Multistable equilibrium (MSE) systems are those which have multiple statically stable equilibrium positions. This paper gives an overview of what MSE systems are, how they can be used, and how they can be designed. We describe the numerical optimization and synthesis of an example system composed of energy storage elements from various energy domains including mechanical rotation, mechanical translation, and magnetism.

1.
Giles
,
C. R.
,
Barber
,
B.
,
Aksyuk
,
V.
,
Ruel
,
L.
, and
Bishop
,
D.
,
1999
, “
Reconfigurable 16-Channel WDM DROP Module Using Silicon MEMS Optical Switches
,”
IEEE Photonics Technol. Lett.
,
11
, pp.
63
65
.
2.
Aksyuk, V. L., Barber, B., Bishop, D., Giles, C., and Stulz, L., March 20, 2001, U.S. Patent No. 6205267, “Optical Switch.”
3.
Hoffman
,
M.
,
Kopka
,
P.
, and
Voges
,
E.
,
1999
, “
Bistable Micromechanical Fiber-Optic Switches on Silicon with Thermal Actuators
,”
Sens. Actuators, A
,
78
, pp.
28
35
.
4.
Michalicek, M. A., March 21, 2000, U.S. Patent No. 6040935, “Flexureless Multi-Stable Micromirrors for Optical Switching.”
5.
Greenwood, D. T., 1988, Principles of Dynamics (2nd Ed.), Prentice-Hall, Englewood Cliffs, NJ, Chaps. 3 and 6.
6.
Kim, Y., and Neikirk, D. P., 1995, “Micromachined Fabry–Perot Pressure Transducer with Optical Fiber Interconnects,” Proceedings of the SPIE conference: Micromachined Devices and Components, R. Roop and K. Chau, eds., SPIE 2642, Austin, Texas, pp. 242–249.
7.
Wingert, A., Lichter, M., and Dubowsky, S., 2002, “On the Kinematics of Parallel Mechanisms with Bi-Stable Polymer Actuators.” Proceedings of the 8th International Symposium on Advances in Robot Kinematics, Caldes de Malavella, Spain.
8.
Hafez, M., Lichter, M. D., and Dubowsky, S., 2002, “Optimized Binary Modular Reconfigurable Robotic Devices,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation, Institute of Electrical and Electronics Engineers, Washington, DC.
9.
Nanua
,
P.
, and
Waldron
,
K. J.
,
1995
, “
Energy Comparison Between Trot, Bound, and Gallop using a Simple Model
,”
ASME J. Biomech. Eng.
,
117
, pp.
466
473
.
10.
Heglund
,
N.
,
Taylor
,
C. R.
, and
McMahon
,
T. A.
,
1974
, “
Scaling Stride Frequency and Gait to Animal Size: Mice to Horses
,”
Science
,
186
, pp.
1112
1113
.
11.
Fisher, G., Cox, A., Gogola, M., Gordon, M., Lobontiu, N., Monopoli, D., Garcia, E., and Goldfarb, M., 1999, “Elastodynamic locomotion in mesoscale robotic insects,” Proceedings of the 1999 SPIE Conference on Smart Structures and Materials: Electroactive Polymers and Devices, G. Washer and V. Varadan, eds., SPIE 5049, Newport Beach, CA, pp. 262–368.
12.
Capanu
,
M.
,
Boyd
,
J. G.
, and
Hesketh
,
P. J.
,
2000
, “
Design, Fabrication, and Testing of a Bistable Electromagnetically Actuated Microvalve
,”
J. Microelectromech. Syst.
,
9
, pp.
181
188
.
13.
Howell
,
L. L.
,
Rao
,
S. S.
, and
Midha
,
A.
,
1994
, “
Reliability-Based Optimal Design of a Bistable Compliant Mechanism
,”
J. Mech. Des.
,
116
, pp.
1115
1121
.
14.
Jensen
,
B. D.
, and
Howell
,
L. L.
,
2003
, “
Identification of Compliant Pseudo-Rigid-Body Four-Link Mechanism Configurations Resulting in Bistable Behavior
,”
J. Mech. Des.
,
25
, pp.
701
708
.
15.
Jensen, B. D., Howell, L. L., and Salmon, L. G., 1998, “Introduction of Two-Link, In-Plane, Bistable Compliant MEMS,” paper DETC98/MECH-5837, The Proceedings of the 1998 ASME Design Engineering Technical Conference, ASME, Atlanta, GA.
16.
Opdahl, P. G., Jensen, B. D., and Howell, L. L., 1998, “An Investigation into Compliant Bistable Mechanisms,” paper DETC98/MECH-5914, The Proceedings of the 1998 ASME Design Engineering Technical Conference, ASME, Atlanta, GA.
17.
Saif
,
M.
, and
Taher
,
A.
,
2000
, “
On a Tunable Bistable MEMS—Theory and Experiment
,”
J. Microelectromech. Syst.
,
9
, pp.
157
170
.
18.
Schulze
,
E. F.
, November
1955
, “
Designing Snap-Action Toggles
,”
Prod. Eng. (N.Y.)
,
26
, pp.
168
170
.
19.
Chironis, N. P. (ed.), 1991, Mechanisms and Mechanical Devices Sourcebook, McGraw-Hill, New York.
20.
Schomburg
,
W. K.
, and
Goll
,
C.
,
1998
, “
Design Optimization of Bistable Microdiaphragm Valves
,”
Sens. Actuators, A
,
64
, pp.
259
264
.
21.
Vangbo
,
M.
, and
Ba¨cklund
,
Y.
,
1998
, “
A Lateral Symmetrically Bistable Buckled Beam
,”
J. Micromech. Microeng.
,
8
, pp.
29
32
.
22.
Fitzgerald, A. E., Kingsley, C., Jr., and Umans, S., 1990, Electric Machinery (5th Ed.), McGraw-Hill, New York, Chap. 1.
23.
Limaye, A. A., King, C. W., and Campbell, M. I., 2003, “Analysis of Multiple Equilibrium Positions in Magnetostatic Field,” paper DETC2003/DAC-48841, The Proceedings of the ASME 2003 Design Engineering Technical Conferences, ASME, Chicago, IL.
24.
Alexandrov
,
N. M.
, and
Lewis
,
R. M.
,
2001
, “
An Overview for First-Order Model Management for Engineering Optimization
,”
Opt. Eng. (Bellingham)
,
2
, pp.
413
430
.
You do not currently have access to this content.