Usage of compliant micromechanical oscillators has increased in recent years, due to their reliable performance despite the growing demand for miniaturization. However, ambient vibrations affect the momentum of such oscillators, causing inaccuracy, malfunction, or even failure. Therefore, this paper presents a compliant force-balanced mechanism based on rectilinear motion, enabling usage of prismatic oscillators in translational accelerating environments. The proposed mechanism is based on the opposite motion of two coplanar prismatic joints along noncollinear axes via a shape-optimized linkage system. Rigid-body replacement with shape optimized X-bob, Q-LITF, and LITF joints yielded a harmonic (R > 0.999), low frequency (f=27Hz) single piece force-balanced micromechanical oscillator ( 35 mm). The experimental evaluation of large-scale prototypes showed a low ratio of the center of mass (CoM) shift compared to the stroke of the device ( 0.01) and proper decoupling of the mechanism from the base, as the oscillating frequency of the balanced devices during ambient disturbances was unaffected, whereas unbalanced devices had frequency deviations up to 1.6%. Moreover, the balanced device reduced the resultant inertial forces transmitted to the base by 95%.

References

References
1.
Hsu
,
W.-T.
,
2008
, “
Recent Progress in Silicon MEMS Oscillators
,” DTIC Report No.
ADA504079
, Defense Technical Information Center, Fort Belvoir, VA.
2.
Lee
,
J.-Y.
,
Bahreyni
,
B.
,
Zhu
,
Y.
, and
Seshia
,
A. A.
,
2008
, “
A Single-Crystal-Silicon Bulk-Acoustic-Mode Microresonator Oscillator
,”
IEEE Electron Device Lett.
,
29
(
7
), pp.
701
703
.
3.
Van Beek
,
J.
, and
Puers
,
R.
,
2012
, “
A Review of MEMS Oscillators for Frequency Reference and Timing Applications
,”
J. Micromech. Microeng.
,
22
(
1
), p.
013001
.
4.
Riley
,
W. J.
,
2008
,
Handbook of Frequency Stability Analysis
,
U.S. Department of Commerce, National Institute of Standards and Technology
,
Boulder, CO
.
5.
van der Wijk
,
V.
,
Herder
,
J. L.
, and
Demeulenaere
,
B.
,
2009
, “
Comparison of Various Dynamic Balancing Principles Regarding Additional Mass and Additional Inertia
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041006
.
6.
Hilpert
,
H.
,
1968
, “
Weight Balancing of Precision Mechanical Instruments
,”
J. Mech.
,
3
(
4
), pp.
289
302
.
7.
Kamenskii
,
V.
,
1968
, “
On the Question of the Balancing of Plane Linkages
,”
J. Mech.
,
3
(
4
), pp.
303
322
.
8.
Lowen
,
G.
, and
Berkof
,
R.
,
1968
, “
Survey of Investigations Into the Balancing of Linkages
,”
J. Mech.
,
3
(
4
), pp.
221
231
.
9.
Lowen
,
G.
,
Tepper
,
F.
, and
Berkof
,
R.
,
1983
, “
Balancing of Linkages: An Update
,”
Mech. Mach. Theory
,
18
(
3
), pp.
213
220
.
10.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley-Interscience
,
New York
.
11.
Yan
,
H.-S.
,
1992
, “
A Methodology for Creative Mechanism Design
,”
Mech. Mach. Theory
,
27
(
3
), pp.
235
242
.
12.
Arponen
,
T.
,
2001
, “
Regularization of Constraint Singularities in Multibody Systems
,”
Multibody Syst. Dyn.
,
6
(
4
), pp.
355
375
.
13.
Hubbard
,
N. B.
,
Wittwer
,
J. W.
,
Kennedy
,
J. A.
,
Wilcox
,
D. L.
, and
Howell
,
L. L.
,
2004
, “
A Novel Fully Compliant Planar Linear-Motion Mechanism
,”
ASME
Paper No. DETC2004-57008.
14.
Pei
,
X.
,
Yu
,
J.
,
Zong
,
G.
, and
Bi
,
S.
,
2012
, “
A Family of Butterfly Flexural Joints: Q-LITF Pivots
,”
ASME J. Mech. Des.
,
134
(
12
), p.
121005
.
15.
Xu
,
P.
,
Jingjun
,
Y.
,
Guanghua
,
Z.
,
Shusheng
,
B.
, and
Zhiwei
,
Y.
,
2008
, “
Analysis of Rotational Precision for an Isosceles-Trapezoidal Flexural Pivot
,”
ASME J. Mech. Des.
,
130
(
5
), p.
052302
.
16.
Guerinot
,
A. E.
,
Magleby
,
S. P.
,
Howell
,
L. L.
, and
Todd
,
R. H.
,
2005
, “
Compliant Joint Design Principles for High Compressive Load Situations
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
774
781
.
17.
Van der Wijk
,
V.
,
2014
, “
Methodology for Analysis and Synthesis of Inherently Force and Moment-Balanced Mechanisms
,” Ph.D. thesis, University of Twente, Enschede, The Netherlands.
18.
Rao
,
S. S.
, and
Yap
,
F. F.
,
1995
,
Mechanical Vibrations
, Vol.
4
,
Addison-Wesley
,
New York
.
You do not currently have access to this content.