This paper explores the deflection and buckling of fixed-guided beams used in compliant mechanisms. The paper’s main contributions include the addition of an axial deflection model to existing beam bending models, the exploration of the deflection domain of a fixed-guided beam, and the demonstration that nonlinear finite element models typically incorrectly predict a beam’s buckling mode unless unrealistic constraints are placed on the beam. It uses an analytical model for predicting the reaction forces, moments, and buckling modes of a fixed-guided beam undergoing large deflections. The model for the bending behavior of the beam is found using elliptic integrals. A model for the axial deflection of the buckling beam is also developed. These two models are combined to predict the performance of a beam undergoing large deflections including higher order buckling modes. The force versus displacement predictions of the model are compared to the experimental force versus deflection data of a bistable mechanism and a thermomechanical in-plane microactuator (TIM). The combined models show good agreement with the force versus deflection data for each device.

References

References
1.
Howell
,
L. L.
, 2001,
Compliant Mechanisms
,
Wiley
,
New York
.
2.
Parkinson
,
M. B.
,
Jensen
,
B. D.
, and
Roach
,
G. M.
, 2000. “
Optimization-Based Design of a Fully-Compliant Bistable Micromechanism
,”
ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, no. DETC2000/MECH-14119.
3.
Ananthasuresh
,
G. K.
, and
Howell
,
L. L.
, 2005, “
Mechanical Design of Compliant Microsystems—A Perspective and Prospects
,”
ASME J. Mech. Des.
,
127
, pp.
736
738
.
4.
Jensen
,
B. D.
,
Howell
,
L. L.
, and
Salmon
,
L. G.
, 1999, “
Design of Two-Link, In-Plane, Bistable Compliant Micro-Mechanisms
,”
ASME J. Mech. Des.
,
121
, pp.
416
423
.
5.
Jensen
,
B. D.
, and
Howell
,
L. L.
, 2003, “
Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior
,”
ASME J. Mech. Des.
,
125
, pp.
701
708
.
6.
Qiu
,
J.
,
Lang
,
J. H.
, and
Slocum
,
A. H.
, 2004, “
A Curved-Beam Bistable Mechanism
,”
J. Microelectromech. Syst.
,
13
, pp.
137
146
.
7.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
, 2007, “
Charactersitics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
625
639
.
8.
Awtar
,
S.
, and
Sen
,
S.
, 2010, “
A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Strain Energy Formulation
,”
ASME J. Mech. Des.
,
132
(
8
), p.
081009.
9.
Shoup
,
T. E.
, and
McLarnan
,
C. W.
, 1971, “
On the Use of the Undulating Elastica for the Analysis of Flexible Link Mechanisms
,”
J. Eng. Ind.
,
93
, pp.
263
267
.
10.
Oh
,
Y. S.
, and
Kota
,
S.
, 2008, “
Robust Design of Bistable Compliant Mechanisms Using the Bistability of a Clamped-Pinned Beam
,”
ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, no. DETC2008-49755, pp.
273
282
.
11.
Todd
,
B.
,
Jensen
,
B. D.
,
Shultz
,
S. M.
, and
Hawkins
,
A. R.
, 2010, “
Design and Testing of a Thin-Flexure Bistable Mechanism Suitable for Stamping from Metal Sheets
,”
ASME J. Mech. Des.
,
132
, p.
071011
.
12.
Tekeş
,
A.
,
Sönmez
,
Ü.
, and
Güvenç
,
B. A.
, 2010, “
Trajectory Control of Compliant Parallel-Arm Mechanisms
,”
ASME J. Mech. Des.
,
132
, p.
011006.
13.
Wittwer
,
J. W.
,
Baker
,
M. S.
, and
Howell
,
L. L.
, 2006, “
Simulation, Measurement, and Asymmetric Buckling of Thermal Microactuators
,”
Sens. Actuators, A
,
128
, pp.
395
401
.
14.
Shamshirasaz
,
M.
, and
Asgari
,
M. B.
, 2008, “
Polysilicon Micro Beams Buckling with Temperature-Dependent Properties
,”
Microsyst. Technol.
,
14
, pp.
975
961
.
15.
Masters
,
N. D.
, and
Howell
,
L. L.
, 2003, “
A Self-Retracting Fully Compliant Bistable Micromechanism
,”
J. Microelectromech. Syst.
,
12
, pp.
273
280
.
16.
Messenger
,
R. K.
,
Aten
,
Q. T.
,
McLain
,
T. W.
, and
Howell
,
L. L.
, 2010, “
Piezoresistive Feedback Control of a MEMS Thermal Actuator
,”
J. Microelectromech. Syst.
,
18
, pp.
1267
1278
.
17.
Jensen
,
B. D.
,
Parkinson
,
M. B.
,
Kurabayahi
,
K.
,
Howell
,
L. L.
, and
Baker
,
M. S.
, 2001, “
Design Optimization of a Fully-Compliant Bistable Micro-Mechanism
,”
ASME International Mechanical Engineering Congress and Exposition
, no. IMECE001/MEMS-23852.
18.
Zhao
,
J.
,
Jia
,
J.
,
He
,
X.
, and
Wang
,
H.
, 2008, “
Post-Buckling and Snap-Through Behavior of Inclined Slender Beams
,”
ASME J. Appl. Mech.
,
75
, p.
041020
.
19.
Beyer
,
W. H.
, 1979,
CRC Standard Mathematical Tables
,
CRC Press, Inc.
20.
Abramowitz
,
M.
, and
Stegun
,
I. A.
, 1972,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
,
U.S. Government Printing Office
.
21.
Pendleton
,
T. M.
, 2006, “
Design and Fabrication of Rotationally Tristable Compliant Mechanisms
,” Master’s thesis, Brigham Young University.
22.
Dutta
,
N. K.
, and
Edward
,
G. H.
, 1997, “
Generic Relaxation Spectra of Solid Polymers. I Development of Spectral Distribution Model and its Application to Stress Relaxation of Polypropylene
,”
J. Appl. Polym. Sci.
,
66
, pp.
1101
1115
.
23.
Teichert
,
K.
, and
Jensen
,
B.
, 2008, “
Thermal Correction Values for Analysis of Lineshape Microstructure Arrays
,”
Sens. Actuators, A
,
148
, pp.
168
175
.
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