This paper addresses the issue of determining the optimal geometric parameters of a 3-DOF parallel manipulator. One of the advantages of the manipulator is that the moving platform exhibits high tilting capabilities, e.g., as much as ±50deg. The first step of the new optimal methodology proposed in this paper to achieve the optimum design involves developing a design space that includes all possible basic similarity manipulators. The next step deals with the graphical representation of atlases that can illustrate relationships between performance criteria and design parameters. With such atlases, the designer can identify an optimum region with respect to the specification on performances. The region contains the optimum candidates, from which we can select one directly. Finally, the geometric parameters of the manipulator can be reached by comparing the desired workspace and the good-conditioning workspace. The design methodology discussed in this paper has no process to establish the objective function and does not involve any optimization algorithm, which is normally used in traditional optimization. We expect that since each manipulator in the developed design space represents all of its similarity manipulators in terms of performances, this method will guarantee an optimum design result.

1.
Liu
,
X.-J.
,
Wang
,
J.
,
Gao
,
F.
, and
Wang
,
L.-P.
, 2001, “
On the Analysis of a New Spatial Three Degrees of Freedom Parallel Manipulator
,”
IEEE Trans. Rob. Autom.
1042-296X,
17
(
6
), pp.
959
968
.
2.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2002, “
Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory
,”
Proceedings of DETC’02 ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference
,
Montreal
,
Canada
, DETC2002/MECH-34259, Sponsor American Society of Mechanical Engineering.
3.
Di Gregorio
,
R.
, 2002, “
A New Family of Spherical Parallel Manipulators
,”
Robotica
0263-5747,
20
(
4
), pp.
353
358
.
4.
Hess-Coelho
,
Tarcisio A.
, 2006, “
Topological Synthesis of a Parallel Wrist Mechanism
,”
ASME J. Mech. Des.
1050-0472, Paper No. MD-04–1195.
5.
Kim
,
H. S.
, and
Tsai
,
L.-W.
, 2003, “
Design Optimization of a Cartesian Parallel Manipulator
,”
ASME J. Mech. Des.
1050-0472,
125
(
1
), pp.
43
51
.
6.
Chablat
,
D.
, and
Wenger
,
P.
, 2003, “
Architecture Optimization of a 3-DOF Translational Parallel Mechanism for Machining Applications, the Orthoglide
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
3
), pp.
403
410
.
7.
Liu
,
X.-J.
,
Jeong
,
J.
, and
Kim
,
J.
, 2003, “
A Three Translational DOFs Parallel Cube-Manipulator
,”
Robotica
0263-5747,
21
(
6
), pp.
645
653
.
8.
Carricato
,
M.
, and
Parenti-Castelli
,
V.
, 2003, “
Kinematics of a Family of Translational Parallel Mechanisms With Three 4-DOF Legs and Rotary Actuators
,”
J. Rob. Syst.
0741-2223,
20
(
7
), pp.
373
389
.
9.
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.
1050-0472,
126
, pp.
625
639
.
10.
Liu
,
X.-J.
, and
Wang
,
J.
, 2003, “
Some New Parallel Mechanisms Containing the Planar Four-Bar Parallelogram
,”
Int. J. Robot. Res.
0278-3649,
22
(
9
), pp.
717
732
.
11.
Ottaviano
,
E.
, and
Ceccarelli
,
M.
, 2002, “
Optimal Design of CaPaMan (Cassino Parallel Manipulator) With a Specified Orientation Workspace
,”
Robotica
0263-5747,
20
, pp.
159
166
.
12.
Kosinska
,
A.
,
Galicki
,
M.
, and
Kedzior
,
K.
, 2002, “
Determination of Parameters of 3-DOF Spatial Orientation Manipulators for a Specified Workspace
,”
Robotica
0263-5747,
20
, pp.
179
183
.
13.
Ceccarelli
,
M.
, and
Ottaviano
,
E.
, 2002, “
A Workspace Evaluation of an Eclipse Robot
,”
Robotica
0263-5747,
20
, pp.
299
313
.
14.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1989, “
The Optimum Kinematic Design of a Spherical Three Degree-of-Freedom Parallel Manipulator
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
111
, pp.
202
207
.
15.
Merlet
,
J.-P.
, 1997, “
Designing a Parallel Manipulator for a Specific Workspace
,”
Int. J. Robot. Res.
0278-3649,
16
, pp.
545
556
.
16.
Arsenault
,
M.
, and
Boudreau
,
R.
, 2006, “
Synthesis of Planar Parallel Mechanisms While Considering Workspace, Dexterity, Stiffness and Singularity Avoidance
,”
ASME J. Mech. Des.
1050-0472, Paper No. MD-04–1250 (in press).
17.
Schonherr
,
J.
, 2000, “
Evaluation and Optimum Design of Parallel Manipulators Having a Defined Workspace
,”
Proceedings of the ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference
,
Baltimore
, DETC2000/MECH-14092, Sponsor American Society of Mechanical Engineerings.
18.
Stoughton
,
R. S.
, and
Arai
,
T.
, 1993, “
A Modified Stewart Platform Manipulator With Improved Dexterity
,”
IEEE Trans. Rob. Autom.
1042-296X,
9
(
2
), pp.
166
173
.
19.
Carretero
,
J. A.
,
Podhorodeski
,
R. P.
,
Nahon
,
M. A.
, and
Gosselin
,
C. M.
, 2000, “
Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator
,”
ASME J. Mech. Des.
1050-0472,
122
, pp.
17
24
.
20.
Ryu
,
J.
, and
Cha
,
J.
, 2001, “
Optimal Architecture Design of Parallel Manipulators for Best Accuracy
,”
Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Maui
,
Hawwaii
, USA, pp.
1281
1286
.
21.
Zhang
,
D.
,
Wang
,
L.
, and
Lang
,
S. Y. T.
, 2005, “
Parallel Kinematic Machines: Design, Analysis and Simulation in an Integrated Virtual Environment
,”
ASME J. Mech. Des.
1050-0472,
127
, pp.
580
588
.
22.
Fattah
,
A.
, and
Agrawal
,
S. K.
, 2005, “
On the Design of Cable-Suspended Planar Parallel Robots
,”
ASME J. Mech. Des.
1050-0472, Paper No. MD-04–1111 (in press).
23.
Stock
,
M.
, and
Miller
,
K.
, 2003, “
Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot
,”
ASME J. Mech. Des.
1050-0472,
125
(
2
), pp.
292
301
.
24.
Merlet
,
J.-P.
, 2002, “
Still a Long Way to Go on the Road for Parallel Mechanisms
,” A keynote speech presented in
ASME 27th Biennial Mechanisms and Robotics Conf.
,
Montréal
, Canada, Sept. 29–Oct. 2.
25.
Boudreau
,
R.
, and
Gosselin
,
C. M.
, 1999, “
The Synthesis of Planar Parallel Manipulators With a Genetic Algorithm
,”
ASME J. Mech. Des.
1050-0472,
121
, pp.
533
537
.
26.
Merlet
,
J.-P.
, 2001, “
An Improved Design Algorithm Based on Interval Analysis for Parallel Manipulator With Specified Workspace
,”
Proceedings of IEEE International Conference on Robotics and Automation
,
Seoul
,
Korea
, pp.
1289
1294
.
27.
Gosselin
,
C.
, and
Angeles
,
J.
, 1991, “
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
,”
ASME J. Mech. Des.
1050-0472,
113
, pp.
220
226
.
28.
Angeles
,
J.
, and
López-Cajún
,
C.
, 1992, “
Kinematic Isotropy and the Conditioning Index of Serial Robotic Manipulators
,”
Int. J. Robot. Res.
0278-3649,
11
(
6
), pp.
560
571
.
29.
Salisbury
,
J. K.
, and
Craig
,
J. J.
, 1982, “
Articulated Hands: Force Control and Kinematic Issues
,”
Int. J. Robot. Res.
0278-3649,
1
(
1
), pp.
4
12
.
30.
Liu
,
X.-J.
,
Wang
,
J.
,
Gao
,
F.
, and
Wang
,
L.-P.
, 2002, “
The Mechanism Design of a Simplified 6-DOF 6-RUS Parallel Manipulator
,”
Robotica
0263-5747,
20
, pp.
81
91
.
31.
Gao
,
F.
,
Liu
,
X.-J.
, and
Gruver
,
W. A.
, 1998, “
Performance Evaluation of Two-Degree-of-Freedom Planar Parallel Robots
,”
Mech. Mach. Theory
0094-114X,
33
, pp.
661
668
.
32.
Liu
,
X.-J.
,
Wang
,
J.
, and
Zheng
,
H.
, 2003, “
Workspace Atlases for the Computer-Aided Design of the Delta Robot
,” Proc. Inst. Mech. Eng., Part C,
Prog. Low Temp. Phys.
0079-6417,
217
, pp.
861
869
.
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