Proceedings of
2014
IFToMM Asian Conference on Mechanism and Machine Science
July
9
–
10
, 20
14
, Tianjin, China
An Approach for Parameter Identification of 6

DOF Parallel Kinematic Machines
Tian Huang
School of Mechanical Engineering, Tianjin Univers
ity, Tianjin 300072, China
e

mail:
tianhuang
@
tju.edu.cn
David J. Whithehouse
School of Engineering, University of Warwick, Coventry CV4 7AL, UK
Abstract:
This paper presents a general and novel approach that
enables the geometric paramet
ers of 6

DOF parallel kinematic
machines to be identified.
Keywords:
Parallel Kinematic Machines, Calibration
1 Introduction
Accuracy is a important performance specification of
parallel kinematic machines (PKM)
.
It has been
acknowledged that the k
inematic calibration is a practical
and economical way for enhancing accuracy of the PKM
systems
[1~5]
.
It is well recognizded that the pose error of a PKM with
six degrees of freedom (DOF) can in principle be fully
compensated by software.
2 Full Po
se Data Based Identification
Consider a 6

DOF PKM system with purely parallel
architecture, the vector form of the forward kinematic
model can be expressed by
)
,
(
0
0
p
q
f
x
j
j
n
j
,
,
2
,
1
(1)
3 The Minimum Pose D
ata Based Identification
3.1 Basic idea
As shown Figure 1, the essential distinction of PKM
systems from the conventional machines is that pose of
end

effector along/about any single axis of the Cartesian
coordinate system is the nonlinear mapping of all
the
actuated joint variables.
3.2 Identifiability
In order to select the minimum set of pose error data, it is
necessary to investigate the identifiablilty of the parameter
errors. The component associated with the
z
axis can be
expressed by
p
J
zj
j
zj
z
e
n
j
,
,
2
,
1
(2)
3.3 Formulation of the constraint equations
3.3.1 Determination of the position offsets
The measurement can be prevented by shifting the frame
xyz
O
such
that
O
is coincident with
1
O
while keeping
the
x
,
y
and
z
axes unchanged. This leads to
δ
H
H
H
p
T
1
T
(3)
4
Conclusions
The Conclusion can be drawn as follows:
(1)
The parameter errors of the system can be estimated
by simply measuring the “flatness” of a fictitious
plane parallel to the
x

y
plane.
(2)
This method is so general that it can also be used to
handle the
parameter identification problems of the
PKM with fewer than 6

DOF.
Acknowledgements
This research is sponsored by the NSFC(Grant No.
50075006) and the Royal Society UK

China Joint
Research Grant.
References
1.
Besnard, S., Khalil, W., Identifiable pa
rameters for parallel
robots kinematic calibration, In:
Proc. of ICRA
, Seoul,
Korea, 2859

2866, 2001
2.
Khalil
,
W
.
et al
,
Self calibration of
S
tewart

G
ough parallel
robots without extra sensors
,
IEEE Trans
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on Robotics and
Automation
,
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(6):
1118

1121
,1999
3.
Mo
oring B, Roth Z, Driels, M, Fundamentals of manipulator
calibration, John Wiley & Sons, New York, 1992
4.
Huang
,
T.
et al
,
A simple yet
effective
approach for error
compensation of a tripod

based parallel kinematic machine
,
Annals of CIRP
, 49(1): 285

288
,2000
5.
Zhuang, H., et al. Calibration of Stewart platform and other
parallel manipulators by minimizing inverse kinematic
residual,
J. of Robotic System
, 15(7): 395

405, 1998
Figure 1 The topological structure of PKM system
s
20mm
18mm
18mm
15mm
83mm
8mm
83mm
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