The precision of parallel robots is limited by backlash in their joints. This paper investigates algorithms for designing inexpensive planar parallel robots with prescribed backlash-free workspace. The method of closing the backlash of the actuators uses preloaded flexible joints to replace the passive joints. These flexible joints may be made using standard joints with preloaded springs or by using preloaded flexure joints. Given a norm-bounded wrench acting on the robot, an algorithm is presented for determining the required preload for the flexible joints in order to guarantee backlash-free operation along a path or within a prescribed workspace. An investigation of the effects of the preloaded flexible joints on the stiffness is carried out using performance measures comparing the same robot with or without preloaded joints. These performance measures use an extended stiffness definition based on three noncollinear vertices on the moving platform. This paper presents simulations of the statics, stiffness, and backlash prevention algorithm, followed by experimental validations.

1.
Pollard
,
W.
, 1942, “
Position Controlling Apparatus
,” U.S. Patent No. 2,236,571.
2.
Stewart
,
D.
, 1965, “
A Platform With 6 Degrees of Freedom
,”
Proc. Inst. Mech. Eng.
0020-3483,
180
, pp.
371
386
.
3.
Bamberger
,
H.
,
Wolf
,
A.
, and
Shoham
,
M.
, 2008, “
Assembly Mode Changing in Parallel Mechanisms
,”
IEEE Trans. Rob.
1552-3098,
24
(
4
), pp.
765
772
.
4.
Alici
,
G.
, and
Shirinzadeh
,
B.
, 2005, “
Vibration Analysis of Piezo-Actuated Flexure-Jointed Mechanisms
,”
Proc. SPIE
0277-786X,
5649
(
2
), pp.
445
453
.
5.
Ohya
,
Y.
,
Arai
,
T.
,
Mae
,
Y.
,
Inoue
,
K.
, and
Tanikawa
,
T.
, 1999, “
Development of 3-DOF Finger Module for Micro Manipulation
,”
Proceedings of the IEEE International Conference on Intelligent Robots and Systems
, pp.
894
899
.
6.
Yan
,
S.
,
Zhang
,
F.
,
Qin
,
Z.
, and
Wen
,
S.
, 2006, “
A 3-DOFs Mobile Robot Driven by a Piezoelectric Actuator
,”
Smart Mater. Struct.
0964-1726,
15
(
1
), pp.
N7
N13
.
7.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley
,
New York
.
8.
Lobontiu
,
N.
, 2003,
Compliant Mechanisms Design of Flexure Hinges
,
CRC
,
Boca Raton, FL
.
9.
Pham
,
H. -H.
, and
Chen
,
I. -M.
, 2005, “
Micro-Motion Selective-Actuation X Y Z Flexure Parallel Mechanism: Design and Modeling
,”
Journal of Micromechatronics
,
3
(
1
), pp.
51
73
.
10.
Trease
,
B. P.
,
Moon
,
Y. -M.
, and
Kota
,
S.
, 2005, “
Design of Large-Displacement Compliant Joints
,”
ASME J. Mech. Des.
0161-8458,
127
(
4
), pp.
788
798
.
11.
Chen
,
I. -M.
, 2002, “
Kinematics, Workspace and Static Analyses of Two DOF Flexure Parallel Mechanism
,”
Proceedings of the Seventh Intertional Conference on Control, Automation, Robotics and Vision
, Singapore, pp.
968
973
.
12.
Oetomo
,
D.
,
Daney
,
D.
,
Shirinzadeh
,
B.
, and
Merlet
,
J. -P.
, 2008, “
Certified Workspace Analysis of 3RRR Planar Parallel Flexure Mechanism
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Pasadena, CA, pp.
3838
3843
.
13.
Xu
,
Q.
, and
Li
,
Y.
, 2006, “
A Novel Design of a 3-PRC Translational Compliant Parallel Micromanipulator for Nanomanipulation
,”
Robotica
0263-5747,
24
(
4
), pp.
527
528
.
14.
Kang
,
B. H.
,
Wen
,
J. T.-Y.
,
Dagalakis
,
N. G.
, and
Gorman
,
J. J.
, 2005, “
Analysis and Design of Parallel Mechanisms With Flexure Joints
,”
IEEE Trans. Rob.
1552-3098,
21
(
6
), pp.
1179
1184
.
15.
Yi
,
B. -J.
,
Chung
,
G. B.
,
Na
,
H. Y.
,
Kim
,
W. K.
, and
Suh
,
I. H.
, 2003, “
Design and Experiment of a 3-DOF Parallel Micromechanism Utilizing Flexure Hinges
,”
IEEE Trans. Rob. Autom.
1042-296X,
19
(
4
), pp.
604
612
.
16.
Awtar
,
S.
, and
Slocum
,
A. H.
, 2007, “
Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms
,”
ASME J. Mech. Des.
0161-8458,
129
(
8
), pp.
816
830
.
17.
Bacher
,
J. P.
,
Bottinelli
,
S.
,
Breguet
,
J. M.
, and
Clavel
,
R.
, 2001, “
Delta3: Design and Control of a Flexure Hinges Mechanism
,”
Proc. SPIE
0277-786X,
4568
, pp.
135
142
.
18.
Cash
,
M.
,
Bruch
,
D.
,
Jahn
,
B.
, and
Keas
,
P.
, 2008, “
Practical Considerations of Joint Friction and Backlash in Large Ground-Based Telescope Secondary Optic Positioning Systems
,”
Proc. SPIE
0277-786X,
7018
, pp.
1
12
.
19.
Zubir
,
M. N. M.
, and
Shirinzadeh
,
B.
, 2008, “
Development of a Compliant-Based Microgripper for Microassembly
,”
Proceedings of the 2008 IEEE/ASME International Conference on Mechtronic and Embedded Systems and Applications (MESA)
, Piscataway, NJ, pp.
522
527
.
20.
Hesselbach
,
J.
, and
Raatz
,
A.
, 2000, “
Pseudo-Elastic Flexure-Hinges in Robots for Micro Assembly
,”
Proc. SPIE
0277-786X,
4194
, pp.
157
167
.
21.
Dong
,
W.
,
Sun
,
L.
, and
Du
,
Z.
, 2008, “
Stiffness Research on a High-Precision, Large-Workspace Parallel Mechanism With Compliant Joints
,”
Precis. Eng.
0141-6359,
32
(
3
), pp.
222
231
.
22.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
, 2007, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
0161-8458,
129
(
6
), pp.
625
639
.
23.
Lan
,
C. -C.
, and
Cheng
,
Y. -J.
, 2008, “
Distributed Shape Optimization of Compliant Mechanisms Using Intrinsic Functions
,”
ASME J. Mech. Des.
0161-8458,
130
(
7
), p.
072304
.
24.
Kock
,
S.
, and
Schumacher
,
W.
, 1998, “
A Parallel X-Y Manipulator With Actuation Redundancy for High-Speed and Active-Stiffness Applications
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
2295
2300
.
25.
Yi
,
B. -J.
, and
Freeman
,
R. A.
, 1992, “
Synthesis of Actively Adjustable Springs by Antagonistic Redundant Actuation
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
114
(
3
), pp.
454
461
.
26.
Muller
,
A.
, 2005, “
Internal Preload Control of Redundantly Actuated Parallel Manipulators—Its Application to Backlash Avoiding Control
,”
IEEE Trans. Rob.
1552-3098,
21
(
4
), pp.
668
677
.
27.
Pashkevich
,
A.
,
Chablat
,
D.
, and
Wenger
,
P.
, 2008, “
Stiffness Analysis of 3-D.O.F. Overconstrained Translational Parallel Manipulators
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
1562
1567
.
28.
Pham
,
H. -H.
, and
Chen
,
I. -M.
, 2005, “
Stiffness Modeling of Flexure Parallel Mechanism
,”
Precis. Eng.
0141-6359,
29
(
4
), pp.
467
478
.
29.
Simaan
,
N.
, and
Shoham
,
M.
, 2003, “
Stiffness Synthesis of a Variable Geometry Six-Degree-of-Freedom Double Planar Parallel Robot
,”
Int. J. Robot. Res.
0278-3649,
22
(
9
), pp.
757
775
.
30.
Zhang
,
D.
, and
Gosselin
,
C. M.
, 2001, “
Kinetostatic Modeling of N-DOF Parallel Mechanisms With a Passive Constraining Leg and Prismatic Actuators
,”
ASME J. Mech. Des.
0161-8458,
123
(
3
), pp.
375
381
.
31.
Chen
,
S. -F.
, and
Cao
,
I.
, 2000, “
Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers
,”
Int. J. Robot. Res.
0278-3649,
19
(
9
), pp.
835
847
.
32.
Kövecses
,
J.
, and
Angeles
,
J.
, 2007, “
The Stiffness Matrix in Elastically Articulated Rigid-Body Systems
,”
Multibody Syst. Dyn.
1384-5640,
18
(
2
), pp.
169
184
.
33.
Quennouelle
,
C.
, and
Gosselin
,
C. M.
, 2008, “
Stiffness Matrix of Compliant Parallel Mechanisms
,”
Advances in Robot Kinematics: Analysis and Design
,
Springer
,
New York
, pp.
331
341
.
34.
Angeles
,
J.
, 2002,
Fundamentals of Robotic Mechanical Systems, Mechanical Engineering Series
,
Springer
,
New York
.
35.
Angeles
,
J.
, and
Lopez-Cajun
,
C. S.
, 1992, “
Kinematic Isotropy and the Conditioning Index of Serial Robotic Manipulators
,”
Int. J. Robot. Res.
0278-3649,
11
(
6
), pp.
560
571
.
36.
Lee
,
J.
, 1997, “
A Study on the Manipulability Measures for Robot Manipulators
,”
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, Grenoble, France, pp.
1458
1465
.
37.
Yoshikawa
,
T.
, 1985, “
Manipulability of Robotic Mechanisms
,”
Int. J. Robot. Res.
0278-3649,
4
(
2
), pp.
3
9
.
38.
Valasek
,
M.
,
Belda
,
K.
, and
Florian
,
M.
, 2002, “
Control and Calibration of Redundantly Actuated Parallel Robots
,”
Proceedings of the Third Parallel Kinematics Seminar
, Chemnitz, pp.
411
427
.
39.
Merlet
,
J. -P.
, 2006,
Parallel Robots
,
Springer
,
Dordrecht, The Netherlands
.
40.
Cleary
,
K.
, and
Uebel
,
M.
, 1994, “
Jacobian Formulation for a Novel 6-DOF Parallel Manipulator
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
2377
2382
.
41.
Simaan
,
N.
,
Glozman
,
D.
, and
Shoham
,
M.
, 1998, “
Design Considerations of New Six Degrees-of-Freedom Parallel Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
1327
1333
.
42.
Arora
,
J. S.
, 2004,
Introduction to Optimum Design
,
Academic
,
CA
.
43.
Simaan
,
N.
, 2002, “
Task-Based Design and Synthesis of Variable Geometry Parallel Robots
,” Ph.D. thesis, Technion, Haifa, Isarel.
44.
Bicchi
,
A.
, and
Prattichizzo
,
D.
, 2000, “
Manipulability of Cooperating Robots With Unactuated and Closed-Chain Mechanisms
,”
IEEE Trans. Robot. Autom.
,
16
(
4
), pp.
336
345
.
45.
Chiacchio
,
P.
,
Chiaverini
,
S.
,
Sciavicco
,
L.
, and
Siciliano
,
B.
, 1991, “
Global Task Space Manipulability Ellipsoids for Multiple-Arm Systems
,”
IEEE Trans. Robot. Autom.
,
7
(
5
), pp.
678
685
.
46.
Fattah
,
A.
, and
Hasan Ghasemi
,
A. M.
, 2002, “
Isotropic Design of Spatial Parallel Manipulators
,”
Int. J. Robot. Res.
0278-3649,
21
(
9
), pp.
811
824
.
47.
Gosselin
,
C.
, 1992, “
The Optimum Design of Robotic Manipulators Using Dexterity Indices
,”
Rob. Auton. Syst.
0921-8890,
9
(
4
), pp.
213
226
.
48.
Gosselin
,
C. M.
, and
Angeles
,
J.
, 1991, “
A Global Performance Index for the Kinematic Optimization of Robotic Manipulators
,”
ASME J. Mech. Des.
0161-8458,
113
(
3
), pp.
220
226
.
49.
Merlet
,
J. -P.
, 2006, “
Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,”
ASME J. Mech. Des.
0161-8458,
128
(
1
), pp.
199
206
.
50.
Park
,
F.
, and
Brockett
,
R.
, 1994, “
Kinematic Dexterity of Robotic Mechanisms
,”
Int. J. Robot. Res.
0278-3649,
13
(
1
), pp.
1
15
.
51.
Wei
,
W.
, and
Simaan
,
N.
, “
Multimedia Extension: Design of Planar Parallel Robots With Preloaded Flexures for Guaranteed Backlash Prevention
,” http://www.columbia.edu/cu/mece/arma/projects/BP/BP.shtmlhttp://www.columbia.edu/cu/mece/arma/projects/BP/BP.shtml
You do not currently have access to this content.