The autoderivation of valid topological graph (TGs) of planar 3DOF parallel mechanisms is studied systematically based on topology embryonic graphs (TEGs) and arrays. First, some TEGs without any binary links are constructed, some paths with only binary links are distributed over the TEGs, and some valid TGs of the planar 3DOF PMs are derived. Second, a complicated derivation of the TG is transformed into an easy derivation of array. Third, some programs are compiled in VB, all valid arrays corresponding to nonisomorphic TGs are derived automatically, and some invalid arrays corresponding to the isomorphic TGs and invalid TGs are determined by compiled programs. Finally, many valid TGs of planar 3DOF PMs with various basic links are derived from valid arrays.

1.
Yang
,
T. -L.
, 2003,
Topology Structure Design of Robot Mechanisms
,
China Machine
,
Beijing
.
2.
Jin
,
Q.
, and
Yang
,
T. -L.
, 2004, “
Theory for Topology Synthesis of Parallel Manipulators and Its Application to Three-Dimension-Translation Parallel Manipulators
,”
ASME J. Mech. Des.
0161-8458,
126
(
4
), pp.
625
639
.
3.
Johnson
,
R. C.
, 1987,
Mechanical Design Synthesis-Creative Design and Optimize
, 2nd ed.,
Huntington
,
New York
.
4.
Gogu
,
G.
, 2008,
Structural Synthesis of Parallel Robots: Part 1: Methodology
,
Springer
, New York.
5.
Lu
,
Y.
, and
Leinonen
,
T.
, 2005, “
Type Synthesis of Unified Planar-Spatial Mechanisms by Systematic Linkage and Topology Matrix-Graph Technique
,”
Mech. Mach. Theory
0094-114X,
40
(
10
), pp.
1145
1163
.
6.
Vucina
,
D.
, and
Freudenstein
,
F.
, 1991, “
Application of Graph Theory and Nonlinear Programming to the Kinematic Synthesis of Mechanisms
,”
Mech. Mach. Theory
0094-114X,
26
(
6
), pp.
553
563
.
7.
Yan
,
H. -S.
, and
Kang
,
C. -H.
, 2009, “
Configuration Synthesis of Mechanisms With Variable Topologies
,”
Mech. Mach. Theory
0094-114X,
44
(
5
), pp.
896
911
.
8.
Herve
,
J. H.
, 1999, “
The Lie Group of Rigid Displacements, A Fundamental Tool for Mechanical Design
,”
Mech. Mach. Theory
0094-114X,
34
, pp.
719
730
.
9.
Pucheta
,
M.
, and
Cardona
,
A.
, 2007, “
An Automated Method for Type Synthesis of Planar Linkages Based on a Constrained Subgraph Isomorphism Detection
,”
Multibody Syst. Dyn.
1384-5640,
18
(
2
), pp.
233
258
.
10.
Pucheta
,
M. A.
, and
Cardona
,
A.
, 2008, “
Synthesis of Planar Multiloop Linkages Starting From Existing Parts or Mechanisms: Enumeration and Initial Sizing
,”
Mech. Based Des. Struct. Mach.
1539-7734,
36
(
4
), pp.
364
391
.
11.
Huang
,
Z.
, and
Li
,
Q.
, 2002, “
Type Synthesis Principle of Minor-Mobility Parallel Manipulators
,”
Sci. China, Ser. E: Technol. Sci.
1006-9321,
45
(
3
), pp.
241
248
.
12.
Wang
,
X. -Y.
,
Baron
,
L.
, and
Cloutier
,
G.
, 2008, “
Topological and Geometrical Synthesis of Three-Degree-Of-Freedom Fully Parallel Manipulators by Instantaneous Kinematics
,”
ASME J. Mech. Des.
0161-8458,
130
(
3
), pp.
032301
8
.
13.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory
,”
ASME J. Mech. Des.
0161-8458,
126
(
1
), pp.
83
92
.
14.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2005, “
Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain
,”
ASME J. Mech. Des.
0161-8458,
127
(
6
), pp.
1113
1121
.
15.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2004, “
Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory
,”
ASME J. Mech. Des.
0161-8458,
126
(
1
), pp.
101
108
.
16.
Hess-Coelho
,
T. A.
, 2006, “
Topological Synthesis of a Parallel Wrist Mechanism
,”
ASME J. Mech. Des.
0161-8458,
128
(
1
), pp.
230
235
.
17.
Rico
,
J. M.
,
Cervantes-Sanchez
,
J. J.
,
Tadeo-Chavez
,
A.
,
Perez-Soto
,
G. I.
, and
Rocha-Chavarria
,
J.
, 2006, “
A Comprehensive Theory of Type Synthesis of Fully Parallel Platforms
, ”
Proceedings of the ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Philadelphia, PA, Sept. 10–13.
18.
Tsai
,
L. W.
, and
Joshi
,
S.
, 2000, “
Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator
,”
ASME J. Mech. Des.
0161-8458,
122
(
4
), pp.
439
446
.
19.
Lu
,
Y.
,
Shi
,
Y.
, and
Hu
,
B.
, 2008, “
Kinematics Analysis of Two Novel 3UPU I and 3UPU II PKMs
,”
Rob. Auton. Syst.
0921-8890,
56
(
4
), pp.
296
305
.
20.
Ruggiu
,
M.
, 2008, “
Kinematics Analysis of the CUR Translational Manipulator
,”
Mech. Mach. Theory
0094-114X,
43
(
9
), pp.
1087
1098
.
21.
Huang
,
T.
,
Li
,
M.
,
Zhao
,
X. -M.
,
Mei
,
J. -P.
,
Chetwynd
,
D. G.
, and
Hu
,
S. J.
, 2005, “
Conceptual Design and Dimensional Synthesis for a 3-DOF Module of the TriVariant—A Novel 5-DOF Reconfigurable Hybrid Robot
,”
IEEE Trans. Rob.
1552-3098,
21
(
3
), pp.
449
456
.
22.
Kim
,
H. S.
, and
Tsai
,
L. W.
, 2003, “
Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator
,”
ASME J. Mech. Des.
0161-8458,
125
(
1
), pp.
92
97
.
23.
Lu
,
Y.
, and
Hu
,
B.
, 2008, “
Unification and Simplification of Velocity/Acceleration of Limited-DOF Parallel Manipulators With Linear Active Legs
,”
Mech. Mach. Theory
0094-114X,
43
(
9
), pp.
1112
1128
.
24.
Gao
,
F.
,
Zhang
,
Y.
, and
Li
,
W.
, 2005, “
Type Synthesis of 3-DOF Reducible Translational Mechanisms
,”
Robotica
0263-5747,
23
(
2
), pp.
239
245
.
25.
Di Gregorio
,
R.
, 2001, “
A New Parallel Wrist Using Only Revolute Pairs: The 3-RUU Wrist
,”
Robotica
0263-5747,
19
, pp.
305
309
.
26.
Xi
,
F.
,
Zhang
,
D.
,
Xu
,
Z.
, and
Mechefske
,
C. M.
, 2003, “
A Comparative Study on Tripod Units for Machine Tools
,”
Int. J. Mach. Tools Manuf.
0890-6955,
43
(
7
), pp.
721
730
.
27.
Alici
,
G.
, and
Shirinzadeh
,
B.
, 2004, “
Topology Optimization and Singularity Analysis of a 3-SPS Parallel Manipulator With a Passive Constraining Spherical Joint
,”
Mech. Mach. Theory
0094-114X,
39
(
2
), pp.
215
235
.
28.
Lu
,
Y.
,
Shi
,
Y.
,
Li
,
S. H.
, and
Tian
,
X. B.
, 2008, “
Synthesis, Kinematics Analysis and Statics of a 2SPS+SPR+SP Parallel Manipulator
,”
ASME J. Mech. Des.
0161-8458,
130
(
9
), pp.
092302
.
You do not currently have access to this content.