Structural analysis of variable topology mechanisms (VTMs) is the leading task when studying the topological variability of mechanisms. Of several major concerns, structure decomposition and homomorphism identification are two dominating issues for the structural analysis of VTMs. This paper presents a systematic computational approach for the structure decomposition and homomorphism identification of planar VTMs. Along with the proposed method, a constraint matrix representation, that records the potential motion constraints and the topological structures of a VTM, is introduced for serving as the basis of the approach. In addition, a new index, namely, degrees of homomorphism (DOHs), is suggested for quantifying the topological similarity among VTMs. For illustration, an automatic steel clamping and sawing mechanism and a group of mechanisms with similar topologies are adopted, from which their structure decomposition and homomorphism identification are carried out. As shown, the method is both symbolically readable and computationally considerable. The result is helpful for the automated structural analysis and synthesis of variable topology mechanisms.

References

References
1.
Dai
,
J. S.
, and
Rees Jones
,
J.
,
1998
, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME Design Engineering Technical Conference
, Atlanta, GA., Sept.
13
16
.
2.
Dai
,
J. S.
, and
Rees Jones
,
J.
,
1999
, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
375
382
.10.1115/1.2829470
3.
Yan
,
H.-S.
, and
Liu
,
N.-T.
,
1999
, “
Configuration Synthesis of One Step Push-Button Stopper Lock With Variable Passwords
,”
Proceedings of the 10th World Congress on the Theory of Machines and Mechanisms
, Oulu, Finland, June
20
24
.
4.
Yan
,
H.-S.
, and
Liu
,
N.-T.
,
2000
, “
Finite-State-Machine Representations for Mechanisms and Chains With Variable Topologies
,”
ASME Design Engineering Technical Conference
, Baltimore, MD., Sept.
10
13
.
5.
Lan
,
Z. H.
, and
Du
,
R.
,
2008
, “
Representation of Topological Changes in Metamorphic Mechanisms With Matrices of the Same Dimension
,”
ASME J. Mech. Des.
,
130
(
7
), p.
074501
.10.1115/1.2918917
6.
Li
,
S.
, and
Dai
,
J. S.
,
2011
, “
Augmented Adjacency Matrix for Topological Configuration of the Metamorphic Mechanisms
,”
J. Adv. Mech. Des., Syst., Manuf.
,
5
(
3
), pp.
187
198
.10.1299/jamdsm.5.187
7.
Li
,
D.
, and
Zhang
,
Z.
,
2011
, “
Configuration Analysis of Metamorphic Mechanisms Based on Extended Adjacency Matrix Operations
,”
Chin. J. Mech. Eng.
,
24
(
5
), pp.
1
7
.10.3901/CJME.2011.01.001
8.
Dai
,
J. S.
, and
Rees Jones
,
J.
,
2005
, “
Matrix Representation of Topological Changes in Metamorphic Mechanisms
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
837
840
.10.1115/1.1866159
9.
Yan
,
H.-S.
, and
Kuo
,
C.-H.
,
2006
, “
Topological Representations and Characteristics of Variable Kinematic Joints
,”
ASME J. Mech. Des.
,
128
(
2
), pp.
384
391
.10.1115/1.2166854
10.
Yan
,
H.-S.
, and
Kuo
,
C.-H.
,
2006
, “
Representations and Identifications of Structural and Motion State Characteristics of Mechanisms With Variable Topologies
,”
Trans. Can. Soc. Mech. Eng.
,
30
(
1
), pp.
19
40
.
11.
Zhang
,
K. T.
,
Dai
,
J. S.
,
Fang
,
Y. F.
, and
Zeng
,
Q.
,
2011
, “String Matrix Based Geometrical and Topological Representation of Mechanisms,”
The 13th World Congress in Mechanism and Machine Science
, Guanajuato, México, June
19
25
.
12.
Zhang
,
K.
,
Dai
,
J. S.
, and
Fang
,
Y.
,
2010
, “
Topology and Constraint Analysis of Phase Change in the Metamorphic Chain and Its Evolved Mechanism
,”
ASME J. Mech. Des.
,
132
(
12
), p.
121001
.10.1115/1.4002691
13.
Slaboch
,
B. J.
, and
Voglewede
,
P. A.
,
2011
, “
Mechanism State Matrices for Planar Reconfigurable Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
1
), p.
011012
.10.1115/1.4003270
14.
Korves
,
B. A.
,
Slaboch
,
B. J.
, and
Voglewede
,
P. A.
,
2012
, “
Mechanism State Matrices for Spatial Reconfigurable Mechanisms
,”
ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2012)
, Chicago, IL., Aug.
12
15
, Paper No. DETC2012-71361.
15.
Zhang
,
K.
,
Fang
,
Y.
,
Wei
,
G.
, and
Dai
,
J. S.
,
2012
, “
Structural Representation of Reconfigurable Linkages
,”
Advances in Reconfigurable Mechanisms and Robots I
,
J. S.
Dai
,
M.
Zoppi,
and
X.
Kong
, eds. (Proceedings of the 2nd ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, Tianjin, China, July 7–11, 2012),
London
,
Springer
, pp.
127
137
.
16.
Zhang
,
W.
, and
Ding
,
X.
,
2012
, “
A Method for Configuration Representation of Metamorphic Mechanisms With Information of Component Variation
,”
Advances in Reconfigurable Mechanisms and Robots I
,
J. S.
Dai
,
M.
Zoppi
, and
X.
Kong
, eds. (Proceedings of the 2nd ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, Tianjin, China, July 7–11, 2012),
London
,
Springer
, pp.
13
24
.
17.
Huang
,
H.-H.
,
2006
, “
Representation of the Variable Chain Mechanisms With Sequential Movement
,”
ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2006)
, Philadelphia, PA., Sept. 10–13, Paper No. DETC2006-99300.
18.
Slaboch
,
B.
, and
Voglewede
,
P.
,
2013
, “
Planar, Higher Variable Joints for Reconfigurable Mechanisms
,”
ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2013)
, Portland, OR., Aug 4–7, Paper No. DETC2013-13120.
19.
Kuo
,
C.-H.
, and
Yan
,
H.-S.
,
2007
, “
On the Mobility and Configuration Singularity in Mechanisms With Variable Topologies
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
617
624
.10.1115/1.2717230
20.
Shieh
,
W.-B.
,
Sun
,
F.
, and
Chen
,
D.-Z.
,
2011
, “
On the Operation Space and Motion Compatibility of Variable Topology Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
2
), p.
021007
.10.1115/1.4003579
21.
Ding
,
X.
, and
Yang
,
Y.
,
2012
, “
Reconfiguration Theory of Mechanism From a Traditional Artifact
,”
ASME J. Mech. Des.
,
132
(
11
), p.
114501
.10.1115/1.4002692
22.
Gan
,
D.
,
Dai
,
J. S.
, and
Liao
,
Q.
,
2010
, “
Constraint Analysis on Mobility Change of a Novel Metamorphic Parallel Mechanism
,”
Mech. Mach. Theory
,
45
(
12
), pp.
1864
1876
.10.1016/j.mechmachtheory.2010.08.004
23.
Ren
,
P.
, and
Hong
,
D.
,
2011
, “
Mobility Analysis of a Spoked Walking Machine With Variable Topologies
,”
ASME J. Mech. Rob.
,
3
(
4
), p.
041005
.10.1115/1.4004892
24.
Dai
,
J. S.
, and
Rees
,
J. J.
,
1999
, “
Configuration Transformations in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
Proceedings of the 10th World Congress on the Theory of Machines and Mechanisms
, Oulu, Finland, June 20–24, Vol.
2
, pp.
542
547
.
25.
Liu
,
C.-H.
,
2009
, “
The Configuration-Function Transition Digraphs of Metamorphic Mechanisms or Variable Topology Mechanisms
,”
ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots
, London, UK., June
22
24
.
26.
Zhang
,
W. X.
,
Ding
,
X. L.
, and
Dai
,
J. S.
,
2011
, “
Morphological Synthesis of Metamorphic Mechanisms Based on Constraint Variation
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
225
(
12
), pp.
2997
3010
.10.1177/0954406211408953
27.
Ding
,
X.
,
Yang
,
Y.
, and
Dai
,
J. S.
,
2011
, “
Topology and Kinematic Analysis of Color-Changing Ball
,”
Mech. Mach. Theory
,
46
(
1
), pp.
67
81
.10.1016/j.mechmachtheory.2010.08.010
28.
Zhang
,
L.
, and
Dai
,
J. S.
,
2009
, “
Reconfiguration of Spatial Metamorphic Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
1
), p.
011012
.10.1115/1.2963025
29.
Kuo
,
C.-H.
, and
Chang
,
L.-Y.
,
2013
, “
An Algebraic and Computational Strategy for Structure Decomposition of Variable Topology Mechanisms
,”
ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2013)
, Portland, OR., Aug. 4–7, Paper No. DETC2013-12510.
30.
Li
,
S.
, and
Dai
,
J. S.
,
2012
, “
Structure Synthesis of Single-Driven Metamorphic Mechanisms Based on the Augmented Assur Groups
,”
ASME J. Mech. Rob.
,
4
(
3
), p.
031004
.10.1115/1.4006741
31.
Chang
,
L.-Y.
, and
Kuo
,
C.-H.
,
2012
, “
On the Matrix Representation Methods for Variable Topology Mechanisms
,”
Advances in Reconfigurable Mechanisms and Robots I
,
J. S.
Dai
,
M.
Zoppi
, and
X.
Kong
, eds. (Proceedings of The 2nd ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, Tianjin, China, July 7–11, 2012),
London
,
Springer
, pp.
73
81
.
32.
Tsai
,
L.-W.
,
2001
,
Mechanism Design: Enumeration of Kinematic Structures According to Function
,
CRC Press LLC
,
Boca Raton, FL
.
33.
Kuo
,
C.-H.
,
Dai
,
J. S.
, and
Yan
,
H.-S.
,
2009
, “
Reconfiguration Principles and Strategies for Reconfigurable Mechanisms
,”
ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR 2009)
, London, UK., June
22
24
.
34.
Chen
,
F.-C.
, and
Yan
,
H.-S.
,
1999
, “
A Methodology for the Configuration Synthesis of Machining Centers With Automatic Tool Changer
,”
ASME J. Mech. Des.
,
121
(
3
), pp.
359
367
.10.1115/1.2829468
35.
Mruthyunjaya
,
T. S.
,
2003
, “
Kinematic Structure of Mechanisms Revisited
,”
Mech. Mach. Theory
,
38
(
4
), pp.
279
320
.10.1016/S0094-114X(02)00120-9
You do not currently have access to this content.