Large-stroke flexure mechanisms inherently lose stiffness in supporting directions when deflected. A systematic approach to synthesize such hinges is currently lacking. In this paper, a new building block-based spatial topology synthesis method is presented for optimizing large-stroke flexure hinges. This method consists of a layout variation strategy based on a building block approach combined with a shape optimization to obtain the optimal design tuned for a specific application. A derivative-free shape optimization method is adapted to include multiple system boundaries and constraints to optimize high complexity flexure mechanisms in a broad solution space. To obtain the optimal layout, three predefined three-dimensional (3D) “building blocks” are proposed, which are consecutively combined to find the best layout with respect to specific design criteria. More specifically, this new method is used to optimize a flexure hinge aimed at maximizing the frequency of the first unwanted vibration mode. The optimized topology shows an increase in frequency of a factor ten with respect to the customary three flexure cross hinge (TFCH), which represents a huge improvement in performance. The numerically predicted natural frequencies and mode shapes have been verified experimentally.

References

References
1.
Smith
,
S. T.
,
2000
,
Flexures: Elements of Elastic Mechanisms
,
Taylor & Francis
,
London
.
2.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
3.
Soemers
,
H.
,
2010
,
Mechanisms, Design Principles for Precision
,
T-Pointprint
,
Enschede, The Netherlands
.
4.
Henein
,
S.
,
Spanoudakis
,
P.
,
Droz
,
S.
,
Myklebust
,
L. I.
, and
Onillon
,
E.
,
2003
, “
Flexure Pivot for Aerospace Mechanisms
,”
10th European Space Mechanisms and Tribology Symposium
(
ESMATS
), San Sebastian, Spain, Sept. 24–26, pp.
285
288
.
5.
Hale
,
L. C.
,
1999
, “
Principles and Techniques for Designing Precision Machines
,”
Ph.D. thesis
, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA.
6.
Brouwer
,
D. M.
,
Meijaard
,
J. P.
, and
Jonker
,
J. B.
,
2013
, “
Large Deflection Stiffness Analysis of Parallel Prismatic Leaf-Spring Flexures
,”
Precis. Eng.
,
37
(
3
), pp.
505
521
.
7.
Zelenika
,
S.
, and
De Bona
,
F.
,
2002
, “
Analytical and Experimental Characterisation of High-Precision Flexural Pivots Subjected to Lateral Loads
,”
Precis. Eng.
,
26
(
4
), pp.
381
388
.
8.
Nijenhuis
,
M.
, and
Brouwer
,
D. M.
,
2016
, “
A Closed-Form Model for the Support Stiffness of Spatial Flexure Strips With Limited Twist
,”
ASME
Paper No. DETC2016-59979.
9.
Van Eijk
,
J.
,
1985
, “
On the Design of Plate-Spring Mechanisms
,”
Ph.D. thesis
, TU Delft, Delft University of Technology, Delft, The Netherlands.
10.
Hao
,
G.
,
Kong
,
X.
, and
Reuben
,
R. L.
,
2011
, “
A Nonlinear Analysis of Spatial Compliant Parallel Modules: Multi-Beam Modules
,”
Mech. Mach. Theory
,
46
(
5
), pp.
680
706
.
11.
Hopkins
,
J. B.
, and
Panas
,
R. M.
,
2013
, “
A Family of Flexures That Eliminate Underconstraint in Nested Large-Stroke Flexure Systems
,”
13th International Conference on European Society for Precision Engineering and Nanotechnology
(
EUSPEN
), Berlin, Germany, May 27–31, pp.
1
4
.
12.
Gunnink
,
K.
,
Aarts
,
R. G. K. M.
, and
Brouwer
,
D. M.
,
2013
, “
Performance Optimization of Large Stroke Flexure Hinges for High Stiffness and Eigenfrequency
,”
28th Annual Meeting of the American Society for Precision Engineering
(
ASPE
), Saint Paul, MN, Oct. 20–25, pp.
1
6
.
13.
Wiersma
,
D. H.
,
Boer
,
S. E.
,
Aarts
,
R. G. K. M.
, and
Brouwer
,
D. M.
,
2014
, “
Design and Performance Optimization of Large Stroke Spatial Flexures
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
1
), p.
11016
.
14.
Marković
,
K.
, and
Zelenika
,
S.
,
2016
, “
Optimized Cross-Spring Pivot Configurations With Minimized Parasitic Shifts and Stiffness Variations Investigated Via Nonlinear FEA
,”
Mech. Based Des. Struct. Mach.
(in press).
15.
Farhadi Machekposhti
,
D.
,
Tolou
,
N.
, and
Herder
,
J. L.
,
2015
, “
A Review on Compliant Joints and Rigid-Body Constant Velocity Universal Joints Toward the Design of Compliant Homokinetic Couplings
,”
ASME J. Mech. Des.
,
137
(
3
), p.
032301
.
16.
Frecker
,
M. I.
,
Ananthasuresh
,
G. K.
,
Nishiwaki
,
S.
,
Kikuchi
,
N.
, and
Kota
,
S.
,
1997
, “
Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization
,”
ASME J. Mech. Des.
,
119
(
2
), pp.
238
245
.
17.
Allaire
,
G.
,
de Gournay
,
F.
,
Jouve
,
F.
, and
Toader
,
A.-M.
,
2005
, “
Structural Optimization Using Topological and Shape Sensitivity Via a Level Set Method
,”
Control Cybern.
,
34
(
1
), pp.
59
80
.
18.
Allaire
,
G.
,
Jouve
,
F.
, and
Toader
,
A.-M.
,
2004
, “
Structural Optimization Using Sensitivity Analysis and A Level-Set Method
,”
J. Comput. Phys.
,
194
(
1
), pp.
363
393
.
19.
Bendsoe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.
20.
Buhl
,
T.
,
Pedersen
,
C. B. W.
, and
Sigmund
,
O.
,
2000
, “
Stiffness Design of Geometrically Nonlinear Structures Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
19
(
2
), pp.
93
104
.
21.
Krishnan
,
G.
,
Kim
,
C.
, and
Kota
,
S.
,
2011
, “
An Intrinsic Geometric Framework for the Building Block Synthesis of Single Point Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
3
(
1
), p.
011001
.
22.
Nelder
,
J. A.
, and
Mead
,
R.
,
1965
, “
A Simplex Method for Function Minimization
,”
Comput. J.
,
7
(
4
), pp. 308–313.
23.
Jonker
,
J. B.
, and
Meijaard
,
J. P.
,
1990
, “
SPACAR—Computer Program for Dynamic Analysis of Flexible Spatial Mechanisms and Manipulators
,”
Multibody Systems Handbook
,
Springer
,
Berlin
, pp.
123
143
.
24.
Meijaard
,
J. P.
,
Brouwer
,
D. M.
, and
Jonker
,
J. B.
,
2010
, “
Analytical and Experimental Investigation of a Parallel Leaf Spring Guidance
,”
Multibody Syst. Dyn.
,
23
(
1
), pp.
77
79
.
25.
Gao
,
F.
, and
Han
,
L.
,
2012
, “
Implementing the Nelder–Mead Simplex Algorithm With Adaptive Parameters
,”
Comput. Optim. Appl.
,
51
(
1
), pp.
259
277
.
26.
Haringx
,
J. A.
,
1949
, “
The Cross-Spring Pivot as a Constructional Element
,”
Flow, Turbul. Combust.
,
1
(
1
), pp.
313
332
.
27.
Hopkins
,
J. B.
,
2007
, “
Design of Parallel Flexure Systems Via Freedom and Constraint Topologies (FACT)
,”
Ph.D. thesis
, Massachusetts Institute of Technology, Cambridge, MA.
28.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
,
2007
, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
625
639
.
29.
Folkersma
,
K. G. P.
,
Boer
,
S. E.
,
Brouwer
,
D. M.
,
Herder
,
J. L.
, and
Soemers
,
H.
,
2012
, “
A 2-DOF Large Stroke Flexure Based Positioning Mechanism
,”
ASME
Paper No. DETC2012-70377.
You do not currently have access to this content.