The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015
DOI Number: 10.6567/IFToMM.14TH.WC.PS3.013
Configuration Change Analysis and Design of Metamorphic Mechanisms
with Isomeric Structure
LI Duanling1
Beijing University of
Posts and Telecommunications
Beijing, China
WANG Zhongbao2
Beijing University of
Posts and Telecommunications
Beijing, China
Abstract: In order to analyze the isomers of the molecules
for the configuration change of metamorphic mechanisms
and use the structure of the isomers of the molecules to
design metamorphic mechanisms, a new method in
studying the connection between the molecular structures
of isomers and the Metamorphic mechanisms is proposed
for the first time in this paper. In the new method,
researches on the molecular structures of isomers and the
types of chemical bonds are carried on. Based on the
researches above, the effective adjacency matrices are
established to express the connections of atoms in the
molecular. Then some traditional methods are used to
verify the feasibility of the new method. A metamorphic
logging mechanisms is designed via molecular structures
of isomers. So a bridge between mechanisms and organic
molecules is set up, and a new way for designing the
development of Metamorphic mechanisms is provided in
this paper. It can greatly broaden the development scope
of metamorphic mechanisms.
Keywords: Configuration Analysis, Metamorphic mechanism,
Molecule modeling, Adjacency matrix
I. Introduction
Metamorphic mechanism is a new concept in
Mechanisms field, it is proposed by Professor J Dai at the
25th mechanisms conference of the ASME in Atlanta
based on cell division and regeneration in Biology[1]. We
all known that traditional mechanisms have fixed numbers
of components and the degrees of freedom, the
topological structures of traditional mechanisms do not
change too. Compared to the traditional mechanisms,
metamorphic mechanisms have the characteristics that
they have variable topology and variable degrees of
freedom. With these characteristics, metamorphic
mechanisms rapidly become the focus of Mechanisms
field. Various experts in related field carry out their
original ideas in the configuration of metamorphic
mechanisms. In 1999, after the presentation of the
metamorphic mechanism, Professor J Dai established the
configuration change model of typical metamorphic
mechanism, using the theory of graph theory and
adjacency matrix, and this became the basis research of
metamorphic mechanisms.
1
[email protected]
[email protected]
3
[email protected]
2
M. Ceccarelli3
University of Cassino
Cassino, Italy
In 2002, according to the change of the number of
components and the degree of freedom when the
metamorphic mechanisms configuration transform
mutually, Professor D. L. Li presented a rank-reduction
method for analyzing of metamorphic mechanisms by the
adjacency matrix. A synthesis procedure is presented
too[2].In 2005, J Dai and X. L. Ding discussed the
differences between the metamorphic mechanisms and
others, then put forward the mathematics model of
metamorphic mechanism[3]. Professor D. L. Li put
forward the detailed definition and determination
conditions of metamorphic mechanism[4]. Based on the
traditional topology graph and the adjacency matrix, Z. H.
Zhang proposed color topology and the generalized
incidence matrix, researches on the flexible metamorphic
mechanism were also carried out[5]. In 2008, L. P. Zhang
proposed gene evolution theory of metamorphic
mechanism, and this was the first time people put the
principles of biology into the metamorphic mechanism[6].
In 2009, D. M. Gan did the kinematics analysis of the
metamorphic mechanisms and designed some new types
of metamorphic mechanisms[7]. In 2010, K. T. Zhang
analyzed the designing method and kinetic characteristic
of metamorphic mechanisms[8]. In 2014, B. Y. Chang
proposed the variable constraint spinor model
configuration of metamorphic mechanism[9].
On the other hand, with the developments of
microscopy, people known the molecular structure more
deeply, in 2002, Dr. Constantinos Mavroidis proposed
protein based nano machines, and they were used for
space applications[10]. In 2007, D. J. Huang and D. H.
Huang analyzed the connection of molecular structures,
molecular mechanisms and some nano machines were
designed[11], such as molecular motor, nano electro
mechanical system and so on. In 2011, Wu Jiangyong did
the research on energy storage of F0F1ATPase motor
based on robotic mechanisms[12]. In the research
scientists found that in the process of organic molecular
structure, there are some commonness between topology
structure and organic molecular: the molecule is the
minimal functional unit of organisms, molecule is
composed of atoms, atoms form different spatial
configurations through chemical bond, resulting in
different types of molecules. All institutions are composed
of components, components are connected together
through a hinge forming different topological structure, so
there are different mechanisms.
There are many kinds of organic molecules, they are
connected in different ways and there are many spatial
configurations of them, and various molecules can also be
transformed to each other under certain conditions, all of
these are a great revelation to the research of machinery.
In this paper, we analyze the isomerism in organic
molecules, and explore the relationship between organic
molecules and metamorphic mechanism.
II. Construction and equivalent adjacency matrix
based on the isomeric molecular structure
Metamorphic mechanism is a new type of mechanism
proposed in 1999, it has the characteristic that it does not
have fixed number of components and degree of freedom,
when a metamorphic mechanism is operating, its number
of components and degree of freedom can change, and the
metamorphic mechanism keeps operating, so a
metamorphic mechanism can realize two or several
functions, this is the biggest advantage of metamorphic.
There is a method to express metamorphic mechanism,
there are N components in a metamorphic, so a N N
matrix is used to express the mechanism, in the matrix,
the element representative the component in the
metamorphic mechanism, and 1 says there is connection
between the two components, 0 says no connection
between the two components, so all the connections can
be expressed and this is called a adjacency matrix, and is
the foundation of this paper.
And isomer is a common phenomenon in Organic
Chemistry, inter molecular isomers have the same
molecular formula but different atomic arrangement of
compounds, and they are different molecules, also the
isomers can transform into each other under certain
conditions, shown in Figure 1.
(a)
×
Fig.1
(b)
Fig.2 Two Structures of C2H6O (a) Ethanol (b) Methyl Ether
，
As shown in Figure 2, we take the atoms of
molecular structure as components, and the chemical
bonds as movable hinges, and then we number on each
atom sequentially, so we can establish the adjacency
matrix of the molecule.(1says connection, and 0 says no
connection), so we can obtain the adjacency matrices of
the two isomers of C2H6O, as shown in M N.
、
0
1

0

0
M = 0

0
0

0
0

0
1

0

0
N = 0

0
0

0
0

isomers of C5H12
When the isomers transform into another, in the process
of transformation, there must be breaking and
re-combination of chemical bonds, so the configurations
of molecules will change. Metamorphic mechanism is that:
in continuous operation, there are topology changes
caused by the number of the effective links or the changes
of kinematic pair types and geometric relations and which
lead to the change of organization activity. During the
continuous operation of the mechanism, there is at least
one activity change, and after the change, the mechanism
still keeps running. Therefore, there are common places
between isomerism and metamorphic mechanism.
Generally, there are two kinds of isomers.
(1) Molecules which have the same chemical bond
types but have different configurations, such as
ethanol and ether (C2H6O), and their structures are
shown in Figure 2.
，
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1 0 0 1
0 0 0 1
1 0 0 0
0 1 1 1
1 0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0 
0

0
1

0
0

0
0 
0
0 
0

0
0

0
0

1
0 
、
From the matrices M N we can see, the number of the
components does not change, both have 9, only the space
configuration changes, so this is not a metamorphic
mechanism.
(2)
Molecules which have the different chemical bond
types and different configurations, such as propine
and allene(C3H4), and their structures are shown in
Figure 3.
Known from the organic chemistry, during the process
of the transformation, the metamorphic process mainly
occurs in the non-hydrogen atoms, therefore, the
matrix of C3H4 can be further simplified, which neglect
the hydrogen atom, as shown in Figure 4.
C1 −C ≡ C2 ⇒ C = C = C1
Fig.4 Structures of C3H4 after Simplification
(a)
(b)
Fig.3 Two Structures of C3H4 a Propine
，（ ）
，（b）Allene
Known from the organic chemistry, there are three
types of chemical bonds, single, double and triple bonds.
Atoms which are connected with single bond can rotate
freely, so there is 1 degree of freedom. Atoms which are
connected with double or triple bonds cannot rotate, so
there is no degree of freedom. The two atoms which are
connected with double or triple bonds can be seen as one
component. According to the method above, each
component is numbered, so we can get the initial matrix A
and the final matrix B.
0 1 0 0 0 0
0 1 0 0 0
1 0 1 1 1 0 
1 0 1 1 1 




0 1 0 0 0 0
B = 0 1 0 0 0
A=



0 1 0 0 0 0
0 1 0 0 0
0 1 0 0 0 1 
 0 1 0 0 0 


This method can reduce the number of components
largely. At the same time it reduces the order of the
adjacency matrix. Through this method, we can analyze
some complicated organic molecules.
In conclusion, the step of the method is:
(1) Analyze the structure of the isomers, find out the
number of C and H in the molecule.
(2) Find out the connections in the molecule.
(3) Establish an adjacency and fill in the elements.
(4) Remove the irrelevant H elements and simplify the
adjacency matrix.
(5) If the structure of the isomer is useful, then design
a new metamorphic mechanism according to it.
III..Verification of isomeric transformation based
on the structure of organic molecule
We establish the component diagram, topology of the
structure of the isomers C3H4, as shown in Figure 5. The
initial matrix is A2, and A2=A1.
0 0 0 0 1 0
From the matrices A and B we can see , during the
process of the transformation, the number of the effective
components changes from 6 to 5, and the degree of
freedom changes from 5 to 4. In a word, the number of
components and the degree of freedom both change, so it
is a metamorphic mechanism.
In order to express the connection relation of isomers
more simply, in this section, we will do some
simplification to the matrices A and B. For example, the
elements A12 A21 in A both say that there is connection
between component 1 and component 2, for further
observation, the elements Aij and Aji both mean that there
is connection between components i and component j.
Ignoring the repeat ,we can obtain the simple adjacency
matrices A1 B1.
(a)
、
0
0

0
A1 = 
0
0

0
、
1 0 0 0 0
0 1 1 1 0 
0 0 0 0 0

0 0 0 0 0
0 0 0 0 1

0 0 0 0 0
0
0

B1 =  0

0
 0
1 0 0 0
0 1 1 1 
0 0 0 0

0 0 0 0
0 0 0 0 
Fig.5
(b)
Component Diagram a and Topological Graph
（）
（b）
In this mechanism, before the transformation, it has 6
links. During the process of the transformation, link 2 and
link 5 become one link, so there are 5 links after the
transformation. During the process, the component
diagram and the topological graph are as shown in Figure
6.
In the metamorphic process, when a triple bond breaks,
it is combined with the next triple bond, which results in
three double bonds, as shown in Figure 8.
C = C = C = C −C ≡ C3 LL−C ≡ Cn
1
M
Fig.8 Process of the first triple bond breaking
And so on, at last the whole chain is made of 2n-1
double bonds, because the two atoms which connect with
double bonds cannot rotate freely, the whole chain
becomes a construction. According to the method
proposed in this paper, we can get the initial adjacency
matrix C1 and the final adjacency matrix D1.
1 2 3 4 L n −1 n
(a)
0 1



2
 0 1



3
0 1


C1 = M
O
O



M
O O 


n −1 
0 1

n
0

1
(b)
Fig.6 Component Diagram a and Topological Graph b after
Transformation
（）
（）
In the final graph, the component number of the
mechanism changes, the relationship changes too. There
is reflection in the adjacency matrix. According to the
method in the literature [2], the component 2 and 5 are
combined, so in the adjacency matrix, we add the 5th line
to the 2nd line, and then we delete the 5th line to get a 5×5
final matrix B2.
0
0

B2 =  0

0
 0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1 
0

0
0 
D1 = [0]
According to the method proposed in literature [2], we
take component diagram to express the chain, as shown in
Figure 9, and its initial adjacency matrix C2=C1.
Fig.9 Component Diagram of Chain Molecule
Obviously, B2=B1, the final adjacency matrix from the
two methods are the same, so the idea that we obtain new
metamorphic mechanism from the isomers C3H4 is
entirely feasible.
During the metamorphic process, all the components
are finally combined into one, and all the relationships
transfer to the component 1, so in the initial adjacency
matrix C2, all the elements are added to the 1st line, so we
′
get the intermediate matrix C2 .
1 2 3 4 L n −1 n
0 1 1 1 1 1 1
 0 1

2




3
0 1


C2' M
O
O



M
O O 


n −1 
0 1

n
0 

1
IV. Analysis of metamorphic mechanism based on
any isomer
In the last section, we do some analysis on the isomer
C3H4, and at last we prove that we can get new
metamorphic mechanisms from it. But the structure of
C3H4 is simple, and there is only two components
combining. So in this section, we will put this method into
some common situations if there is a chain of the
molecule which has N triple bonds, as shown in Figure 7.
C ≡ C − C ≡ C −LL− C ≡ C
1
2
Fig.7 Chain Molecule Consist of n Triple Bond
n
So we get the final adjacency matrix D2.
D2 = [ 0] = D1
Thus it can be seen, we can get the same final
Congress in Mechanism and Machine
ience, Taipei, Taiwan, 25
adjacency matrix from different methods, all of these
prove the theory that we can get new metamorphic
mechanisms from the structures of organic molecules.
V.. Example of a metamorphic mechanism
In order to prove the correctness of the theory
proposed above, and to broaden the application of
metamorphic mechanism in the life, in this section, we
will design an example, the mechanism is equal to the
isomer C3H4.
a logging device is shown in Figure 10. it can be used
to cut trees and so on. This device is made of frame 0,
drive link 1, transmission link 2, working link 3, blessing
link 4, and 5 is the goal. Frame 0 and blessing link 4 are
connected by prismatic pair, and the other in revolute
pairs. There is a torsion spring between 2 and 3.
molecular structure changes are associated, and this is
the theoretical foundation for the organic molecule
and the metamorphic mechanism.
(3) In this paper, a metamorphic logging device is
designed, the three working stages are introduced. It
is meaningful to the application of metamorphic
mechanisms.
Acknowledgment
The
work was supported by the National
Natural Science Foundation of China (51375058), the
New Century Excellent Talents in University
(NCET-12-0796), the Specialized Research Fund for
the Doctoral Program of Higher Education
(20120005110008).
References
(a)
(a)
(b)
Fig. 10 Structural Diagram of Logging Device
present the first phase (b) present the second phase
The logging device is divided into three stages, the first
stage is moving-blessing, the transmission link 2 and the
working link 3 are fixed together, so the mechanism is a
restricted five-bar mechanism, The blessing link 4 moves
approach the goal 5, and the degree of the freedom is 1;
The second stage is blessing-cutting, when the blessing
link 4 approaches the goal 5, the degree of freedom is 0. If
the driving force keeps increasing, the torsion spring will
break, the working link rotates around the joint D, and in
this stage, the tree will be cut down; The third stage is
recovering, after the tree cut down, the torsion spring
works, so the logging device will recover back to its
initial stage. So the number of the links changes from 5 to
3,and then to 4, and then 5, the degree of freedom changes
from 1 to 0, and then to 1.
VI.. Conclusions
(1) In this paper, we analyze the changes of molecular
space structure when the isomers change to each
other, the adjacency matrix based on isomer is built
up, and the relevance between metamorphic
mechanism and isomerism is proved.
(2) According to the traditional method, we prove that
metamorphic process and the process of the
[1] Dai Jiansheng and Rees Jones. Mobility in metamorphic
mechanisms of foldable/erectable kinds[J]. Transaction of ASME,
Journal of Mechanical Design,1999,121(3): 375~382
[2] Li Duanling and Dai Jiansheng and Zhang Qixian and Jin Guoguang.
Structural synthesis of metamorphic mechanism based on
configuration transformation[J]. Chinese Journal of Mechanical
Engineering. 2005, vol 38 No.7:12~16.
[3] Dai Jiansheng and Ding Xilun and Zou Huijun. Metamorphic
Principle and the type of metamorphic mechanism[J]. Chinese
Journal of Mechanical Engineering. 2005, vol 41 No.6 :7~12
[4] Li Duanling and Zhang Zhonghai and Dai Jiansheng and Zhang
Ketao. Overview and Prospects of Metamorphic mechanism[J].
Chinese Journal of Mechanical Engineering. 2010, vol 46,
No.13:14~21
[5] Zhang Zhonghai. Research and Application of Structure Theory of
Metamorphic Mechanism[D]. Beijing University of Posts and
Telecommunications, 2009
[6] Zhang Liping and Wang Delun and Dai Jiansheng. Fundamentals of
Metamorphic-mechanism Biological Modeling and Analysis of
Configuration Evolution[J]. Chinese Journal of Mechanical
Engineering. 2008, vol.44 No. 12:49~56
[7] Gan Dongming. Kinematics of spatial mechanisms and innovative
design of metamorphic parallel mechanisms[D]. Beijing University
of Posts and Telecommunications,2009
[8] Zhang Ketao. Topological and geometrical representation of
kinematic structure of metamorphic mechanisms[D]. Beijing
Jiaotong University, 2010
[9] Chang Boyan and Jin Guoguang and Dai Jiansheng. Type Synthesis
of Metamorphic Mechanism Based on Variable Constraint Screw
Theory[J]. Chinese Journal of Mechanical Engineering. 2014, vol
50, No.5: 17~25
[10] Dr. Constantinos Mavroidis and Dr Robert A. Cassanova. Protein
Based Nano-machines for Space Application[J]. Phase INIAC Grant
Final Report, 2002
[11] Huang Dejuan and Huang Dehuan. Molecular Structures and
Molecular Mechanisms[J]. FRONTIER,2007,vol 59, No. 2:20~22
[12] Wu Jiangyong. Research On Energy Storage of F0F1ATPase Motor
Based On Robotic Mechanisms[D]. Southwest Jiaotong University
Master Degree Thesis, 2011