An underactuated or underconstrained compliant mechanism may have a determined equilibrium position because its energy storage elements cause a position of local minimum potential energy. The minimization of potential energy (MinPE) method is a numerical approach to finding the equilibrium position of compliant mechanisms with more degrees of freedom (DOF) than inputs. Given the pseudorigid-body model of a compliant mechanism, the MinPE method finds the equilibrium position by solving a constrained optimization problem: minimize the potential energy stored in the mechanism, subject to the mechanism’s vector loop equation(s) being equal to zero. The MinPE method agrees with the method of virtual work for position and force determination for underactuated 1-DOF and 2-DOF pseudorigid-body models. Experimental force-deflection data are presented for a fully compliant constant-force mechanism. Because the mechanism’s behavior is not adequately modeled using a 1-DOF pseudorigid-body model, a 13-DOF pseudorigid-body model is developed and solved using the MinPE method. The MinPE solution is shown to agree well with nonlinear finite element analysis and experimental force-displacement data.

References

References
1.
Howell
,
L.
, 2001,
Compliant Mechanisms
,
Wiley
,
New York
.
2.
Dado
,
M. H.
, 2001. “
Variable Parametric Pseudo-Rigid-Body Model for Large-Deflection Beams With End Loads
,”
Int. J. Non-Linear Mech.
,
36
(
7
), pp.
1123
1133
.
3.
Pei
,
X.
,
Yu
,
J.
,
Zonga
,
G.
, and
Bia
,
S.
, 2010, “
An Effective Pseudo-Rigid-Body Method for Beam-Based Compliant Mechanisms
,”
Precis. Eng.
,
34
(
3
), pp.
634
639
.
4.
Sreetharan
,
P. S.
, and
Wood
,
R. J.
, 2010, “
Passive Aerodynamic Drag Balancing in a Flapping-Wing Robotic Insect
,”
ASME J. Mech. Des.
,
132
(
5
),
051006
.
5.
Kragten
,
G. A.
, and
Herder
,
J. L.
, 2010, “
A Platform for Grasp Performance Assessment in Compliant or Underactuated Hands
,”
ASME J. Mech. Des.
,
132
(
2
),
024502
.
6.
Tian
,
Y.
,
Shirinzadeh
,
B.
, and
Zhang
,
D.
, 2010, “
Design and Dynamics of a 3-Dof Flexure-Based Parallel Mechanism for Micro/Nano Manipulation
,”
Microelectron. Eng.
,
87
(
2
), pp.
230
241
.
7.
Wu
,
T.-L.
,
Chen
,
J.-H.
, and
Chang
,
S.-H.
, 2008, “
A Six-DOF Prismatic-Spherical-Spherical Parallel Compliant Nanopositioner
,”
IEEE Trans. Ultrason., Ferroelectr. Freq. Control
,
55
(
12
), pp.
2544
2551
.
8.
Su
,
H.-J.
, and
McCarthy
,
J. M.
, 2006, “
A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms
,”
ASME J. Mech. Des.
,
128
(
4
), pp.
776
786
.
9.
Desrochers
,
S.
,
Pasini
,
D.
, and
Angeles
,
J.
, 2010, “
Optimum Design of a Compliant Uniaxial Accelerometer
,”
ASME J. Mech. Des.
,
132
(
4
),
041011
.
10.
Blanding
,
D. L.
, 1999,
Exact Constraint: Machine Design Using Kinematic Principles
,
ASME
,
New York
.
11.
Su
,
H.-J.
, 2009, “
A Pseudorigid-Body 3r Model for Determining Large Deflection of Cantilever Beams Subject to Tip Loads
,”
ASME J. Mech. Rob.
,
1
(
2
), pp.
1
9
.
12.
Masters
,
N. D.
, and
Howell
,
L. L.
, 2005, “
A Three Degree-of-Freedom Model for Self-Retracting Fully Compliant Bistable Micromechanisms
,”
ASME J. Mech. Des.
,
127
(
4
), pp.
739
744
.
13.
Oh
,
Y. S.
, and
Kota
,
S.
, 2009, “
Synthesis of Multistable Equilibrium Compliant Mechanisms Using Combinations of Bistable Mechanisms
,”
ASME J. Mech. Des.
,
131
(
2
),
021002
.
14.
Chen
,
G.
,
Wilcox
,
D. L.
, and
Howell
,
L. L.
, 2009, “
Fully Compliant Double Tensural Tristable Micromechanisms (DTTM)
,”
J. Micromech. Microeng.
,
19
(
2
),
025011
.
15.
Wang
,
N. F.
, and
Tai
,
K.
, 2010, “
Design of 2-DOF Compliant Mechanisms to Form Grip-and-Move Manipulators for 2D Workspace
ASME J. Mech. Des.
,
123
(
3
),
031007
.
16.
Pardalos
,
P. M.
,
Shalloway
,
D.
, and
Xue
,
G.
, 1994, “
Optimization Methods for Computing Global Minima of Nonconvex Potential Energy Functions
,”
J. Global Optim.
,
4
(
2
), pp.
117
133
.
17.
Lavor
,
C.
, and
Maculan
,
N.
, 2004, “
A Function to Test Methods Applied to Global Minimization of Potential Energy of Molecules
,”
Numer. Algorithms
,
35
(
2–4
), pp.
287
300
.
18.
Moloi
,
N. P.
, and
Ali
,
M. M.
, 2005, “
An Iterative Global Optimization Algorithm for Potential Energy Minimization
,”
Comput. Optim. Appl.
,
30
(
2
), pp.
119
132
.
19.
Weight
,
B. L.
,
Mattson
,
C. A.
,
Magleby
,
S. P.
, and
Howell
,
L. L.
, 2007, “
Configuration Selection, Modeling, and Preliminary Testing in Support of Constant Force Electrical Connectors
,”
ASME J. Electron. Packag.
,
129
(
3
), pp.
236
246
.
20.
van Dorsser
,
W. D.
,
Barents
,
R.
,
Wisse
,
B. M.
,
Schenk
,
M.
, and
Herder
,
J. L.
, 2008, “
Energy-Free Adjustment of Gravity Equilibrators by Adjusting the Spring Stiffness
,”
Proc. Instit. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
222
(
9
), pp.
1839
1846
.
21.
Saravanan
,
R.
,
Ramabalan
,
S.
, and
Babu
,
P. D.
, 2008, “
Optimum Static Balancing of an Industrial Robot Mechanism
,”
Eng. Applic. Artif. Intell.
,
21
(
6
), pp.
824
834
.
22.
Jacobsen
,
J. O.
,
Winder
,
B. G.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
, 2010, “
Lamina Emergent Mechanisms and Their Basic Elements
,”
ASME J. Mech. Rob.
,
2
(
1
),
011003
.
23.
Dai
,
J. S.
, and
Jones
,
J.
, 1999, “
Mobility in Metamorphic Mechanisms of Foldable/Erectable Kinds
,”
ASME J. Mech. Des.
,
121
(
3
), p.
375
.
24.
Jacobsen
,
J. O.
,
Chen
,
G.
,
Howell
,
L. L.
, and
Magleby
,
S. P.
, 2009, “
Lamina Emergent Torsional (LET) Joint
,”
Mech. Mach. Theory
,
44
(
11
), pp.
2098
2109
.
You do not currently have access to this content.