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.
Issue Section:
Design of Mechanisms and Robotic Systems
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
.
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