This paper introduces a new concept of applying a parallel mechanism in automated fiber placement (AFP) for aerospace part manufacturing. By investigating the system requirements, a 4DOF parallel mechanism consisting of two revolute–prismatic–spherical joints (2RPS) and two universal–prismatic–spherical joints (2UPS) limbs with two rotational (2R) and two translational (2T) motions is proposed. Both inverse and forward kinematics models are obtained and solved analytically. Based on the overall Jacobian matrix in screw theory, singularity loci are presented and the singularity-free workspace is correspondingly illustrated. To maximize the singularity-free workspace, locations of the 2UPS limbs with the platform and base sizes are used in the optimization which gives a new design of a 4DOF parallel mechanism. A dimensionless Jacobian matrix is also defined and its condition number is used for optimizing the kinematics performance in the optimization process. A numerical example is presented with physical constraint considerations of a test bed design for AFP.

References

1.
Lukaszewicz
,
D.
,
Ward
,
C.
, and
Potter
,
K.
,
2012
, “
The Engineering Aspects of Automated Prepreg Layup: History, Present and Future
,”
Composites, Part B
,
43
(
3
), pp.
997
1009
.10.1016/j.compositesb.2011.12.003
2.
Shirinzadeh
,
B.
,
Alici
,
G.
,
Foong
,
C. W.
, and
Cassidy
,
G.
,
2004
, “
Fabrication Process of Open Surfaces by Robotic Fibre Placement
,”
Rob. Comput.-Integr. Manuf.
,
20
(
1
), pp.
17
28
.10.1016/S0736-5845(03)00050-4
3.
Aized
,
T.
, and
Shirinzadeh
,
B.
,
2011
, “
Robotic Fiber Placement Process Analysis and Optimization Using Response Surface Method
,”
Int. J. Adv. Manuf. Technol.
,
55
(
1–4
), pp.
393
404
.10.1007/s00170-010-3028-1
4.
Shirinzadeh
,
B.
,
Cassidy
,
G.
,
Oetomo
,
D.
,
Alici
,
G.
, and
Ang
,
M. H.
,
2007
, “
Trajectory Generation for Open-Contoured Structures in Robotic Fibre Placement
,”
Rob. Comput.-Integr. Manuf.
,
23
(
4
), pp.
380
394
.10.1016/j.rcim.2006.04.006
5.
Shirinzadeh
,
B.
,
Teoh
,
P. L.
,
Tian
,
Y.
,
Dalvand
,
M. M.
,
Zhong
,
Y.
, and
Liaw
,
H. C.
,
2010
, “
Laser Interferometry-Based Guidance Methodology for High Precision Positioning of Mechanisms and Robots
,”
Rob. Comput.-Integr. Manuf.
,
26
(
1
), pp.
74
82
.10.1016/j.rcim.2009.04.002
6.
Debout
,
P.
,
Chanal
,
H.
, and
Duc
,
E.
,
2011
, “
Tool Path Smoothing of a Redundant Machine: Application to Automated Fiber Placement
,”
Comput.-Aided Des.
,
43
(
2
), pp.
122
132
.10.1016/j.cad.2010.09.011
7.
Cui
,
L.
, and
Dai
,
J. S.
,
2011
, “
Axis Constraint Analysis and Its Resultant 6R Double-Centered Overconstrained Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
3
), p.
031004
.10.1115/1.4004225
8.
Gan
,
D. M.
,
Liao
,
Q. Z.
,
Dai
,
J. S.
,
Wei
,
S. M.
, and
Qiao
,
S. G.
,
2008
, “
Dual Quaternion-Based Inverse Kinematics of the General Spatial 7R Mechanism
,”
Proc. Inst. Mech. Eng., Part C
,
222
(
8
), pp.
1593
1598
.10.1243/09544062JMES1082
9.
Merlet
,
J. P.
,
2006
,
Parallel Robots
, 2nd ed.,
Springer
, Dordrecht.10.1007/978-94-010-9587-7
10.
Zhang
,
D.
,
2009
,
Parallel Robotic Machine Tools
,
Springer
,
New York
.10.1007/978-1-4419-1117-9
11.
Gosselin
,
C.
,
1990
, “
Determination of the Workspace of 6-DOF Parallel Manipulators
,”
ASME J. Mech. Design
,
112
(
3
), pp.
331
336
.10.1115/1.2912612
12.
Angeles
,
J.
,
Yang
,
G. L.
, and
Chen
,
I.-M.
,
2003
, “
Singularity Analysis of Three-Legged, Six-DOF Platform Manipulators With URS Legs
,”
IEEE/ASME Trans. Mechatronics
,
8
(
4
), pp.
469
475
.10.1109/TMECH.2003.820005
13.
Gan
,
D. M.
,
Liao
,
Q. Z.
,
Dai
,
J. S.
,
Wei
,
S. M.
, and
Seneviratne
,
L. D.
,
2009
, “
Forward Displacement Analysis of a New 1CCC–5SPS Parallel Mechanism Using Grobner Theory
,”
Proc. Inst. Mech. Eng.
, Part C,
223
(
5
), pp.
1233
1241
.10.1243/09544062JMES1185
14.
Huang
,
Z.
,
Tao
,
W. S.
, and
Fang
,
Y. F.
,
1996
, “
Study on the Kinematic Characteristics of 3 DOF In-Parallel Actuated Platform Mechanisms
,”
Mech. Mach. Theory
,
31
(
8
), pp.
999
1007
.10.1016/0094-114X(96)84593-9
15.
Liu
,
X.-J.
,
Bonev
,
I. A.
,
Wang
,
L.-P.
, and
Xie
,
F. G.
,
2010
, “
Design of a Three-Axis Articulated Tool Head With Parallel Kinematics Achieving Desired Motion/Force Transmission Characteristics
,”
ASME J. Manuf. Sci. Eng.
,
132
(
2
), p.
021009
.10.1115/1.4001244
16.
Gan
,
D. M.
,
Liao
,
Q. Z.
,
Dai
,
J. S.
, and
Wei
,
S. M.
,
2010
, “
Design and Kinematics Analysis of a New 3CCC Parallel Mechanism
,”
Robotica
,
28
(
7
), pp.
1065
1072
.10.1017/S0263574709990555
17.
Zhang
,
K. T.
,
Dai
,
J. S.
, and
Fang
,
Y. F.
,
2012
, “
Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms
,”
ASME J. Mech. Des.
,
135
(
1
), p.
011001
.10.1115/1.4007920
18.
Dai
,
J. S.
,
Huang
,
Z.
, and
Lipkin
,
H.
,
2006
, “
Mobility of Overconstrained Parallel Mechanisms, Special Supplement on Spatial Mechanisms and Robot Manipulators
,”
ASME J. Mech. Des.
,
128
(
1
), pp.
220
229
.10.1115/1.1901708
19.
Yang
,
T. L.
,
2003
,
Topology Structure Design of Robot Mechanisms
,
Machinery Industry Press
,
Beijing
.
20.
Li
,
Q. C.
, and
Huang
,
Z.
,
2003
, “
Type Synthesis of 4-DOF Parallel Manipulators
,”
IEEE International Conference on Robotics and Automation
(
ICRA '03
),
Taipei, Taiwan
, Sept. 14–19, pp.
755
760
.10.1109/ROBOT.2003.1241684
21.
Gao
,
F.
,
Yang
,
J. L.
, and
Ge
,
Q. J.
,
2011
, “
Type Synthesis of Parallel Mechanisms Having the Second Class GF Sets and Two Dimensional Rotations
,”
ASME J. Mech. Rob.
,
3
(
1
), p.
011003
.10.1115/1.4002697
22.
Fan
,
C.
,
Liu
,
H.
, and
Zhang
,
Y.
,
2013
, “
Type Synthesis of 2T2R, 1T2R and 2R Parallel Mechanisms
,”
Mech. Mach. Theory
,
61
, pp.
184
190
.10.1016/j.mechmachtheory.2012.10.006
23.
Gogu
,
G.
,
2005
, “
Fully-Isotropic Parallel Robots With Four Degrees of Freedom T2R2-Type
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS 2005
),
Edmonton, AB, Canada
, Aug. 2–6, pp.
960
965
.10.1109/IROS.2005.1545141
24.
Zhang
,
Y.
, and
Ting
,
K.
,
2012
, “
Type Synthesis of Uncoupled 2T2R Parallel Manipulators
,”
ASME
Paper No. DETC2012-70626.10.1115/DETC2012-70626
25.
Chen
,
W. J.
,
Zhao
,
M. Y.
, and
Fang
,
L. J.
,
2001
, “
Development of a Novel Machine Tool Based on a 4-DOF Parallel Mechanism
,”
J. Yangzhou Univ.
,
4
(
2
), pp.
50
54
.
26.
Wang
,
J. S.
,
Liu
,
X. J.
, and
Duan
,
G. H.
,
2000
, “
Parallel Machine Tool Structure of Two Dimensional Translation and Two Dimensional Rotation
,” China Patent CN00105936.X.
27.
Chen
,
W. J.
,
Zhao
,
M. Y.
, and
Chen
,
S. H.
,
2001
, “
A Novel 4-DOF Parallel Manipulator and Its Kinematic Modeling
,”
IEEE International Conference on Robotics and Automation
(
2001 ICRA
),
Seoul, Korea
, May 21–26, pp.
3350
3355
.10.1109/ROBOT.2001.933135
28.
Liu
,
H. J.
,
Qin
,
Y. F.
, and
Zhao
,
M. Y.
,
2003
, “
The Reachable Workspace Analysis of a Kind of 4-DOF Parallel Mechanism Based on Constraints
,”
IEEE International Conference on Robotics, Intelligent Systems and Signal Processing
(
RISSP
),
Changsha, China
, Oct. 8–13, pp.
799
803
.10.1109/RISSP.2003.1285688
29.
Wang
,
S.
,
2011
, “
The Singularity Research of a Novel 2T2R Parallel Mechanism
,”
Second International Conference on Mechanic Automation and Control Engineering
(
MACE
), Hohhot, Inner Mongolia, China, July 15–17, pp.
866
869
.10.1109/MACE.2011.5987066
30.
Kumar
,
N.
,
Piccin
,
O.
, and
Bayle
,
B.
,
2014
, “
A Task-Based Type Synthesis of Novel 2T2R Parallel Mechanisms
,”
Mech. Mach. Theory
,
77
, pp.
59
72
.10.1016/j.mechmachtheory.2014.02.007
31.
Wei
,
G.
, and
Dai
,
J. S.
,
2010
, “
Geometric and Kinematic Analysis of a Seven-Bar Three-Fixed-Pivoted Compound-Joint Mechanism
,”
Mech. Mach. Theory
,
45
(
2
), pp.
170
184
.10.1016/j.mechmachtheory.2009.05.009
32.
Liu
,
H.
,
Huang
,
T.
, and
Chetwynd
,
D. G.
,
2011
, “
A Method to Formulate a Dimensionally Homogeneous Jacobian of Parallel Manipulators
,”
IEEE Trans. Rob.
,
27
(
1
), pp.
150
156
.10.1109/TRO.2010.2082091
33.
Siciliano
,
B.
, and
Khatib
,
O.
,
2008
,
Springer Handbook of Robotics
,
Springer-Verlag
,
New York
.10.1007/978-3-540-30301-5
34.
Coriolis, 2015, Coriolis Composites, Lorient, France,
http://www.coriolis-composites.com
35.
Bottema
,
O.
, and
Roth
,
B.
,
1979
,
Theoretical Kinematics
,
North-Holland
,
New York
.
36.
Dai
,
J. S.
, and
Rees
,
J. J.
,
2001
, “
Interrelationship Between Screw Systems and Corresponding Reciprocal Systems and Applications
,”
Mech. Mach. Theory
,
36
(
5
), pp.
633
651
.10.1016/S0094-114X(01)00004-0
37.
Gan
,
D. M.
,
Dai
,
J. S.
,
Dias
,
J.
, and
Seneviratne
,
L. D.
,
2013
, “
Unified Kinematics and Singularity Analysis of a Metamorphic Parallel Mechanism With Bifurcated Motion
,”
ASME J. Mech. Rob.
,
5
(
3
), p.
041104
.10.1115/1.4024292
38.
Jiang
,
Q.
, and
Gosselin
,
C.
,
2008
, “
Singularity Equations of Gough–Stewart Platforms Using a Minimal Set of Geometric Parameters
,”
ASME J. Mech. Des.
,
130
(
11
), p.
112303
.10.1115/1.2976450
39.
Merlet
,
J. P.
,
1989
, “
Singular Configurations of Parallel Manipulators and Grassmann Geometry
,”
Int. J. Rob. Res.
,
8
(
5
), pp.
45
56
.10.1177/027836498900800504
40.
Jiang
,
Q.
, and
Gosselin
,
C.
,
2008
, “
The Maximal Singularity-Free Workspace of the Gough–Stewart Platform for a Given Orientation
,”
ASME J. Mech. Des.
,
130
(
11
), p.
112304
.10.1115/1.2976452
41.
Li
,
H.
,
Gosselin
,
C.
, and
Richard
,
M.
,
2007
, “
Determination of the Maximal Singularity-Free Zones in the Six-Dimensional Workspace of the General Gough–Stewart Platform
,”
Mech. Mach. Theory
,
42
(
4
), pp.
497
511
.10.1016/j.mechmachtheory.2006.04.006
42.
Jiang
,
Q.
, and
Gosselin
,
C. M.
,
2009
, “
Determination of the Maximal Singularity-Free Orientation Workspace for the Gough–Stewart Platform
,”
Mech. Mach. Theory
,
44
(
6
), pp.
1281
1293
.10.1016/j.mechmachtheory.2008.07.005
43.
Sun
,
T.
,
Song
,
Y.
,
Li
,
Y.
, and
Zhang
,
J.
,
2010
, “
Workspace Decomposition Based Dimensional Synthesis of a Novel Hybrid Reconfigurable Robot
,”
ASME J. Mech. Rob.
,
2
(
3
), p.
031009
.10.1115/1.4001781
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