We present an improved flexure linkage design for removing underconstraint in a double parallelogram (DP) linear flexural mechanism. This new linkage alleviates many of the problems associated with current linkage design solutions such as static and dynamic performance losses and increased footprint. The improvements of the new linkage design will enable wider adoption of underconstraint eliminating (UE) linkages, especially in the design of linear flexural bearings. Comparisons are provided between the new linkage design and existing UE designs over a range of features including footprint, dynamics, and kinematics. A nested linkage design is shown through finite element analysis (FEA) and experimental measurement to work as predicted in selectively eliminating the underconstrained degrees-of-freedom (DOF) in DP linear flexure bearings. The improved bearing shows an 11 × gain in the resonance frequency and 134× gain in static stiffness of the underconstrained DOF, as designed. Analytical expressions are presented for designers to calculate the linear performance of the nested UE linkage (average error < 5%). The concept presented in this paper is extended to an analogous double-nested rotary flexure design.

References

References
1.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
,
2007
, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
625
639
.
2.
Krijnen
,
B.
, and
Brouwer
,
D. M.
,
2014
, “
Flexures for Large Stroke Electrostatic Actuation in MEMS
,”
J. Micromech. Microeng.
,
24
(
1
), p.
015006
.
3.
Saggere
,
L.
,
Kota
,
S.
, and
Crary
,
S. B.
,
1994
, “
A New Design for Suspension of Linear Microactuators
,”
International Mechanical Engineering Congress and Exposition: Dynamic Systems and Control
, Chicago, pp.
671
676
.
4.
Suh
,
N. P.
,
2001
,
Axiomatic Design: Advances and Applications
,
Oxford University
,
New York
.
5.
Slocum
,
A.
,
1992
,
Precision Machine Design
,
Prentice-Hall, Inc.
,
Eaglewood Cliffs, NJ
.
6.
Blanding
,
D. L.
,
1999
,
Exact Constraint: Machine Design Using Kinematic Principles
,
ASME
,
New York
.
7.
Smith
,
S. T.
,
2000
,
Flexures: Elements of Elastic Mechanisms
,
CRC
,
Boca Raton, FL
.
8.
Smith
,
S. T.
,
1992
,
Foundations of Ultraprecision Mechanism Design
,
CRC
,
Boca Raton, FL
.
9.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Synthesis of Multi-Degrees-of-Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT)—Part I: Principles
,”
Precis. Eng.
,
34
(2), pp.
259
270
.
10.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
2010
, “
Synthesis of Multi-Degree-of-Freedom, Parallel Flexure System Concepts Via Freedom and Constraint Topology (FACT)—Part II: Practice
,”
Precis. Eng.
,
34
(
2
), pp.
271
278
.
11.
Panas
,
R. M.
,
Cullinan
,
M. A.
, and
Culpepper
,
M. L.
,
2012
, “
Design of Piezoresistive-Based MEMS Sensor Systems for Precision Microsystems
,”
Precis. Eng.
,
36
(
1
), pp.
44
54
.
12.
Zhao
,
H.
,
Bi
,
S.
, and
Yu
,
J.
,
2012
, “
A Novel Compliant Linear-Motion Mechanism Based on Parasitic Motion Compensation
,”
Mech. Mach. Theory.
,
50
, pp.
15
28
.
13.
Hongzhe
,
Z.
,
Bi
,
S.
,
Yu
,
J.
, and
Guo
,
J.
,
2012
, “
Design of a Family of Ultra-Precision Linear Motion Mechanisms
,”
J. Mech. Rob.
,
4
(
4
), p.
041012
.
14.
Howell
,
L. L.
,
2001
,
Compliant Mechanisms
,
Wiley
,
New York
.
15.
Duarte
,
R. M.
,
Howells
,
M. R.
,
Hussain
,
Z.
,
Lauritzen
,
T.
,
McGill
,
R.
,
Moler
,
E. J.
, and
Spring
,
J.
,
1997
, “
Linear Motion Machine for Soft X-Ray Interferometry
,”
Proc. SPIE
,
3132
,
Optomechanical Design and Precision Instruments
, pp.
224
232
.
16.
Brouwer
,
D. M.
,
Otten
,
A.
,
Engelen
,
J. B. C.
,
Krijnen
,
B.
, and
Soemers
,
H. M. J. R.
,
2010
, “
Long-Range Elastic Guidance Mechanisms for Electrostatic Comb-Drive Actuators
,”
International Conference of the European Society for Precision Engineering and Nanotechnology (EUSPEN)
, May 31–Jun. 4, pp.
41
50
.
17.
Hubbard
,
N. B.
,
Wittwer
,
J. W.
,
Kennedy
,
J. A.
,
Wilcox
,
D. L.
, and
Howell
,
L. L.
,
2004
, “
A Novel Fully Compliant Planar Linear-Motion Mechanism
,”
ASME International Design Engineering Technical Conference and Computers and Information in Engineering Conference (IDETC/CIE)
,
Salt Lake City, UT
, pp.
1
5
.
18.
Chang
,
S. H.
, and
Li
,
S. S.
,
1999
, “
A High Resolution Long Travel Friction-Drive Micropositioner With Programmable Step Size
,”
Rev. Sci. Instrum.
,
70
(
6
), pp.
2776
2782
.
19.
Awtar
,
S.
,
2004
,
Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms
, Sc.D. thesis,
Massachusetts Institute of Technology
,
Cambridge MA
.
20.
Brouwer
,
D. M.
,
de Jong
,
B. R.
, and
Soemers
,
H. M. J. R.
,
2010
, “
Design and Modeling of a Six DOFs MEMS-Based Precision Manipulator
,”
Precis. Eng.
,
34
(
2
), pp.
307
319
.
21.
Xu
,
Q.
, and
Li
,
Y.
,
2010
, “
Novel Design of a Totally Decoupled Flexure-Based XYZ Parallel Micropositioning Stage
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)
,
IEEE, Montreal, Canada
, pp.
866
871
.
22.
Seggelen
,
J. K. V.
,
Rosielle
,
P. C. J. N.
,
Schellekens
,
P. H. J.
,
Spaan
,
H. A. M.
,
Bergmans
,
R. H.
, and
Kotte
,
G. J. W. L.
,
2005
, “
An Elastically Guided Machine Axis With Nanometer Repeatability
,”
CIRP Ann.—Manuf. Technol.
,
54
(
1
), pp.
487
490
.
23.
Li
,
Y.
, and
Xu
,
Q.
,
2009
, “
Design and Analysis of a Totally Decoupled Flexure-Based XY Parallel Micromanipulator
,”
IEEE Trans. Rob.
,
25
(
3
), pp.
645
657
.
24.
Parmar
,
G.
,
Barton
,
K.
, and
Awtar
,
S.
,
2014
, “
Large Dynamic Range Nanopositioning Using Iterative Learning Control
,”
Precis. Eng.
,
38
(
1
), pp.
48
56
.
25.
Hao
,
G.
,
Kong
,
X.
, and
Meng
,
Q.
,
2010
, “
Design and Modelling of Spatial Compliant Parallel Mechanisms For Large Range of Translation
,”
ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)
, Vol.
44
,
QC, Canada
.
26.
Pusl
,
K. E.
, “
Folded Spring Flexure Suspension For Linearly Actuated Devices
,” U.S. patent application 7550880B1, June 23, 2009.
27.
Eijk
,
J. V.
,
1985
,
On the Design of Plate Spring Mechanisms
, Ph.D. thesis,
Delft University of Technology, Delft
,
The Netherlands
.
28.
Zhou
,
G.
, and
Dowd
,
P.
,
2003
, “
Tilted Folded-Beam Suspension for Extending the Stable Travel Range of Comb-Drive Actuators
,”
J. Micromech. Microeng.
,
13
(
2
), pp.
178
183
.
29.
Brouwer
,
D. M.
,
De Jong
,
B. R.
,
Soemers
,
H. M. J. R.
, and
Van Dijk
,
J.
,
2006
, “
Sub-Nanometer Stable Precision MEMS Clamping Mechanism Maintaining Clamp Force Unpowered for TEM Application
,”
J. Micromech. Microeng.
,
16
(
6
), pp.
S7
S12
.
30.
Chang
,
S.
,
Wang
,
C. S.
,
Xiong
,
C. Y.
, and
Fang
,
J.
,
2005
, “
Nanoscale In-Plane Displacement Evaluation by AFM Scanning and Digital Image Correlation Processing
,”
Nanotechnology
,
16
(
4
), pp.
344
349
.
31.
Krijnen
,
B.
, and
Brouwer
,
D. M.
,
2011
, “
Position Control of a MEMS Stage With Integrated Sensor
,”
11th International Conference on European Society for Precision Engineering and Nanotechnology (EUSPEN)
,
Como, Italy
, pp.
2
3
.
32.
Olfatnia
,
M.
,
Sood
,
S.
, and
Awtar
,
S.
,
2012
, “
Note: An Asymmetric Flexure Mechanism for Comb-Drive Actuators
,”
Rev. Sci. Instrum.
,
83
(
11
), p.
116105
.
33.
Olfatnia
,
M.
,
Sood
,
S.
,
Gorman
,
J. J.
, and
Awtar
,
S.
,
2013
, “
Large Stroke Electrostatic Comb-Drive Actuators Enabled by a Novel Flexure Mechanism
,”
J. Microelectromech. Syst.
,
22
(
2
), pp.
483
494
.
34.
Trutna
,
T. T.
, and
Awtar
,
S.
,
2010
, “
An Enhanced Stability Model for Electrostatic Comb-Drive Actuator Design
,”
ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE)
,
Montreal, Canada
, pp.
1
9
.
35.
Ferreira
,
P. M.
,
Dong
,
J.
, and
Mukhopadhyay
,
D.
,
2012
, “
High Precision Silicon-on-Insulator MEMS Parallel Kinematic Stages
,” U.S. patent application 8310128B2.
36.
Jaecklin
,
V. P.
,
Linder
,
C.
,
De Rooij
,
N. F.
,
Moret
,
J. M.
,
Bischof
,
R.
, and
Rudolf
,
F.
,
1992
, “
Novel Polysilicon Comb Actuators for XY-Stages
,” An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots,
IEEE MEMS '92
, Travemunde, Germany, pp.
147
149
.
37.
Jones
,
R. V.
,
Phil
,
D.
, and
Young
,
I. R.
,
1956
, “
Some Parasitic Deflexions in Parallel Spring Movements
,”
J. Sci. Instrum.
,
33
(
1
), pp.
11
15
.
38.
Jones
,
R. V.
,
1962
, “
Some Uses of Elasticity in Instrument Design
,”
J. Sci. Instrum.
,
39
(
5
), pp.
193
203
.
39.
Brouwer
,
D.
,
2007
,
Design Principles for Six Degrees-of-Freedom MEMS-Based Precision Manipulators
, Ph.D. thesis,
University of Twente, Eindhoven
,
The Netherlands
.
40.
Plainevaux
,
J. E.
,
1954
, “
Mouvement parasite vertical d'une suspension élastique symétrique à compensation et asservissement
,”.
Nuovo Cimento
,
11
(
6
), pp.
626
638
.
41.
Plainevaux
,
J. E.
,
1954
, “
Guidage rectiligne sur lames élastiques. Comparaison de divers types connus et nouveaux
,”
Nuovo Cimento
,
12
(
1
), pp.
37
59
.
42.
Hopkins
,
J. B.
, and
Culpepper
,
M. L.
,
1954
, “
Synthesis of Precision Serial Flexure Systems Using Freedom and Constraint Topologies (FACT)
,”
Precis. Eng.
,
35
(
4
), pp.
638
649
.
43.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Naeini
,
A. E.
,
2006
,
Feedback Control of Dynamic Systems
,
5th ed.
,
Prentice Hall
,
Upper Saddle River, NJ
.
44.
Smith
,
S. T.
,
1987
,
Mechanical Systems in Nanometre Metrology
, Ph.D. thesis,
University of Warwick
,
Coventry, UK
.
45.
Grade
,
J. D.
,
Jerman
,
H.
, and
Kenny
,
T. W.
,
2003
, “
Design of Large Deflection Electrostatic Actuators
,”
J. Microelectromech. Syst.
,
12
(
3
), pp.
335
343
.
46.
Chen
,
C.
, and
Lee
,
C.
,
2004
, “
Design and Modeling for Comb Drive Actuator With Enlarged Static Displacement
,”
Sens. Actuators, A
,
115
(
2–3
), pp.
530
539
.
47.
Jerman
,
J. H.
, and
Grade
,
J. D.
,
2003
, “
Miniature Device With Translatable Member
,” U.S. Patent 6664707 B2, Dec 16, 2003.
48.
Valois
,
M.
, “
Linear Flexure Bearing
,” U.S. Patent Application 20130015616 A1, Jan 17, 2013.
49.
Genequand
,
P.-M.
, “
Device for the Guidance in Rectilinear Translation of an Object That is Mobile in Relation to a Fixed Object
,” U.S. Patent 6059481 A, May 9, 2000.
50.
Spanoudakis
,
P.
,
Schwab
,
P.
, and
Johnson
,
P.
,
2003
, “
Design and Production of the METOP Satellite IASI Corner Cube Mechanisms
,”
10th European Space Mechanisms and Tribology Symposium
, Noordwijk,
The Netherlands
, pp.
97
103
.
51.
Henein
,
S.
,
Kjelberg
,
I.
, and
Zelenika
,
S.
,
2002
, “
Flexible Bearings for High-Precision Mechanisms in Accelerator Facilities
,” Proc. NANOBEAM 2002, Lausanne, Switzerland, pp.
103
110
.
52.
Hao
,
G.
,
Li
,
H.
,
He
,
X.
, and
Kong
,
X.
,
2014
, “
Conceptual Design of Compliant Translational Joints for High-Precision Applications
,”
Front. Mech. Eng.
,
9
(
4
), pp.
331
343
.
53.
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
,
Berlin, Germany
, pp.
1
4
.
This content is only available via PDF.
You do not currently have access to this content.