This paper deals with the sensitivity analysis of 3-RPR planar parallel manipulators (PPMs). First, the sensitivity coefficients of the pose of the manipulator moving platform to variations in the geometric parameters and in the actuated variables are expressed algebraically. Moreover, two aggregate sensitivity indices are determined, one related to the orientation of the manipulator moving platform and another one related to its position. Then, a methodology is proposed to compare 3-RPR PPMs with regard to their dexterity, workspace size and sensitivity. Finally, the sensitivity of a 3-RPR PPM is analyzed in detail and four 3-RPR PPMs are compared as illustrative examples.

1.
Wang
,
J.
, and
Masory
,
O.
, 1993, “
On the Accuracy of a Stewart Platform–Part I, The Effect of Manufacturing Tolerances
,”
Proceedings of the IEEE International Conference on Robotics Automation, ICRA ‘93
, Atlanta, GA, pp.
114
120
.
2.
Kim
,
H. S.
, and
Choi
,
Y. J.
, 2000, “
The Kinematic Error Bound Analysis of the Stewart Platform
,”
J. Rob. Syst.
0741-2223,
17
, pp.
63
73
.
3.
Kim
,
H. S.
, and
Tsai
,
L. -W.
, 2003, “
Design Optimization of a Cartesian Parallel Manipulator
,”
ASME J. Mech. Des.
0161-8458,
125
, pp.
43
51
.
4.
Caro
,
S.
,
Bennis
,
F.
, and
Wenger
,
P.
, 2005, “
Tolerance Synthesis of Mechanisms: A Robust Design Approach
,”
ASME J. Mech. Des.
0161-8458,
127
(
1
), pp.
86
94
.
5.
Caro
,
S.
,
Wenger
,
P.
,
Bennis
,
F.
, and
Chablat
,
D.
, 2006, “
Sensitivity Analysis of the Orthoglide, A 3-DOF Translational Parallel Kinematics Machine
,”
ASME J. Mech. Des.
0161-8458,
128
(
2
), pp.
392
402
.
6.
Yu
,
A.
,
Bonev
,
I. A.
, and
Zsombor-Murray
,
P. J.
, 2008, “
Geometric Method for the Accuracy Analysis of a Class of 3-DOF Planar Parallel Robots
,”
Mech. Mach. Theory
0094-114X,
43
(
3
), pp.
364
375
.
7.
Meng
,
J.
,
Zhang
,
D.
and
Li
,
Z.
(2009). “
Accuracy Analysis of Parallel Manipulators With Joint Clearance
,”
ASME J. Mech. Des.
0161-8458,
131
, p.
011013
.
8.
Bonev
,
I. A.
,
Zlatanov
,
D.
, and
Gosselin
,
C. M.
, 2003, “
Singularity Analysis of 3-DOF Planar Parallel Mechanisms Via Screw Theory
,”
ASME J. Mech. Des.
0161-8458,
125
, pp.
573
581
.
9.
Merlet
,
J. P.
, 2006,
Parallel Robots
, 2nd ed.,
Springer
,
New York
.
10.
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
.
11.
Liu
,
X. -J.
,
Wang
,
J.
, and
Pritschow
,
G.
, 2006, “
Kinematics, Singularity and Workspace of Planar 5R Symmetrical Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
41
(
2
), pp.
145
169
.
12.
Liu
,
X. -J.
,
Wang
,
J.
, and
Pritschow
,
G.
, 2006, “
Performance Atlases and Optimum Design of Planar 5R Symmetrical Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
41
(
2
), pp.
119
144
.
13.
Liu
,
X. -J.
,
Wang
,
J.
, and
Pritschow
,
G.
, 2006, “
On the Optimal Design of the PRRRP 2-DOF Parallel Mechanism
,”
Mech. Mach. Theory
0094-114X,
41
(
9
), pp.
1111
1130
.
14.
Merlet
,
J. P.
, 2006, “
Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,”
ASME J. Mech. Des.
0161-8458,
128
, pp.
199
206
.
15.
Caro
,
S.
,
Chablat
,
D.
,
Wenger
,
P.
, and
Angeles
,
J.
, 2003, “
Isoconditioning Loci of Planar Three-Dof Parallel Manipulators
,”
Recent Advances in Integrated Design and Manufacturing in Mechanical Engineering
,
G.
Gogu
,
D.
Coutellier
,
P.
Chedmail
, and
P.
Ray
, eds.,
Kluwer Academic
,
Dordrecht, The Netherlands
, pp.
129
138
.
16.
Alba-Gomez
,
O.
,
Wenger
,
P.
, and
Pamanes
,
A.
, 2005, “
Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion
,”
ASME Design Engineering Technical Conferences
, Long Beach, CA, Sept.
17.
Chablat
,
D.
,
Wenger
,
P.
,
Majou
,
F.
, and
Merlet
,
J. P.
, 2004, “
An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines
,”
Int. J. Robot. Res.
0278-3649,
23
(
6
), pp.
615
624
.
18.
Khan
,
W. A.
, and
Angeles
,
J.
, 2006, “
The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems
,”
ASME J. Mech. Des.
0161-8458,
128
, pp.
168
178
.
19.
Al-Sultan
,
K. S.
, and
Al-Fawzan
,
M. A.
, 1997, “
A Tabu Search Hooke and Jeeves Algorithm for Unconstrained Optimization
,”
Eur. J. Oper. Res.
0377-2217,
103
, pp.
198
208
.
20.
Li
,
H.
,
Gosselin
,
C.
, and
Richard
,
M. J.
, 2006, “
Determination of Maximal Singularity-Free Zones in the Workspace of Planar Three-Degree-of-Freedom Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
41
(
10
), pp.
1157
1167
.
21.
Hunt
,
K. H.
, 1978,
Kinematic Geometry of Mechanisms
,
Oxford University Press
,
Cambridge, England
.
22.
Hunt
,
K. H.
, 1983, “
Structural Kinematics of In-Parallel Actuated Robot Arms
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
105
(
4
), pp.
705
712
.
23.
Gosselin
,
C.
,
Sefrioui
,
J.
, and
Richard
,
M. J.
, 1992, “
Solutions Polynomiales au Problème de la Cinématique des Manipulateurs Parallèles Plans à Trois Degrés de Liberté
,”
Mech. Mach. Theory
0094-114X,
27
, pp.
107
119
.
24.
Pennock
,
G. R.
, and
Kassner
,
D. J.
, 1990, “
Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot
,”
ASME Proceedings of the 21st Biennial Mechanisms Conference
, Chicago, IL, Sept., pp.
37
43
.
25.
Gosselin
,
C. M.
, and
Merlet
,
J. -P.
, 1994, “
On the Direct Kinematics of Planar Parallel Manipulators: Special Architectures and Number of Solutions
,”
Mech. Mach. Theory
0094-114X,
29
(
8
), pp.
1083
1097
.
26.
Kong
,
X.
, and
Gosselin
,
C. M.
, 2001, “
Forward Displacement Analysis of Third-Class Analytic 3-RPR Planar Parallel Manipulators
,”
Mech. Mach. Theory
0094-114X,
36
(
9
), pp.
1009
1018
.
27.
Wenger
,
P.
,
Chablat
,
D.
, and
Zein
,
M.
, 2007, “
Degeneracy Study of the Forward Kinematics of Planar 3-RPR Parallel Manipulators
,”
ASME J. Mech. Des.
0161-8458,
129
, pp.
1265
1268
.
28.
Binaud
,
N.
, 2009, “
Sensitivity Comparison of Planar Parallel Manipulators
,” IRCCyN Internal Report No. IRCCyN091023.
You do not currently have access to this content.