To measure unbalanced moments, the knife-edge is used as a support module in traditional platforms, but performances rapidly deteriorate as the edge is worn down. In this paper, considering the requirements of measurements, a two degree-of-freedom (DOF) flexure mechanism is, thus, presented to overcome this drawback. First, off-axis stiffness and manufacturability are improved qualitatively by means of configuration analysis. Then, four generalized cross-spring pivots are exploited in the 2DOF flexure mechanism, and the geometric parameters are analyzed to achieve approximately constant rotational stiffness and reduced center shift simultaneously, which benefits calibration procedure and measurement precision. Models are further developed to determine the shape parameters of leaf-springs and transducer performances. Therefore, a low rotational stiffness is obtained to ensure a high resolution for measurements, and a high load-carrying capacity is achieved via strength checking. Finally, finite element analysis (FEA) is carried out to validate the proposed design, and experimental results demonstrate that the developed platform is capable of unbalance measurements with a high precision and resolution.

References

1.
Boynton
,
R.
, and
Wiener
,
K.
,
1998
, “
Mass Properties Measurement Handbook
,”
Weight Eng.
,
58
(
2
), pp.
13
44
.
2.
Masten, M. K., 2008, “
Inertially Stabilized Platforms for Optical Imaging Systems
,”
IEEE Contr. Syst. Mag.
,
28
(1), pp. 47–64.
3.
Schedlinski
,
C.
, and
Link
,
M.
,
2001
, “
A Survey of Current Inertia Parameter Identification Methods
,”
Mech. Syst. Signal Process.
,
15
(
1
), pp.
189
211
.
4.
Bacaro
,
M.
,
Cianetti
,
F.
, and
Alvino
,
A.
,
2014
, “
Device for Measuring the Inertia Properties of Space Payloads
,”
Mech. Mach. Theory
,
74
(
4
), pp.
134
153
.
5.
Gobbi
,
M.
,
Mastinu
,
G.
, and
Previati
,
G.
,
2011
, “
A Method for Measuring the Inertia Properties of Rigid Bodies
,”
Mech. Syst. Signal Process.
,
25
(
1
), pp.
305
318
.
6.
Almeida
,
R. A. B.
,
Urgueira
,
A. P. V.
, and
Maia
,
N. M. M.
,
2007
, “
Identification of Rigid Body Properties From Vibration Measurements
,”
J. Sound Vib.
,
299
(
4
), pp.
884
899
.
7.
Fabbri
,
A.
, and
Molari
,
G.
,
2004
, “
Static Measurement of the Centre of Gravity Height on Narrow-Track Agricultural Tractors
,”
Biosyst. Eng.
,
87
(
3
), pp.
299
304
.
8.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
9.
Smith
,
S. T.
,
2000
,
Flexures: Elements of Elastic Mechanisms
,
Gordon and Breach Science Publishers
,
New York
.
10.
Yan
,
W. X.
,
Zhan
,
S. T.
,
Qian
,
Z. Y.
,
Fu
,
Z.
, and
Zhao
,
Y. Z.
,
2014
, “
Design of a Measurement System for Use in Static Balancing a Two-Axis Gimbaled Antenna
,”
Proc. Inst. Mech. Eng., Part G
,
228
(
13
), pp.
2530
2541
.
11.
Boynton
,
R.
,
Wiener
,
K.
,
Kennedy
,
P.
, and
Rathbun
,
B.
,
2003
, “
Static Balancing a Device With Two or More Degrees of Freedom
,”
62nd Annual Conference of Society of Allied Weight Engineers
(
SAWE
), New Haven, CT, May 19–21, SAWE Paper No. 3320.
12.
Zhao
,
H. Z.
, and
Bi
,
S. S.
,
2010
, “
Stiffness and Stress Characteristics of the Generalized Cross-Spring Pivot
,”
Mech. Mach. Theory
,
45
(
3
), pp.
378
391
.
13.
Zhao
,
H. Z.
, and
Bi
,
S. S.
,
2010
, “
Accuracy Characteristics of the Generalized Cross-Spring Pivot
,”
Mech. Mach. Theory
,
45
(
10
), pp.
1434
1448
.
14.
Zhao
,
H. Z.
,
Bi
,
S. S.
, and
Yu
,
J. J.
,
2011
, “
Nonlinear Deformation Behavior of a Beam-Based Flexural Pivot With Monolithic Arrangement
,”
Precis. Eng.
,
35
(
2
), pp.
369
382
.
15.
Merriam
,
E. G.
,
Jones
,
J. E.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2013
, “
Monolithic 2 DOF Fully Compliant Space Pointing Mechanism
,”
Mech. Sci.
,
4
(
2
), pp.
381
390
.
16.
Yu
,
J. J.
,
Lu
,
D. F.
, and
Hao
,
G. B.
,
2015
, “
Design and Analysis of a Compliant Parallel Pan-Tilt Platform
,”
Meccanica
,
51
(
7
), pp.
1559
1570
.
17.
Hao
,
G. B.
, and
Kong
,
X. W.
,
2013
, “
A Normalization-Based Approach to the Mobility Analysis of Spatial Compliant Multi-Beam Modules
,”
Mech. Mach. Theory
,
59
(
1
), pp.
1
19
.
18.
Hao
,
G. B.
,
2017
, “
Determinate Design and Analytical Analysis of a Class of Symmetrical Flexure Guiding Mechanisms for Linear Actuators
,”
ASME J. Mech. Des.
,
139
(
1
), p.
012301
.
19.
Awtar
,
S.
,
Shimotsu
,
K.
, and
Sen
,
S.
,
2010
, “
Elastic Averaging in Flexure Mechanisms: A Three-Beam Parallelogram Flexure Case Study
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041006
.
20.
Xu
,
Q.
,
2015
, “
Design of a Large-Range Compliant Rotary Micropositioning Stage With Angle and Torque Sensing
,”
IEEE Sens. J.
,
15
(
4
), pp.
2419
2430
.
21.
Xu
,
Q.
,
2013
, “
Design and Implementation of a Novel Rotary Micropositioning System Driven by Linear Voice Coil Motor
,”
Rev. Sci. Instrum.
,
84
(
5
), p.
055001
.
22.
Henein
,
S.
,
Spanoudakis
,
P.
,
Droz
,
S.
,
Myklebust
,
L. I.
, and
Onillon
,
E.
,
2003
, “
Flexure Pivot for Aerospace Mechanisms
,”
Tenth European Space Mechanisms and Tribology Symposium
(
ESMATS
), San Sebastián, Spain, Sept. 24–26, Paper No. ESA SP-524.
23.
Fowler
,
R. M.
,
Maselli
,
A.
,
Pluimers
,
P.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
,
2014
, “
Flex-16: A Large-Displacement Monolithic Compliant Rotational Hinge
,”
Mech. Mach. Theory
,
82
, pp.
203
217
.
24.
Kim
,
K.
,
Ahn
,
D.
, and
Gweon
,
D.
,
2012
, “
Optimal Design of a 1-Rotational DOF Flexure Joint for a 3-DOF H-Type Stage
,”
Mechatronics
,
22
(
1
), pp.
24
32
.
25.
Trease
,
B.
,
Moon
,
Y.
, and
Kota
,
S.
,
2005
, “
Design of Large-Displacement Compliant Joints
,”
ASME J. Mech. Des.
,
127
(
7
), pp.
788
798
.
You do not currently have access to this content.