Flexure hinges inherently lose stiffness in supporting directions when deflected. In this paper a method is presented for optimizing the geometry of flexure hinges, which aims at maximizing supporting stiffnesses. In addition, the new -flexure hinge design is presented. The considered hinges are subjected to a load and deflected an angle of up to ±20 deg. The measure of performance is defined by the first unwanted natural frequency, which is closely related to the supporting stiffnesses. During the optimization, constraints are applied to the actuation moment and the maximum occurring stress. Evaluations of a curved hinge flexure, cross revolute hinge, butterfly flexure hinge, two cross flexure hinge types, and the new -flexure hinge are presented. Each of these hinge types is described by a parameterized geometric model. A flexible multibody modeling approach is used for efficient modeling while it accounts for the nonlinear geometric behavior of the stiffnesses. The numerical efficiency of this model is very beneficial for the design optimization. The obtained optimal hinge designs are validated with a finite element model and show good agreement. The optimizations show that a significant increase in supporting stiffness, with respect to the conventional cross flexure hinge, can be achieved with the -flexure hinge.

References

References
1.
Smith
,
S.
,
2000
,
Flexures: Elements of Elastic Mechanisms
,
Taylor & Francis
,
London, UK
.
2.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
3.
Soemers
,
H. J. M. R.
,
2010
,
Design Principles for Precision Mechanisms
,
T-Pointprint
,
Enschede, The Netherlands
.
4.
Folkersma
,
K. G. P.
,
Boer
,
S. E.
,
Brouwer
,
D. M.
,
Herder
,
J. L.
, and
Soemers
,
H. M. J. R.
,
2012
, “
A 2-dof Large Stroke Flexure Based Position Mechanism
,”
International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
, Chicago, IL, Paper No. DETC2012-70377.
5.
Haringx
,
J. A.
,
1949
, “
The Cross-Spring Pivot as a Constructional Element
,”
Appl. Sci. Res. A
,
A1
, pp.
313
332
.10.1007/BF02120338
6.
Eijk
,
J. van
,
1985
, “
On the Design of Plate Spring Mechanism
,” Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
7.
Awtar
,
S.
,
2007
, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Design
,
129
, pp.
625
639
.10.1115/1.2717231
8.
Bauchau
,
O. A.
,
Li
,
L.
,
Masarati
,
P.
, and
Morandini
,
M.
,
2011
, “
Tensorial Deformation Measures for Flexible Joints
,”
ASME J. Comput. Nonlinear Dyn.
6
(
3
), p.
031002
.10.1115/1.4002517
9.
Trease
,
B. P.
,
Moon
,
Y. M.
, and
Kota
,
S.
,
2005
, “
Design of Large-Displacement Compliant Joints
,”
ASME J. Mech. Design
,
127
, pp.
788
798
.10.1115/1.1900149
10.
Boer
,
S. E.
,
Aarts
,
R. G. K. M.
,
Brouwer
,
D. M.
, and
Jonker
,
J. B.
,
2010
, “
Multibody Modelling and Optimization of a Curved Hinge Flexure
,”
The 1st Joint International Conference on Multibody System Dynamics
, Lappeenranta.
11.
Jonker
,
J. B.
, and
Meijaard
,
J. P.
,
1990
, “
SPACAR—Computer Program for Dynamic Analysis of Flexible Spatial Mechanisms and Manipulators
,”
Multibody Systems Handbook
,
Schiehlen
,
W.
(ed.),
Springer-Verlag
,
Berlin, Germany
, pp.
123
143
.
12.
Jonker
,
J. B.
,
1989
, “
A Finite Element Dynamical Analyses of Spatial Mechanisms With Flexible Links
,”
Comput. Meth. Appl. Mech. Eng.
,
76
, pp.
17
40
.10.1016/0045-7825(89)90139-4
13.
Brouwer
,
D. M.
,
Jong
,
B. R.
,
de, Boer
,
M. J.
,
de, Jansen
,
H. V.
,
Dijk
,
J.
,
van, Krijnen
,
G. J. M.
, and
Soemers
,
H. M. J. R.
,
2009
, “
MEMS-Based Clamp With a Passive Hold Function for Precision Position Retaining of Micro Manipulators
,”
J. Micromech. Microeng.
,
19
(
6
), p.
065027
.10.1088/0960-1317/19/6/065027
14.
Zelenika
,
S.
, and
De Bona
,
F.
,
2002
, “
Analytical and Experimental Characterisation of High-Precision Flexural Pivots Subjected to Lateral Loads
,”
J. Int. Soc. Prec. Eng. Nanotech.
,
26
, pp.
381
388
.10.1016/S0141-6359(02)00149-6
15.
Henein
,
S.
,
Spanoudakis
,
P.
,
Droz
,
S.
,
Myklebust
,
L. I.
, and
Onillon
,
E.
,
2003
, “
Flexure Pivot for Aerospace Mechanisms
,”
Proceedings of the 10th ESMATS/ESA
, San Sebastian, Paper No. ESA SP-524.
16.
Brouwer
,
D. M.
,
Meijaard
,
J. P.
, and
Jonker
,
J. B.
,
2009
, “
Elastic Element Showing Low Stiffness Loss at Large Deflection
,”
Proceedings of the 24th Annual Meeting of the American Society of Precision Engineering
, Monterey, CA., pp.
30
33
.
17.
Nelder
,
J. A.
, and
Mead
,
R.
,
1965
, “
A Simplex Method for Function Minimization
,”
Comput. J.
,
7
(
4
), pp.
308
313
.10.1093/comjnl/7.4.308
18.
Timoshenko
,
S.
,
1922
, “
On the Torsion of a Prism, One of the Cross-Sections of which Remains Plane
,”
Proc. London Math. Soc.
,
20
, pp.
389
397
.10.1112/plms/s2-20.1.389
19.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
,
1970
,
Theory of Elasticity
,
3rd
ed.,
McGraw-Hill Book Company
,
New York
.
20.
Wiersma
,
D. H.
,
Boer
,
S. E.
,
Aarts
,
R. G. K. M.
, and
Brouwer
,
D. M.
,
2012
, “
Performance Optimization of Large Stroke Spatial Flexure Hinges
,”
International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
, Paper No. DETC2012-70502.
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