Kinematic calibration is commonly used to improve the accuracy of a parallel mechanism. This paper presents an effective method for calibrating an overconstrained three degrees-of-freedom parallel manipulator employing a direct kinematic model. An error-mapping function is formulated from the differential of its kinematic model which is established through vector chains with the geometrical errors. To simplify the measurement of the error, the positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which can be measured by a laser tracker accurately. Three different objective functions F1, F2, and F, respectively, representing 1-norm, 2-norm, and inf-norm of the error vector are used to identify the geometrical parameters of the manipulator. The results of computer simulation show that parameters after kinematic calibration through minimizing the objective function F2 is highly accurate and efficient. A calibration experiment is carried out to verify the effectiveness of the method. The maximum residual of calibration points reduces greatly from 3.904 to 0.256 mm during parameter identification. The positioning errors of all points on and inside the space surrounded by the calibration points are smaller than 0.4 mm after error compensation.

References

References
1.
Li
,
Q.
, and
Herve
,
J. M.
,
2014
, “
Type Synthesis of 3-DOF RPR-Equivalent Parallel Mechanisms
,”
IEEE Trans. Rob.
,
30
(
6
), pp.
1333
1343
.
2.
Sun
,
T.
,
Song
,
Y.
,
Dong
,
G.
,
Lian
,
B.
, and
Liu
,
J.
,
2012
, “
Optimal Design of a Parallel Mechanism With Three Rotational Degrees of Freedom
,”
Rob. Comput. Integr. Manuf.
,
28
(
4
), pp.
500
508
.
3.
Wu
,
J. F.
,
Rui
,
Z.
,
Wang
,
R. H.
, and
Yao
,
Y. X.
,
2014
, “
A Systematic Optimization Approach for the Calibration of Parallel Kinematics Machine Tools by a Laser Tracker
,”
Int. J. Mach. Tools Manuf.
,
86
, pp.
1
11
.
4.
Gao
,
M.
,
Li
,
T. M.
, and
Yin
,
W. S.
,
2003
, “
Calibration Method and Experiment of Stewart Platform Using a Laser Tracker
,”
IEEE International Conference on Systems, Man and Cybernetics
(
SMC
), Washington, DC, Oct. 8, pp.
2797
2802
.
5.
Takeda
,
Y.
,
Gang
,
S.
, and
Funabashi
,
H.
,
2004
, “
A DBB-Based Kinematic Calibration Method for In-Parallel Actuated Mechanisms Using a Fourier Series
,”
ASME J. Mech. Des.
,
126
(
5
), pp.
856
865
.
6.
Ni
,
Y. B.
,
Zhang
,
B.
,
Guo
,
W. X.
, and
Shao
,
C. Y.
,
2016
, “
Kinematic Calibration of Parallel Manipulator With Full-Circle Rotation
,”
Ind. Rob.
,
43
(
3
), pp.
296
307
.
7.
Renaud
,
P.
,
Andreff
,
N.
,
Lavest
,
J. M.
, and
Dhome
,
M.
,
2006
, “
Simplifying the Kinematic Calibration of Parallel Mechanisms Using Vision-Based Metrology
,”
IEEE Trans. Rob.
,
22
(
1
), pp.
12
22
.
8.
Traslosheros
,
A.
,
Sebastián
,
J. M.
,
Castillo
,
E.
,
Roberti
,
F.
, and
Carelli
,
R.
,
2010
, “
One Camera in Hand for Kinematic Calibration of a Parallel Robot
,”
IEEE/RSJ
International Conference on Intelligent Robots and Systems
, Taipei, Taiwan, Oct. 18–22, pp.
5673
5678
.
9.
Traslosheros
,
A.
,
Sebastián
,
J. M.
,
Torrijos
,
J.
,
Carelli
,
R.
, and
Castillo
,
E.
,
2013
, “
An Inexpensive Method for Kinematic Calibration of a Parallel Robot by Using One Hand-Held Camera as Main Sensor
,”
Sensors
,
13
(
8
), pp.
9941
9965
.
10.
Majarena
,
A. C.
,
Santolaria
,
J.
,
Samper
,
D.
, and
Aguilar
,
J. J.
,
2011
, “
Modelling and Calibration of Parallel Mechanisms Using Linear Optical Sensors and a Coordinate Measuring Machine
,”
Meas. Sci. Technol.
,
22
(
10
), p.
105101
.
11.
Joubair
,
A.
,
Slamani
,
M.
, and
Bonev
,
I. A.
,
2012
, “
Kinematic Calibration of a 3-DOF Planar Parallel Robot
,”
Ind. Rob.
,
39
(
4
), pp.
392
400
.
12.
Ren
,
X. D.
,
Feng
,
Z. R.
, and
Su
,
C. P.
,
2008
, “
Kinematic Calibration of Parallel Robots Using Orientation Constraint
,”
IEEE
International Symposium on Industrial Electronics
, Cambridge, UK, June 30–July 2, pp.
1435
1440
.
13.
Ren
,
X.
,
Feng
,
Z.
, and
Su
,
C.
,
2009
, “
A New Calibration Method for Parallel Kinematics Machine Tools Using Orientation Constraint
,”
Int. J. Mach. Tools Manuf.
,
49
(
9
), pp.
08
721
.
14.
Yang
,
G. L.
,
Chen
,
I. M.
,
Yeo
,
S. H.
, and
Lim
,
W. K.
,
2002
, “
Simultaneous Base and Tool Calibration for Self-Calibrated Parallel Robots
,”
Robotica
,
20
(
4
), pp.
67
374
.
15.
Hesselbach
,
J.
,
Bier
,
C.
,
Pietsch
,
I.
,
Plitea
,
N.
,
Büttgenbach
,
S.
,
Wogersien
,
A.
, and
Güttler
,
J.
,
2005
, “
Passive-Joint Sensors for Parallel Robots
,”
Mechatronics
,
15
(
1
), pp.
3
65
.
16.
Daney
,
D.
,
2003
, “
Kinematic Calibration of the Gough Platform
,”
Robotica
,
21
(
6
), pp.
77
690
.
17.
Gatti
,
G.
, and
Danieli
,
G.
,
2008
, “
A Practical Approach to Compensate for Geometric Errors in Measuring Arms: Application to a Six-Degree-of-Freedom Kinematic Structure
,”
Meas. Sci. Technol.
,
19
(
1
), p.
015107
.
18.
Huang
,
T.
, and
Whitehouse
,
D. J.
,
2000
, “
A Simple Yet Effective Approach for Error Compensation of a Tripod-Based Parallel Kinematic Machine
,”
CIRP Ann. Manuf. Technol.
,
49
(
1
), pp.
85
288
.
19.
Tian
,
H.
,
Chetwynd
,
D. G.
,
Whitehouse
,
D. J.
, and
Wang
,
J. S.
,
2005
, “
A General and Novel Approach for Parameter Identification of 6-DOF Parallel Kinematic Machines
,”
Mech. Mach. Theory
,
40
(
2
), pp.
19
239
.
20.
Bai
,
S.
, and
Teo
,
M. Y.
,
2003
, “
Kinematic Calibration and Pose Measurement of a Medical Parallel Manipulator by Optical Position Sensors
,”
J. Rob. Syst.
,
20
(
4
), pp.
201
209
.
21.
Majarena
,
A. C.
,
Santolaria
,
J.
,
Samper
,
D.
, and
Aguilar
,
J. J.
,
2013
, “
Analysis and Evaluation of Objective Functions in Kinematic Calibration of Parallel Mechanisms
,”
Int. J. Adv. Manuf. Technol.
,
66
(
5–8
), pp.
751
761
.
22.
Chen
,
G.
,
Wang
,
H.
, and
Lin
,
Z.
,
2014
, “
Determination of the Identifiable Parameters in Robot Calibration Based on the POE Formula
,”
IEEE Trans. Rob.
,
30
(
5
), pp.
1066
1077
.
23.
Varziri
,
M. S.
, and
Notash
,
L.
,
2007
, “
Kinematic Calibration of a Wire-Actuated Parallel Robot
,”
Mech. Mach. Theory
,
42
(
8
), pp.
960
976
.
24.
Imoto
,
J.
,
Takeda
,
Y.
,
Saito
,
H.
, and
Ichiryu
,
K.
,
2009
, “
Optimal Kinematic Calibration of Robots Based on Maximum Positioning-Error Estimation (Theory and Application to a Parallel-Mechanism Pipe Bender)
,”
Fifth International Workshop on Computational Kinematics
, Duisburg, Germany, May 6–8, pp.
133
140
.
25.
Fan
,
C.
,
Zhao
,
G.
,
Zhao
,
J.
,
Zhang
,
L.
, and
Sun
,
L.
,
2015
, “
Calibration of a Parallel Mechanism in a Serial-Parallel Polishing Machine Tool Based on Genetic Algorithm
,”
Int. J. Adv. Manuf. Technol.
,
81
(
1–4
), pp.
27
37
.
26.
Song
,
Y.
,
Zhang
,
J.
,
Lian
,
B.
, and
Sun
,
T.
,
2016
, “
Kinematic Calibration of a 5-DOF Parallel Kinematic Machine
,”
Precis. Eng.
,
45
, pp.
242
261
.
27.
Sun
,
T.
,
Zhai
,
Y.
,
Song
,
Y.
, and
Zhang
,
J.
,
2016
, “
Kinematic Calibration of a 3-DoF Rotational Parallel Manipulator Using Laser Tracker
,”
Rob. Comput. Integr. Manuf.
,
41
, pp.
78
91
.
28.
Lee
,
S.
,
Zeng
,
Q.
, and
Ehmann
,
K. F.
,
2017
, “
Error Modeling for Sensitivity Analysis and Calibration of the Tri-Pyramid Parallel Robot
,”
Int. J. Adv. Manuf. Technol.
,
93
(
1–4
), pp.
1319
1332
.
29.
Ahmed
,
J.
,
Mohamed
,
S.
, and
Ilian
,
A.
,
2012
, “
Kinematic Calibration of a Five-Bar Planar Parallel Robot Using All Working Modes
,”
Rob. Comput. Integr. Manuf.
,
29
(
4
), pp.
15
25
.
30.
Wang
,
F.
,
Chen
,
Q.
, and
Li
,
Q.
,
2015
, “
Optimal Design of a 2-UPR-RPU Parallel Manipulator
,”
ASME J. Mech. Des.
,
137
(
5
), pp.
054501
054504
.
You do not currently have access to this content.