+G42YXW3,D 9H324H424+J,L JGo2+G8+K1c,A Z+G68GAG41c,A +I1851KQQ4+,M

+e2aeXX34+9,B HKb24HI24+1,A XK2YeL+X8+1,A HGb+G42YX29,D HKYmG82C8+X,K +a2J8GK4+P6,B Z+G68GA+KGc,A 48GY2Wg5189,G

+e2aeXX34+3,B HKb24H2A4+1,A XK2YeL+X+G1,A HGb+G42YX23,D HCYWH835++X,A JGo2+G8+4Xc,A Z+G68GA+K1c,A O1W1+gAG4Gc,B

+e2aeX1JC+1,B HKb24H22C+1,A XK2YeL+X+11,A HGb+G42YX+J,D HCYWG8J5++X,A +A+h8Ga4+h4,B +a2H1n45+P4,B O1W1+gAG41c,B

+e2aeX1J4G1,B HKb24H224G1,A XK2YeL+X++9,A Iaq8W48X241,E HCYWG83D++X,A +K1J8GK4+P6,B Z+G68GA+4Xc,A O1W1+gA+KGc,B

+e2aeX1J411,B HKb24H22411,A XK2YeL+X++3,A Iaq+X48X241,A HCYWG8358+X,A +A+h8Ga4+gC,B +A+f2n45+h+,B O1W1+gA+K1c,B

+e2aeX1J4+9,B HKb24H224+9,A XG2YgLGX++1,E Iaq+W4OX241,A HCYWG835+GX,A 84WJ8H441D1,B +K1H1n45+P4,B 42G8I4gb+O4,G

+e2aeX1J4+3,B HKb24H224+3,A XG2YgL+f++1,A Iaq+W48f241,A HCYWG835+1X,A 84WJ8H441C9,B +A+f2n45+g8,B O1W1+gA+4Xc,B

+e2aeX13KG1,B GAWgYKX14+8,L XG2YgL+X8+1,A Iaq+W48XA41,A HCYWG835++f,A J+o28H8+4GL,A 44GH4m451D1,B 44GG51Qb+f+,G

+e2aeX13K11,B HGb26H2A4+1,A XG2YgL+X+G1,A Iaq+W48X2K1,A HCYWG835++Z,A J+o28G8G4Gc,A 44GH4m451C9,B 42G8A2gb+O4,G

+e2aeX13K+9,B HGb26H22C+1,A XG2YgL+X+11,A Iaq+W48X251,A H4YGO92C8+X,K J+o28G8G41c,A Z+G6+IAG4Gc,A 44GG51Qb+e8,G

+e2aeX13K+3,B HGb26H224G1,A XG2YgL+X++9,A Iaq+W48X249,A H8YWI83D++X,A J+o28G8+KGc,A Z+G6+IAG41c,A 48GX2Gg5191,G

+e2aeX134X1,B HGb26H22411,A XG2YgL+X++3,A Iaq+W48X243,A H8YWI8358+X,A J+o28G8+K1c,A Z+G6+IA+KGc,A O1W1+eB+KGc,B

+e2aeX134W9,B HGb26H224+9,A XG2YeL+n8+1,E IWq+Y4OX241,E H8YWI835+GX,A +a2J8HK4+P4,B Z+G6+IA+K1c,A O1W1+eB+K1c,B

+e2aeX134W3,B HGb26H224+3,A XG2YeL+n+G1,A IWq+Y48f241,A H8YWI835+1X,A J+o28G8+4Xc,A +a2H1m4b+P4,B 42G8I4g5WO4,G

+e2aeX13429,B GAWg2Gb34+8,L XG2YeL+n+11,A IWq+Y48XA41,A H8YWI835++f,A +A+h8Ha4+h+,B Z+G6+IA+4Xc,A O1W1+eB+4Xc,B

+e2aeX13423,B HGb24H2I4G1,A XG2YeL+n++9,A IWq+Y48X2K1,A H8YWI835++Z,A +K1J8HK4+P4,B +A+f2m4b+h+,B 44GG51Q5Wf+,G

+e2aeX134+J,B HGb24H2I411,A XG2YeL+n++3,A IWq+Y48X251,A H4YGG83Ce+X,K +A+h8Ha4+g8,B +K1H1m4b+P4,B 5+K1GK1+WpK,M

5IAgYKe+++W,K HGb24H2I4+9,A XG2YeL+X+X1,E IWq+Y48X249,A H8YWG83L+GX,A 248J8H441D1,B +A+f2m4b+g8,B 44GG51Q5We8,G

5KBI5HG+4+1,L HGb24H2I4+3,A XG2YeL+X+W9,A IWq+Y48X243,A H8YWG83L+1X,A 248J8H441C9,B 9n622GI2++c,A 48GWY8g5191,G

5KAfOf8+++1,E HGb24H224X1,D XG2YeL+X+W3,A IWq+W48nA41,E H8YWG83L++f,A J+o2+G9+aGL,A 9n622G228+c,A 48GWY8g5189,G

5KB2aL88++1,A HGb24H224W9,D XG2YeL+X++J,E IWq+W48n2K1,A H8YWG83L++Z,A +a2J8GK4WP4,B 9n62+GYA++c,A 42G8I4g51O4,G

5KB2aL8+8+1,A HGb24H224W3,D SHeWG8+88YX,K IWq+W48n251,A H4YGG82CA4X,K J+o2+G9+4Xc,A 9n62+G2I8+c,A O1W1+eA14Xc,B

5KB2aL8++G1,A HGb24H22429,D i58CW41+Y4X,E IWq+W48n249,A H8YWG835+Wf,A +A+h8Ga4Wh+,B 84WKOG4f24X,B 44GG51Q51f+,G

5KB2aL8++11,A HGb24H22423,D CXI+418HE+X,G IWq+W48n243,A H8YWG835+WZ,A +K1J8GK4WP4,B 84WKOG4X2KX,B 42G8A2g51O4,G

5KB2aL8+++9,A HGb24H224+J,D CXI+418H6GX,G IWq+W48X2b1,E H8YWG835++p,L +A+h8Ga4Wg8,B 8P1YWK19+Y1,A 44GG51Q51e8,G

5KB2aL8+++3,A 2IGf2Wc6++X,K S5e+G8111KX,A IWq+W48X2a9,A iH8WX4GGGYW,K +a2J8H441C9,B 8P1YWK11+Y9,L 44GH1GS264I,H

5GB2aL8G8+1,H 1K2mX4GOS+W,K CXI+418H6+f,G IWq+W48X2a3,A i58+f6+WX41,A J+o2+G8+64U,E 8P1YWK11+Y3,L 5+K1GK+GBCI,H

4eAYeQ++115,D 2KGg8H66++X,E CXI+418H6+Z,G IWq+W48X24J,E i58+e6GWX41,A +C+om314eC1,B 87+QWK+8BC+,K 44GG51Q5+i8,G

4eAYeQ++1+D,D 3+C1898WCAX,B S1e+G818eYX,K H8YY1GH14+n,L i58+e6+eX41,A +C+om314WS1,B 9X628G2I8+c,A +C+s+9Aa291

5GB2aL8G++9,A 3+C1898W4QX,B i184W41Gg4X,E GKX2XO221C1,A i58+e6+Wf41,A L8gW8288+YX,A 144KOH4921C,B +C+s+9Aa289,B

5GB2aL8++X1,H 2KH14X66+GX,A CXI+4181M+f,G GKX2WOI21C1,A i58+e6+WXK1,A LGi+I4884+c,A 9X628G22GGc,A K8mW2+g4391,G

5GB2aL8++W9,A 3+C1898W4Af,B CXI+4181M+Z,G GKX2WO2A1C1,A i58+e6+WX51,A LGi+I48+C+c,A 9X628G22G1c,A K8mW2+g4389,G

5GB2aL8+++J,H 3+C1898W4AZ,B S1e+G81114p,C GKX2WO229C1,A i58+e6+WX49,A LGi+G4e84+c,A +A+iOH4H2IG,B OHW12e824Gc,A

i58C8+64WC1,A 2GH14X6M8+X,H H6YO82+ei+W,L GKX2WO221S1,A i58+e6+WX43,A LGi+G4e+C+c,A 248KOG4X2KX,B OHW12e8241c,A

i5849+64WC1,A 5+C24H8+65b,D 1G52aKI4m81,B GKX2WO221D1,A i18+f5GGGYW,K 248Im2H4896,B 8P1Y+G53+Y9,L OHW1+ee24Gc,A

i5848+M4WC1,A 3+C1898WK8f,B 1G52aK2Cm81,B GKX2WO221C9,A i18+g6+eX41,A LGi+G48GC+c,A 8P1Y+G53+Y3,L OHW1+ee241c,A

i5848+6CWC1,A 2GH14X66+XX,H HCaWG45D+81,A GKX2WO221C3,A i18+g6+Wf41,A LGi+G48G4Gc,A 87+Q+G4ABC+,K OHW1+e8I4Gc,A

i5848+64eC1,A 2GH14X66+Wf,D 1G52aK24mO1,B G8WYXKH14+n,L i18+g6+WXK1,A LGi+G48G41c,A KWg+82+8Bg2,D OHW1+e8I41c,A

i5848+64WS1,A 2GH14X66++p,H 1G52aK24m91,B GGX2YO2A1C1,A i18+g6+WX51,A +A+gm2X4OA4,B 94IHA1+WWHC,V OHW1+e82KGc,A

i5848+64WD1,A K2mC++8Y4ua,G 1G52aK24m89,B GGX2YO229C1,A i18+g6+WX49,A 144Im2H4896,B +m3+Y8g95+X,G OHW1+e82K1c,A

i5848+64WC9,A O5W11Y44a8X,A 1G52aK24m83,B GGX2YO221S1,A i18+g6+WX43,A LGi+G48+KGc,A +m3+Y8g1D+X,G +a2M+8QC286,B

Page 14: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 30

i5848+64WC3,A O5W1+YK4a8X,A G6WOe6+ei+W,L GGX2YO221D1,A i18+X4HGmYW,K LGi+G48+K1c,A 1W61KeI5++L,B OHW1+e824Xc,A

i18K9+64WC1,A O5W1+Y4Ca8X,A H8aWI45D+81,A GGX2YO221C9,A i18+e6+mXK1,A +A+gm2X4GQ4,B K8eW82+GJD1,D +A+k+8gK294,B

i18K8+M4WC1,A O5W1+Y44i8X,A 1G52aKY4WO1,B GGX2YO221C3,A i18+e6+mX51,A 84WIm314eC1,B H8YW821XWY9,L +K1M+8QC286,B

i18K8+6CWC1,A O5W1+Y44aOX,A 1G52aKY4W91,B G8WY1GL34+n,L i18+e6+mX49,A 84WIm314WS1,B H8YW821XWY3,L +A+k+8gK28C,B

i18K8+64eC1,A O5W1+Y44a9X,A 1G52aKY4W89,B GGX2WO2I1S1,A i18+e6+mX43,A K8eWe688+YX,A H4YG1+GORC+,K 48GW61g4391,G

i18K8+64WS1,A O5W1+Y44a8f,A 1G52aKY4W83,B GGX2WO2I1D1,A i18+X4GGIcW,K 248Im3H4894,B L+g1+W1XWY9,L 48GW61g4389,G

i18K8+64WD1,A O5W1+Y44a8Z,A G6WO824gi+W,L GGX2WO2I1C9,A i18+e6+WXa9,A L+i+O48GC+c,A 1W62KK45+GL,B O1W18ee24Gc,B

i18K8+64WC9,A O1W12YK4a8X,B H8aWG45L+O1,G GGX2WO2I1C3,A i18+e6+WXa3,A L+i+O48G4Gc,A HGYWG866++U,E O1W18ee241c,B

i18K8+64WC3,A O1W12Y4Ca8X,B H8aWG45L+91,G GGX2WO221j1,D i18+e6+WX4J,L L+i+O48G41c,A +C+s+9Ab+91,B O1W18e8I4Gc,B

i184A+M4WC1,A O1W12Y44i8X,B H8aWG45L+89,G GGX2WO221i9,D 3KIoXKG+4+W,K +A+gm3X4OA+,B +C+s+9Ab+89,B O1W18e8I41c,B

i184A+6CWC1,A O1W12Y44aOX,B H8aWG45L+83,G GGX2WO221i3,D 4WC2WK+GILX,M 144Im3H4894,B K8mW2+g5191,G O1W18e82KGc,B

============================ CHAIN NUMBERS 5761 – 6400 =================

O1W18e82K1c,B S1e+e+A+K1c,A 3+C2Wg2I+1c,B H8aW82+mq89,D GOXa1+C2CeG,A K4eG824YaGH,A T1e+8+8G58D,A +e2W51S8M2G,G

42G8I4g42O6,G +a2MW5GD884,B 1W6+Y8gXA14,G M+u+G414KGc,G GOXW1+SA4eG,G K4eG824YWHH,L T1e+8+8+L8E,A 4K8mg5aA8++,K

O1W18e824Xc,B S1e+e+A+4Xc,A 3+C2Wg22GGc,B M+u+G414K1c,G GOXW1+S2CeG,G K4eG824YWHO,L T1e+8+8+L8D,A GeYW1+S8M2G,G

44GG51Q42f4,G +A+kW5WLG9+,B 3+C2Wg22G1c,B H4aG82+eiO4,D Z4I61G8+28c,A Z+G62G984C6,A T1e+8+8858L,A M+u41+24I8c,A

42G8A2g42O6,G +K1MW5GD884,B 1W6+51QXII+,G H2a8822IK86,D Z4I6+GO+28c,A J+o2+G8GA4o,E T1e+8+8+D8L,A KWo+9284K+c,A

44GG51Q42eC,G +A+kW5WLG88,B 3+C2Wg22+Xc,B M+u+G4144Xc,G a894e5+GGHX,C Z+G62G9+4S6,A +6+U+8QCW8m,B GIX8414KKO4,D

48GY2Wg4391,G 44GMW5+bW91,B 1W6+A2gXA14,G H4aG82+ei94,D Z+I62G8828c,A Z+G62G9+4CE,A K2m82+g4WOm,G M+u+1+K264L,K

48GY2Wg4389,G 44GMW5+bW89,B 1W6+51QXI28,G H2a8821HK86,D Z+I62G8+A8c,A +I192mK4WgW,B O5W1+e984C6,A eX82G2H4K+b,B

O1W1+g8I4Gc,B S1e+W2AG4Gc,A +e2WmC+moGX,D H4aG82+ei8C,D Z+I62G8+2Oc,A Z+G62G9+4CD,A O5W1+e9+CC6,A GKXG41+eiu+,D

O1W1+g8I41c,B S1e+W2AG41c,A 1G5+K51XWXC,H H8aW824KK91,D Z+I62G8+29c,A K4eG1+K264B,K O5W1+e9+4S6,A M+u41+242eb,A

O1W1+g82KGc,B S1e+W2A+KGc,A +e2WmC+mo+f,D H8aW824KK89,D Z+I62G8+2Ob,A Z+G6+Gf+CC6,A O5W1+e9+4CE,A S1e+W48G396,A

O1W1+g82K1c,B S1e+W2A+K1c,A 48GX4H53+Y9,O H2a8822IL84,D Z+I62G8+29b,A Z+G6+Gf+4S6,A +I1E+8gKW8X,B GKXI4H+8Cu+,D

42G8I4ga2O4,G +a2MW4Gj884,B 48GX4H53+Y3,O M+u+G4+54Xc,G +A+fAmK4+cW,B Z+G6+Gf+4CE,A O5W1+e9+4CD,A S5e+W+9+4S6,A

O1W1+g824Xc,B S1e+W2A+4Xc,A 44GH2GaABC+,M H4aG82+ej9+,D Z+I61G8+2eb,A +I192m4CWgW,B O1W12e984C6,B S5e+W+9+4CE,A

44GG51Qa2f+,G +A+kW4WrG9+,B 144GI4WOQ4A,M H2a8821HL84,D Z+I6+GO+2eb,A Z+G6+Gf+4CD,A O1W1Ge8GA4o,E +I1EW4WKm8X,B

42G8A2ga2O4,G +K1MW4Gj884,B 5+K1WO32+Xc,G H4aG82+ej88,D Z+I62G8+396,A Z+G61G9+4CL,A O1W12e9+4S6,B S1eGW+9+4S6,A

44GG51Qa2e8,G +A+kW4WrG88,B +a2GmC+eg1K,D H8aW822IK89,D Z+I62G8+395,A K8eW8242+pm,L O1W12e9+4CE,B S1eGW+9+4CE,A

48GX2Gg4391,G 248MW5+bW91,B +Y28mC1HI+E,D H2a8821HKC4,D Z+I6+Ge+396,A Z+G61G9+58L,A 44GG92Q4WeX,G +I1EX4WKm8W,B

48GX2Gg4389,G 248MW5+bW89,B +a2GmC+eg+S,D H4aG82+eiC8,D +K+m91L2b81,H J+o2+G88I4o,E O1W12e9+4CD,B G2WE+G221iJ,D

O1W1+e92KGc,B S1e+W+B+KGc,A 48GX4H111c9,O +m3+I4aag41,G J4o2+GO+28c,A Z+G62G814S6,A O1W1+ef+CC6,B G6WS814IM4+,K

O1W1+e92K1c,B S1e+W+B+K1c,A 42G91GH12g6,O +m3+a92IIK1,D J4o2+G8828c,A Z+G62G814CE,A O1W1+e9GCC6,B S1e+Y+9+4S6,A

42G8I4g4YO4,G +a2MW4GDe84,B 44GH2GX11LC,O +m3+a92II43,D J4o2+G8+A8c,A +I192mK41gW,B 42G8Y8g4WOm,G S1e+Y+9+4CE,A

O1W1+e924Xc,B S1e+W+B+4Xc,A +C+pW3H+b81,B 1W63+m4A24L,G J4o2+G8+2Oc,A K4eG1+K264L,K O1W1+e9+KS6,B S1e+Y+9+4CD,A

44GG51Q4Yf+,G +A+kW4WLm9+,B +C+pW318b81,B N+w+C3+++Y3,L J4o2+G8+29c,A Z+G6+Ge14S6,A O1W1+e9+KCE,B GCWo+GC2+Hf,L

42G8A2g4YO4,G +K1MW4GDe84,B +C+pW31+b91,B 64O8oCG+++U,C J4o2+G8+29b,A Z+G6+Ge14CE,A O1W1+e9+KS5,B S1e+W48GA4o,E

44GG51Q4Ye8,G +A+kW4WLm88,B +C+pW31+b89,B 2WA2WeO+64L,B +A+h8Ga4+cX,B +I192m4C1gW,B 44GG92Q4WuW,G S1e+W+f+4S6,A

48GWY8g4391,G 144MW5+bW91,B L8iW92+GK81,A 5+K1GK8+64U,H K8f+e5+GGHX,C Z+G6+Ge14CD,A O1W1+e9+KCD,B S1e+W+f+4CE,A

48GWY8g4389,G 144MW5+bW89,B 4G924H+OQc+,M 2WA2WeI424L,B J+o22G8828c,A K8eW8242+pa,L O1W1+e9+Ci5,B +I1EW4WSm8W,B

42G8I4g43O4,G +a2MW4GD984,B L8iW82+GK91,D 5+K1GK2424U,H J+o22G8+A8c,A 4GH2Gae4C+c,B O3W1+e9+4CL,A S1e+W+f+4CD,A

O1W1+e834Xc,B S1e+W+A14Xc,A L8iW82+GK89,D C2m3W4+2K8c,A J+o22G8+2Oc,A 4GH2Gae44Gc,B O1W11e9+4CL,B S1e+W+9GCC6,A

44GG51Q43f+,G +A+kW4WLH9+,B 448I1GM624I,H 1248I4d39+4,G J+o22G8+29c,A +K1G61aIIL+,M O1W1+e9+CCL,B S1e+W+9G4S6,A

42G8A2g43O4,G +K1MW4GD984,B K6eO4166++e,L +m32XOGGI54,D J+o22G8+29b,A 4WI28Y84KGc,G O1W1+e9+L8E,B 54AIeL+88+K,K

44GG51Q43e8,G +A+kW4WLH88,B 84WJW2H+CO6,B 144G51N3H1+,G +A+h8Gq4+cW,B 4WI28Y84K1c,G O1W1+e9+L8D,B S1e+W+9G4S5,A

48GWI4g4389,G +a2MW5+bW89,B MGu+I4G44+c,A GOXWmC1HG11,D 248J8Ga4+La,B +I1851IIKO4,D O3W1+e9+58L,A 144MW4GCe8m,B

42G8A2g42S4,G +K1MW4GD8C4,B MGu+I4+C4+c,A M+u+C342+Y3,L J+o2+G9+WHL,K 4WI28Y844Xc,G O1W11e9+58L,B S1e+W+9+KS6,A

44GG51Q42i8,G +A+kW4WLGC8,B MGu+I4+4C+c,A S1e+W41XWp+,J J+o2+G8G2Oc,A 4WI29Y844Wb,B O1W1+e9+D8L,B S1e+W+9+KCE,A

KWo41+94K+c,A 48GY2We6391,G MGu+I4+44Gc,A L+q1GK1+W+U,H J+o2+G8G29c,A +K1G61Weif+,D +6+U+8QC18m,B S1e+W+9+KS5,A

KWo41+944Wc,A 48GY2We6389,G MGu+I4+441c,A +C+qm12Z21X,B J+o2+G8G2Ob,A +K1I6He84f+,B K2m82+g41Om,G +I1EW4WKmOW,B

144ICmG1b81,B O1W14YC24GL,B +A+hW2n+Ke4,B +C+qm1IZ2+X,B J+o2+G8G29b,A +K1I6HW8Cf+,D O5W1+e894C6,A S1e+W+9+KCD,A

H8ac+G+GK9X,D SHe+2+C24Gc,A 44GJW2H+CO6,B +C+qm12ZA+X,B +A+h8Ga48cW,B O1W1Gee828c,B O5W1+e81CC6,A GIX8W81mr2+,G

i184W452W+U,E SHe+2+C241c,A MGu+G4WC4+c,A i18+41111cf,L J+o2+G8+2LL,K O1W1Gee+A8c,B O5W1+e814S6,A GCWqW45B8+G,L

+C+sW5+bW91,B O1W1+YCI4Gc,B MGu+G4W4C+c,A j1A+2+X1+HM,L G4WG92KYKaW,G LWk41+11+Wc,A O5W1+e814CE,A 5GAYYKO+++o,E

+C+sW5+bW89,B O1W1+YCI41c,B MGu+G4W44Gc,A DHB24H+8+Y1,A J+o2+GO+2eb,A 42G92Gg4+Ki,G +I1E+8gK18X,B K+m+3+nXca+,G

SHeGW+A+4Gc,A O1W1+YC2KGc,B MGu+G4W441c,A DHB24H+++Y9,L J+o2+G882eb,A O1W1Ge9+WHL,K O5W1+e814CD,A GOXY+G+OTe+,D

SHeGW+A+41c,A O1W1+YC2K1c,B +A+hW2X8Ke4,B DHB24H+++Y3,L J+o2+G8+Aeb,A O1W1Ge8G2Oc,B O1W1Ge88I4o,E S1e+W+9+CCL,A

SHe+Y+A+4Gc,A 42G8I4ec2O4,G i994W4+G8XI,E D3AA2GW+3C+,K J+o2+G8+2fb,A O1W1Ge8G29c,B O1W12e814S6,B 5GAYYKGX++I,E

SHe+Y+A+41c,A O1W1+YC24Xc,B MGu+G4+K4Gc,A 32I1Ge8+64L,A J+o2+Ge+396,A O1W1Ge8G2Ob,B O1W12e814CE,B GGX+X8Hmr2+,G

SHe+W+g+4Gc,A 44GG51Oc2f+,G MGu+G4+K41c,A 3+I1Ge8+64U,H J+o2+G8G396,A O1W1Ge8G29b,B 44GG92Q41eX,G GCWqW453+HG,L

SHe+W+g+41c,A 42G8A2ec2O4,G MGu+G4+4KGc,A 248KeK688+E,B J+o2+G8G395,A 44GG51Q48am,G +C+o2Gi228f,L S1e+W+9858L,A

SHe+W+AG4Gc,A 44GG51Oc2e8,G MGu+G4+4K1c,A CnA2WO+G8+c,A J+o2+G8+J96,A O1W1Ge882eb,B O1W1+ee14S6,B S1e+W+9+D8L,A

SHe+W+AG41c,A +C+oCq448C1,B +a2JW2H+CO6,B CnA2WO+G+Gc,A +O1Z8Ga4+d8,B O1W1Ge8+Aeb,B O1W1+ee14CE,B 184W51PCK8G,G

SHe+W+A+KGc,A K8mW2+e6391,G MGu+G4+44Xc,A i18+X4H1+YE,L 1G3+a54IGHX,M O1W1Ge8G396,B 44GG92QC1eW,G +K1Ga9+eie8,D

SHe+W+A+K1c,A S1e+8+CI4Gc,A +A+hW2X+Kf4,B +A+ieK6GO+K,B L4i+G4194+c,A O1W1Ge8G395,B O1W1+ee14CD,B O1W1+Wi22Oc,B

+a2MW4GD886,B S1e+8+CI41c,A +K1JW2H+CO6,B 144KeK688+E,B L4i+G411C+c,A O1W1Ge8+J96,B 42G92Gg41Om,G O1W1+Wi229c,B

SHe+W+A+4Xc,A +a2MW1GEA84,B +A+hW2X+KeC,B i18+1+L3+YE,L L4i+G4114Gc,A T5e+8+884C6,A O1W1+e8HCC6,B 44GG51OE2aW,G

+A+kW4WLG94,B GIXE+GC2+Y6,L 84WJW318b81,B +A+ieK6GGGK,B L4i+G41141c,A T5e+8+8+CC6,A O1W1+e8H4S6,B HWc6+G19+Wc,A

+K1MW4GD886,B +A+kW1WMI9+,B 84WJW31+j81,B +K1L89AWC81,B L4i+G411C+b,A T1eG8+884C6,A O1W1+e8H4CE,B GKXM+G+WXL1,L

+A+kW4WLG8C,B 48GX2Ge6389,G 84WJW31+bO1,B AHH14X++2g3,L +A+gm2X+nA1,B T1eG8+8+CC6,A 44GG92Q49eW,G 4K8o2Ga24Ge,A

G5+MW5+bW91,B O1W1+WD2aGL,B 84WJW31+b91,B CH924H42+Y3,L KGf+a5+GGHX,C T1e+A+884C6,A O1W1+e8H4CD,B 4K8o2Ga24GY,A

G5+MW5+bW89,B O1W1+WD24Xc,B 84WJW31+b89,B CXA2WO1+W+U,H L+i+I4194+c,A T1e+A+8+CC6,A O1W1+e81KS6,B 2G928Z42KG6,B

S1f+Y+A+4Gc,A 5+K1GK1+WYU,M H8aY8I+GKO1,D o+m+X4GGJC1,K L+i+I411C+c,A T1e+8+e84C6,A O1W1+e81KCE,B 2G928Z42KG5,B

S1f+Y+A+41c,A 42G8A2e6YO4,G H8aY8I+GK91,D +i5G62bAe++,K L+i+I4114Gc,A T1e+8+e+CC6,A O1W1+e81KS5,B 2G928Z42K16,B

S1f+W+g+4Gc,A 44GG51O6Ye8,G H8aY8I+GK89,D +i5G62bAW1+,A L+i+I41141c,A 248MW1GC89m,B 5+K1GK+GILK,M 2G928Z42K15,B

S1f+W+g+41c,A 6GOWoCG+++p,J H8aY8I+GK83,D +i5G62b2WH+,K +A+gm2n+nA+,B T1e+8+8GCC6,A O1W1+e81KCD,B 2G928Z424X6,B

S1f+W+AG4Gc,A 44GGmCQ1Y41,B G6WQ4H66++e,L +m31ImK44+c,B KGf+a5+GGHI,C T1e+8+8G4S6,A +C+o9II24aG,D 2I928Z424W5,A

S1f+W+AG41c,A 1W622Wg1YK1,G 248JW3H+CO4,B +m31Im4C4+c,B L+i+G41H4Gc,A T1e+8+8G4CE,A O1W1+e814iD,B 2G928Z42CW5,B

S1f+W+A+KGc,A 1W622Wg1Y49,G M+u+O4+KC+c,A +a2GX8J4Y4X,H L+i+G41H41c,A T1e+8+8G4S5,A O3W1+e814CL,A 2G928Z424X5,B

S1f+W+A+K1c,A 2G924XC24XI,H M+u+O4+K4Gc,A +m31GmaC4+c,B G4WGX8IWq8m,G +I1EW1WKOAW,B +O1Y4H+OTA+,D 184WA2eoA82,G

+a2Ma4GD884,B GeYW2+c6A+X,G M+u+O4+K41c,A +m31Gma4C+c,B L+i+G41HC+b,A T1e+8+8G4CD,A O1W1+e894CL,B 184X6XW8AA8,D

S1f+W+A+4Xc,A 4eAWmC+GIGX,D +A+hW3X+Se+,B +m31Gma44Gc,B L+i+G41H4Gb,A 144MW1GC89m,B O1W1+e814SL,B 184Y1WOYI8C,G

+A+ka4WLG9+,B 4eAWmC+GI1X,D 144JW3H+CO4,B +m31Gma441c,B L+i+G41H41b,A T1e+8+8+KS6,A +C+o8I2ACaG,D 2G928Z4A425,B

+K1Ma4GD884,B 4eAWmC+GI+f,D M+u+O4+4KGc,A +o31Gma44+b,A K2e882+WWpC,L T1e+8+8+KCE,A 5+K1GK+GAMI,H +O1Wa64hGX+,E

+A+ka4WLG88,B 4eAWmC+GI+Z,D M+u+O4+4K1c,A +O1W51SA4eG,G L+i+G4114Xc,D T1e+8+8+KS5,A O3W1+e8158L,A 2G928Z424I5,B

84WMW5+bW91,B 4K9G92M6++6,L +A+hW3X+Ku+,B +m3+a92C8YX,M L+i+G4194Wb,A +I1EW1WKGQW,B O1W1+e8958L,B 2G928Z4242D,B

84WMW5+bW89,B 58AY4H19+Y1,A +a2JW3H+CO4,B +m31Gm4KC+c,B K4eG82+WXLH,L T1e+8+8+KCD,A O1W1+e81D8L,B +K1G61bB94+,L

S1e+e+g+4Gc,A 58AY4H11+Y9,L M+u+O4+44Xc,A +m31Gm4K4Gc,B K2e882+WYgC,L T1e+8+884i5,A 5+K1GK+GE4J,H +K1G61bAf8+,M

S1e+e+g+41c,A 58AY4H11+Y3,L +A+hW3X+Kf+,B +m31Gm4K41c,B L+i+G41942b,A T1e+8+8+Ci5,A +e2Y2Wi+E1C,G 4GH18I4YCW5,G

S1e+e+AG4Gc,A 54AI2GW8BC+,K +K1JW3H+CO4,B +o31Gm4K4+b,A K4eG82+WXLO,L T1e+8+884CL,A +A+f9YS2+Y4,L 4GH18I4Y42D,G

Page 15: Volume II, Issue VI, June 2015 An Atlas of 12-Link, 1 ...Keywords– Kinematic chain, structural synthesis, mechanisms, isomorphism, Degree matrix, Structural matrix. I. INTRODUCTION

Volume II, Issue VI, June 2015 IJRSI ISSN 2321 - 2705

www.rsisinternational.org/IJRSI.html Page 31

S1e+e+AG41c,A 3+C2Wg2I8+c,B +A+hW3X+Ke8,B +O1W51S2CeG,G 1W62X3+ZGWA,B T1e+8+8+CCL,A 1G52mmW6+1c,B 44GH2Ga264f,G

S1e+e+A+KGc,A 3+C2Wg2I+Gc,B H8aW82+mq91,D GOXa1+CA4eG,A K4eG824YaGO,A T1e+8+8G58E,A 1I52mmW6++b,A 44GH2Ga264B,M

============================ CHAIN NUMBERS 6401 – 6856 =================

iP841+444A5,A i9848+444AE,A i18481444AE,A i18a8+648A5,A O9W1+Y444f6,A H4aIGK8818e,A O1W1+X5342D,B L+i+C2OG485,A

4O9Wa542+Y3,L 4WA28I+GL8Z,D 42GCYX+IK8e,B i18a8+64+Q5,A O9W1+Y444eE,A H4aIGK8818Y,A GIXA4HC2+Y1,L L+i+C28G495,A

iH8a1+444A5,A i9849+444A5,A i184814C4A5,A GOXWY4aYWH+,L O9W1+Y444eD,A CG5BW5+24+M,B S1e+4+53CW5,A L+i+C28+KO6,A

iH8a++K44A5,A 4O9Wa542+Y9,L i1848144CA5,A i184C+64G96,A +K1M+8Og48X,B H4aIGK+898e,D S1e+4+534X5,A L+i+C28+K96,A

iH844+4K496,A i9848+4C4A5,A i18481444Q5,A i184C+64G95,A +6+U+8eo48e,B M+u+a8+94A5,A S1e+4+534WD,A L+i+C28+K95,A

iH844+4K495,A i9848+44CA5,A i18481444AD,A i184C+648A5,A K4mG1+OY4ee,G M+u+a8+1CA5,A 4I8ec6WX24+,C L+i+C28+K8D,A

iH844+4K48E,A i9848+444Q5,A S1e+W418o4I,E i184C+64+Q5,A O9W1+Y4C4A5,A +C+pW4o+9OW,B J8o2+GX14G5,A L+i+C2884e5,A

iH844+4K48D,A i9848+444AD,A q+e4W41+YMI,E i184C+6488L,A O9W1+Y44CA5,A 82WBW4Y+HeY,B J8o2+GX1416,A L+i+C28+Ce5,A

iH844+44K96,A i9848+4C48L,A i18481444OL,A i184C+64+OL,A O9W1+Y444OL,A H4aIGK+898Y,D J8o2+GX1415,A L+i+C28+CA5,A

iH844+44K95,A i9848+44C8L,A i184814449L,A i184814IIL+,K O1W14Y4K496,B i184W418o4I,E 9B3A2Ga224+,K K4eG41C24Go,A

iH844+44K8E,A i9848+444OL,A i1848+4aK96,A i184814IIK2,A O1W14Y4K495,B M+u+a8+14OL,A J8o2+G1H416,A L+i+828W4eE,A

iH844+44K8D,A i9848+4449L,A i1848+4aK95,A i184W41GoL+,C O1W14Y4K48E,B 4K8eg5Q4++1,E J8o2+G1H415,A K8eW1+I27+D,D

iH844+444f6,A i18a8+4K496,A i1848+4aK8E,A i18481648A5,A +O1Y8I4IGH6,L M+u+2+WX2t+,K J8o2+G1142E,A L+i+828W4AE,A

iH844+444f5,A i18a8+4K495,A i1848+4aK8D,A i1848164+Q5,A O1W14Y44K96,B M+u+2+WX2s2,G J8o21G11425,A K4eG41C2+Hu,L

iH844+444eE,A i18a8+4K48E,A i1848+4a4eE,A S1e+W41Go4A,K O1W14Y44K95,B M+u+2+WX2cA,K J8o2+GH1425,A K4eG41C2+Ho,L

iH844+444eD,A G8WYGK+8Aeb,D i1848+4a4eD,A i1848+6aG95,A O1W14Y44K8E,B H2a8G41HH8X,D J8o2+G19425,A IaqI8H++24A,K

+K1KXWWAC8Y,B i18a8+44K96,A i1848+4a4AE,A i1848+6aG8E,A O1W14Y+GIt+,K M+u+W8+X4AE,G aYCKe51+W+I,E mWa+C25BG+5,A

iH844+444AE,A i18a8+44K95,A i1848+4aCA5,A i1848+6aG8D,A O1W14Y+GIs2,B M+u+W8+X4Q5,G J8o2+G1142D,A mWa+C253GG5,A

iH844+K44A5,A 54AI6IW+24A,K i1848+4a4AD,A i1848+6a8A5,A O1W14Y+GIcA,K M+u+W8+X4AD,G J8o2+G114GL,A mWa+C253+I5,A

iH844+4C4A5,A i18a8+44K8D,A +C+qXX+AS8W,B i1848+6a88L,A 42G8A2eY4OX,G M+u+W8+X4OL,G J8o2+G1141L,A mWa+825Z+I5,A

iH844+44CA5,A +K1KZX+AC8W,B 228CYX+IK8Y,B i1848+6a+OL,A O1W14Y444AE,B M+u+W8+X49L,G a894e54A8+K,K q+e+e5+88HL,K

HCZI8H4A8++,K i18a8+444AE,A i1848+4aC8L,A +K1KXX+BCWW,B +O1We64YWY9,L 4C8mf6H114+,C C98We64A8+K,L +O1YI+mAAKG,B

iH844+444AD,A G3+CYX+IK8e,B i1848+4a4OL,A i1848+64WAE,A O1W14Y4C4A5,B GCWm825B+Z+,G J+o24G11KG6,A HGZ+1+KA8YY,L

iH844+4C48L,A i18a8+K44A5,A i1848+4a49L,A 124CYX+JK+e,B O1W14Y44CA5,B 4I98b5GGGY+,Q J+o24G11KG5,A 48Ga9H4I2A1,B

iH844+44C8L,A i18a8+4C4A5,A i1848+44aeE,A i1848+64WQ5,A O1W14Y444Q5,B +6+U+8eIa8e,B J+o24G11K16,A 952I8H42C+e,A

iH844+444OL,A i18a8+44CA5,A i1848+44aAE,A i1848+64WAD,A O1W14Y444AD,B K4mG1+O2aee,G J+o24G11K15,A CXC+I8X8e+K,K

iH844+4449L,A i18a8+444Q5,A HGYY2GS2++D,E +C+qXX+BCWW,B +6+Ob6KII4+,K O9W11W544A5,A Wm4cWK1+WXI,E 9H324G4AK+5,A

iH84+14K496,A i18a8+444AD,A +C+qXX+ACeW,B 124CYX+JK+Y,B O1W1Wa1+YMI,E O9W1+WL44A5,A J+o24G114WE,A I4mGX4H114a,L

iH84+14K495,A G6WOa64II4+,K 124CYX+IK8Y,B i1848+64WOL,A O1W14Y444OL,B O9W1+W54CA5,A J+o24GH14W5,A 5GAYWK8++Yf,A

iH84+14K48E,A i18a8+444OL,A i1848+44aOL,A i1848+64W9L,A O1W14Y4449L,B +C+s+8OAa8X,B J+o24G11CW5,A 2eL1Ge8++YB,K

GOXY+G4IGHO,L i18a8+4449L,A i1848+44a9L,A i1848+641AE,A O1W1+Z44K96,B +6+U+8eIa8Y,B J+o24G114WD,A 34II8I8+4Gi,A

iH84+144K96,A i184C+4K496,A n8Y28I4AG+5,A i1848+641AD,A O1W1+Z44K95,B O9W1+W54C8L,A J+o24G1142E,A YGGXWa+89g1,K

iH84+144K95,A i184C+4K495,A n8Y28I42GG5,A +C+qXX+BC2W,B +C+o4H53+HI,L O1W14W54K8E,B 952I1GK224A,K 3GIYWK8++Ze,A

iH84+144K8E,A i184C+4K48E,A n8Y28I4A+25,A +Y2CYX+JK+Y,B O1W1+Z44CA5,B 42G8A2e2aOX,G J+o24G11C25,A 3GIYWK8++Yf,A

iH84+144K8D,A i184C+4K48D,A 184YAGqAY2+,B i1848+6419L,A O1W1+Y4aK96,B 4GH18I42+pa,O J+o24G1142D,A e5+98X+8IMW,E

iH84+1444f6,A i184C+44K96,A n+Y22Gb2W1e,A 4WI26M4+8Go,B O1W1+Y4aK95,B O1W14WL44A5,B 5GAXXaG+4+L,K GWY24H+GIfX,D

HCZI8H42+H+,K i184C+44K95,A n+Y22Gb2W+f,A GOXYWK+GSGG,A O1W1+Y4aK8E,B O1W14W54C8L,B J+o24G1141L,A 34II8I8++Hi,L

iH84+1444eE,A GIXA+W8GZA4,G +K1I9HKYI1+,B GOXYWK+GKGH,A O1W1+Y4aK8D,B 4C9I2Ga22L+,K KWg+82+WZZ8,D 3GIYWK8++YB,K

iH84+1444eD,A GIX2+WOGZA4,A n+Y28I4Y+2E,A 144ICGq248A,B O1W1+Y4aCA5,B O1W14Y4IIL+,K J+o2+G1GqGY,A H4YI1GH114I,C

+K1KXW+QC8Y,B GGX21WOGZA4,G n+Y28I4Y+2D,A GmZ24G44KG6,A O1W1+Y4aC8L,B 2KGn9XM6+++,H J+o2+G1XCW5,A 1G4WO51GmYA,M

iH84+1444AE,A i184C+4C4A5,A n+Y22Gb2W+B,K i184W4+nI4A,K O1W1+Y44aAE,B +O1Wg6aYWH+,L J+o2+G1X4WD,A +m4WX4H8gc+,K

42GCYW+IK8i,B i184C+44CA5,A n+Y28I4Y+1L,A 82WACGa24OK,B 5+K1GK+GM4B,M 5+K1GK+WYPK,O J+o2+G1X42D,A 182WY4XHWHC,W

iH84+14C4A5,A HGYY2GKhG++,E +O1YAGqA26+,B GmZ24G4CK+5,A 44GGX8OY4eY,G 44GGX8OZ4WY,G J+o2+G+GM4f,A 8f9+YWGWI1C,J

iH84+144CA5,A i184C+44C8L,A n+Y22Ga224f,A GOXYWK+GGHH,L O1W1+Y44aOL,B O1W1+Y64WOL,B J+o2+G+GM4B,K +C+m92HXWp+,F

iH84+1444AD,A L+g+A1WGGHA,K n+Y22Ga224B,K i184W4+nIL+,J M8u+Y8+1496,A +O1YeM+GSG4,B L8i+828+K96,A i184W41114U,C

468Oc6a224+,K i184814K496,A HGZ24G11KG6,A i9841+534W5,A D1A+A1X+WYA,K +O1YeM+GKG5,B L8i+828+K8E,A HGYY2GS2++i,E

iH84+144C8L,A i184814K495,A HGZ24G11K15,A i9841+53425,A M8u+W8W1496,A +m3+a92j8Y+,M L8i+928+K85,A +K+m91HXWp+,J

iH84+1444OL,A i184814K48E,A 4K9Gc5aA8++,L +a2KXWWAh8+,B M8u+W8W1495,A +m32KK44IG6,B L8i+82O+K85,A S1e+W41114U,C

iH84+14449L,A GOXY+G4IGHI,L K8eWG4882ua,A i1844+534X6,A G4WIWO+896u,D +O1WQ9b2WH+,K L8i+828+K8D,A 54CIHKH114+,H

i9848+4K496,A 8G4KaW+oa89,B GOX+W8fA486,A i1844+53CW5,A +K1JW4I+9OX,B 248I1WQ424i,H L8i+82884A5,A H4aIGK+WY1Y,D

i9848+4K495,A i1848144K95,A GOX+W8f2C86,A HGYY4I4A8+K,K +6+RW4Y+Hee,B +m32KK4CI+5,B L8i+828+CA5,A a894e5+88HK,Q

i9848+4K48E,A i1848144K8E,A 4G924H+89x+,M i1844+534WD,A 5+C2GK1XWY9,O +O1YeM+GGH5,L L8i+828848L,A J+o2+G111LK,L

i9848+44K96,A i1848144K8D,A K8eWG4+8Aua,D +K1KXWWAh8+,B M8u+X8+14A5,A 34KAIKG+++U,C L8i+828+C8L,A HGYY4I4IGH+,F

i9848+44K95,A i18481+GIt+,K i9848+648A5,A 82WCYW+Ip88,B M8u+W8G14A5,A O1W1+X534X6,B aG8ae54A8+K,K 5GKXOL+GGH+,F

i9848+44K8E,A i18481+GIs2,A i9848+64+Q5,A i1844+5B425,A 3KIoeL++++A,K O1W1+X53CW5,B CH8We54A8+K,K Y8H2XKGGM4+,F

GWY28I+8Cab,D i18481+GIcA,K i9848+6488L,A HGZ24H4A8+K,L M8u+W8+14AD,A O1W1+X534WD,B o+m+812KI4B,K KGeWKA4IGH+,C

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