This paper presents an approach based on parameterized compliance for type synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. The parameterized compliance matrices have been derived for commonly used flexure elements, which are significantly influenced by flexure parameters including material and geometric properties. Different parameters of flexure elements generate different degree of freedom (DOF) characteristic of types. Enlightened by the compliance analysis of flexure elements, a parameterization approach with detailed processes and steps is introduced in this paper to help analyze and synthesize flexure mechanisms with the case study as serial chains, parallel chains, and combination hybrid chains. For a hybrid flexure, the results of finite element (FE) modeling simulations are compared to analytical compliance elements characteristic. Under linear deformations, the maximum compliance errors of analytical models are less than 6% compared with the FE models. The final goal of this work is to provide a parameterized approach for type synthesis of flexure mechanisms, which is used to configure and change the parameters of flexure mechanisms to achieve the desired DOF requirements of types initially.
Issue Section:
Research Papers
References
1.
Midha
, A.
, Norton
, T. W.
, and Howell
, L. L.
, 1994
, “On the Nomenclature, Classification, and Abstractions of Compliant Mechanisms
,” ASME J. Mech. Des.
, 116
(1
), pp. 270
–279
.10.1115/1.29193582.
Howell
, L. L.
, 2001
, Compliance Mechanisms
, Wiley-Interscience
, New York, NY
.3.
Sin
, J.
, Popa
, D.
, and Stephanou
, H.
, 2002
, “Model Based Automatic Fiber Alignment
,” Proceeding of the Fiber Optic Automation 2002 Conference
, San Diego, CA.4.
Moody
, M. V.
, Paik
, H. J.
, and Canavan
, E. R.
, 2002
, “Three-Axis Superconducting Gravity Gradiometer for Sensitive Gravity Experiments
,” Rev. Sci. Instrum.
, 73
(11
), pp. 3957
–3974
.10.1063/1.15117985.
Bono
, M.
, and Hibbard
, R.
, 2007
, “A Flexure-Based Tool Holder for Sub-μm Positioning of a Single Point Cutting Tool on a Four-Axis Lathe
,” Precis. Eng.
, 31
(2
), pp.169
–176
.10.1016/j.precisioneng.2006.03.0076.
Masters
, N. D.
, and Howell
, L. L.
, 2003
, “A Self-Retracting Fully Compliant Bistable Micromechanism
,” J. Microelectromech. Syst.
, 12
(3
), pp. 273
–280
.10.1109/JMEMS.2003.8117517.
Ball
, R. S.
, 1900
, A Treatise on the Theory of Screw
, Cambridge University Press
, Cambridge, UK
.8.
Hunt
, K. H.
, 1978
, Kinematic Geometry of Mechanisms
, Oxford University Press
, New York
.9.
Phillips
, J.
, 1984
, Freedom in Machinery
(Volume 1
, Introducing Screw Theory), Cambridge University Press
, Cambridge, MA
.10.
Phillips
, J.
, 1990
, Freedom in Machinery
(Volume 2
, Screw Theory Exemplified), Cambridge University Press
, Cambridge, MA
.11.
Loncaric
, J.
, 1987
, “Normal Forms of Stiffness and Compliance Matrix
,” J. Rob. Autom.
, 3
(6
), pp. 567
–572
.10.1109/JRA.1987.108714812.
Lipkin
, H.
, and Timothy
, P.
, 1992
, “Geometrical Properties of Modelled Robot Elasticity: Part I—Decomposition
,” Robotics, Spatial Mechanisms, and Mechanical Systems: ASME Design Technical Conferences, 22nd Biennal Mechanisms Conference, Scottsdale, AZ, Sept. 13–16, pp. 179
–185
.13.
Lipkin
, H.
, and Timothy
, P.
, 1992
, “Geometrical Properties of Modelled Robot Elasticity: Part II—Center of Elasticity
,” Robotics, Spatial Mechanisms, and Mechanical Systems: ASME Design Technical Conferences, 22nd Biennal Mechanisms Conference, Scottsdale, AZ, Sept. 13–16, pp. 187
–193
.14.
Pigoski
, T.
, Griffis
, M.
, and Duffy
, J.
, 1998
, “Stiffness Mappings Employing Different Frames of Reference
,” Mech. Mach. Theory
, 33
(6
), pp. 825
–838
.10.1016/S0094-114X(97)00083-915.
Selig
, J. M.
, 2000
, “The Spatial Stiffness Matrix From Simple Stretched Springs
,” IEEE International Conference
on Robotics and Automation (ICRA '00
), San Francisco, CA, Apr. 24–28, pp. 3314
–3319
10.1109/ROBOT.2000.845218.16.
Huang
, S. G.
, and Schimmels
, J. M.
, 2000
, “The Bounds and Realization of Spatial Compliances Achieved With Simple Serial Elastic Mechanisms
,” IEEE Trans. Rob. Autom.
, 16
(1
), pp. 99
–103
.10.1109/70.83319717.
Huang
, S. G.
, and Schimmels
, J. M.
, 1998
, “The Bounds and Realization of Spatial Stiffness Achieved With Simple Springs Connected in Parallel
,” IEEE Trans. Rob. Autom.
, 14
(3
), pp. 466
–475
.10.1109/70.67845518.
Guerinot
, E.
, Magleby
, S. P.
, Howell
, L. L.
, and Todd
, R. H.
, 2005
, “Compliant Joint Design Principals for High Compressive Load Situation
,” ASME J. Mech. Des.
, 127
(4
), pp. 774
–781
.10.1115/1.186267719.
Slocum
, A. H.
, 1992
, Precision Machine Design
, Prentice-Hall Inc.
, Englewood Cliffs, NJ
.20.
Howell
, L. L.
, and Midha
, A.
, 1995
, “Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms
,” ASME J. Mech. Des.
, 117
(1
), pp. 156
–165
.10.1115/1.282610121.
Maxwell
, J. C.
, and Niven
, W. D.
, 1890
, General Considerations Concerning Scientific Apparatus
, Courier Dover Publications
, New York
.22.
Blanding
, D. L.
, 1999
, Exact Constraint: Machine Design Using Kinematic Processing
, American Society of Mechanical Engineers
, New York
.23.
Kim
, C. J.
, Moon
, Y. M.
, and Sridhar
, K.
, 2008
, “A Building Block Approach to the Conceptual Synthesis of Compliant Mechanisms Utilizing Compliance and Stiffness Ellipsoids
,” ASME J. Mech. Des.
, 130
(2
), p. 022308
10.1115/1.2821387.24.
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 I: Principals
,” Precis. Eng.
, 34
(2
), pp. 259
–270
.10.1016/j.precisioneng.2009.06.00825.
Su
, H. J.
, Dorozhkin
, D. V.
, and Vance
, J. M.
, 2009
, “A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms
,” ASME J. Mech. Rob.
, 1
(4
), p. 041009
.10.1115/1.321102426.
Yu
, J. J.
, Li
, S. Z.
, Su
, H. J.
, and Culpepper
, M. L.
, 2011
, “Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms
,” ASME J. Mech. Rob.
, 3
(3
), p. 031008
.10.1115/1.400412327.
Su
, H. J.
, Shi
, H. L.
, and Yu
, J. J.
, 2012
, “A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms
,” ASME J. Mech. Des.
, 134
(5
), p. 051009
.10.1115/1.400644128.
Li
, S. Z.
, Yu
, J. J.
, Zong
, G. H.
, and Su
, H.-J.
, 2012
, “A Compliance-Based Compensation Approach for Designing High-Precision Flexure Mechanism
,” ASME
Paper No. DETC2012-71018
10.1115/DETC2012-71018.29.
Young
, W. C.
, and Budynas
, R. G.
, 2001
, Roark's Formulas for Stress and Strain
, 7th ed., McGraw-Hill
, New York
.30.
Zhang
, Y.
, Su.
, H.-J.
, and Liao
, Q.
, 2014
, “Mobility Criteria of Compliance Mechanisms Based on Decomposition of Compliance Matrices
,” Mech. Mach. Theory
, 79
, pp. 80
–93
.10.1016/j.mechmachtheory.2014.04.01031.
Lin
, Q.
, Burdick
, J. W.
, and Rimon
, E.
, 2000
, “A Stiffness-Based Quality Measure for Compliant Grasps and Fixtures
,” IEEE Trans. Rob. Autom
, 16
(6
), pp. 675
–688
.10.1109/70.89777932.
Hopkins
, J. B.
, and Culpepper
, M. L.
, 2011
, “Synthesis of Precision Serial Flexure Systems Using Freedom and Constraint Topologies (FACT)
,” Precision Engineering
, 35
(4
), pp. 638
–649
10.1016/j.precisioneng.2011.04.006.Copyright © 2015 by ASME
You do not currently have access to this content.
