It is a generally well-known fact that the design of parallel mechanisms while optimizing performance is quite difficult. In this paper, a reliable synthesis method capable of optimally selecting the geometrical parameters of planar parallel mechanisms is presented. Three different architectures are considered and a genetic algorithm is used to perform the optimization. The performance of each mechanism is evaluated according to four different criteria: workspace, singular configurations, dexterity, and stiffness. In order to make the synthesis method as realistic as possible, mechanical constraints affecting the angular rotation of the 2-RP̱R and 3-RP̱R mechanisms’ passive revolute joints are considered. Moreover, since the conventional methods for computing the dexterity and the stiffness index are not valid for the 3-RP̱R and 3-ṞRR mechanisms, an alternative computation method is used.

1.
Merlet
,
J.-P.
, 1997,
Les Robots Parallèles
, 2nd ed.
Hermès
, Paris, France.
2.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1988, “
The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
110
(
1
), pp.
35
41
.
3.
Murray
,
A. P.
,
Pierrot
,
F.
,
Dauchez
,
P.
, and
McCarthy
,
J. M.
, 1997, “
A Planar Quaternion Approach to the Kinematic Synthesis of a Parallel Manipulator
,”
Robotica
0263-5747,
15
(
4
), pp.
361
365
.
4.
Merlet
,
J.-P.
, 1997, “
Designing a Parallel Manipulator for a Specific Workspace
,”
Int. J. Robot. Res.
0278-3649,
16
(
4
), pp.
545
556
.
5.
Carretero
,
J.
,
Podhorodeski
,
R.
, and
Nahon
,
M.
, 1998, “
Architecture Optimization of a 3-DOF Parallel Mechanism
,” in Proceedings of the
1998 ASME Design Engineering Technical Conference
, Atlanta, Georgia.
6.
Dibakar
,
S.
, and
Mruthyunjaya
,
T.
, 1999, “
Synthesis of Workspaces of Planar Manipulators With Arbitrary Topology Using Shape Representation and Simulated Annealing
,”
Mech. Mach. Theory
0094-114X,
34
(
3
), pp.
391
420
.
7.
Badescu
,
M.
, and
Mavroidis
,
C.
, 2004, “
Workspace Optimization of 3-Legged UPU and UPS Parallel Platforms With Joint Constraints
,”
ASME J. Mech. Des.
1050-0472,
126
(
2
), pp.
291
300
.
8.
Boudreau
,
R.
, and
Gosselin
,
C. M.
, 1999, “
The Synthesis of Planar Parallel Manipulators With a Genetic Algorithm
,”
ASME J. Mech. Des.
1050-0472,
121
(
4
), pp.
533
537
.
9.
Boudreau
,
R.
, and
Gosselin
,
C. M.
, 2001, “
La Synthse d’une Plate-Forme de Gough-Stewart Pour un Espace Atteignable Prescrit
,”
Mech. Mach. Theory
0094-114X,
36
(
3
), pp.
327
342
.
10.
Baron
,
L.
, 2001, “
Workspace-Based Design of Parallel Manipulators of Star Topology With a Genetic Algorithm
,”
Proceedings of the 2001 ASME Design Engineering Technical Conference
, Pittsburgh, Pennsylvania.
11.
Gallant
,
M.
, and
Boudreau
,
R.
, 2002, “
The Synthesis of Planar Parallel Manipulators With Prismatic Joints for an Optimal, Singularity-Free Workspace
,”
J. Rob. Syst.
0741-2223,
19
(
1
), pp.
13
24
.
12.
Kumar
,
V.
, 1992, “
Characterization of Workspaces of Parallel Manipulators
,”
ASME J. Mech. Des.
1050-0472,
114
(
3
), pp.
368
375
.
13.
Merlet
,
J.-P.
,
Gosselin
,
C. M.
, and
Mouly
,
N.
, 1998, “
Workspaces of Planar Parallel Manipulators
,”
Mech. Mach. Theory
0094-114X,
33
(
1-2
), pp.
7
20
.
14.
Gosselin
,
C. M.
, 1990, “
Determination of the Workspace of 6-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
1050-0472,
112
(
3
), pp.
331
336
.
15.
Gosselin
,
C. M.
, and
Jean
,
M.
, 1996, “
Determination of the Workspace of Planar Parallel Manipulators With Joint Limits
,”
Rob. Auton. Syst.
0921-8890,
17
(
3
), pp.
129
138
.
16.
Gosselin
,
C. M.
, and
Guillot
,
M.
, 1991, “
The Synthesis of Manipulators With Prescribed Workspace
,”
ASME J. Mech. Des.
1050-0472,
113
(
4
), pp.
451
455
.
17.
Bonev
,
I. A.
, and
Gosselin
,
C. M.
, 2001, “
Singularity Loci of Planar Manipulators With Revolute Joints
,”
2nd Workshop on Computational Kinematics
, Seoul, South Korea, pp.
1964
1969
.
18.
Chablat
,
D.
, and
Wenger
,
P.
, 1998, “
Working Modes and Aspects in Fully Parallel Manipulators
,”
Proceedings–IEEE International Conference on Robotics and Automation
, Leuven, Belgium, Vol. 3, pp.
1964
1969
.
19.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1990, “
Singularity Analysis of Closed-Loop Kinematic Chains
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
3
), pp.
281
290
.
20.
Bonev
,
I.
,
Zlatanov
,
D.
, and
Gosselin
,
C.
, 2003, “
Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory
,”
ASME J. Mech. Des.
1050-0472,
125
(
3
), pp.
573
581
.
21.
Gosselin
,
C. M.
, 1990, “
Stiffness Mapping for Parallel Manipulators
,”
IEEE Trans. Rob. Autom.
1042-296X,
6
(
3
), pp.
377
382
.
22.
Zanganeh
,
K. E.
, and
Angeles
,
J.
, 1997, “
Kinematic Isotropy and the Optimum Design of Parallel Manipulators
,”
Int. J. Robot. Res.
0278-3649,
16
(
2
), pp.
185
197
.
23.
Chablat
,
D.
, and
Angeles
,
J.
, 2002, “
On the Kinetostatic Optimization of Revolute-Coupled Planar Manipulators
,”
Mech. Mach. Theory
0094-114X,
37
(
4
), pp.
351
374
.
24.
Gosselin
,
C. M.
, 1992, “
The Optimum Design of Robotic Manipulators Using Dexterity Indices
,”
Rob. Auton. Syst.
0921-8890,
9
(
4
), pp.
213
226
.
25.
Kim
,
S.-G.
, and
Ryu
,
J.
, 2003, “
New Dimensionally Homogeneous Jacobian Matrix Formulation by Three End-Effector Points for Optimal Design of Parallel Manipulators
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
4
), pp.
731
736
.
26.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1991, “
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
,”
ASME J. Mech. Des.
1050-0472,
113
(
3
), pp.
220
226
.
27.
Liu
,
X.-J.
,
Jin
,
Z.-L.
, and
Gao
,
F.
, 2000, “
Optimum Design of 3-DOF Spherical Parallel Manipulators With Respect to the Conditioning and Stiffness Indices
,”
Mech. Mach. Theory
0094-114X,
35
(
9
), pp.
1257
1267
.
28.
Arsenault
,
M.
, 2003, “
La Synthèse de Mécanismes Parallèles Plans en Considérant l’Espace Atteignable, la Dextérité, la Raideur et l’Évitement des Singularités
,” Master’s thesis, Faculté d’ingénierie, Université de Moncton, Moncton, New Brunswick, Canada.
You do not currently have access to this content.