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Research Papers

Synthesizing Parallel Flexures That Mimic the Kinematics of Serial Flexures Using Freedom and Constraint Topologies

[+] Author and Article Information
Jonathan B. Hopkins

Lawrence Livermore National Laboratory,
L-223, 7000 East Avenue L-223,
Livermore, CA 94551
e-mail: hopkins30@llnl.gov

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received January 22, 2013; final manuscript received April 29, 2013; published online July 16, 2013. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 5(4), 041004 (Jul 16, 2013) (9 pages) Paper No: JMR-13-1017; doi: 10.1115/1.4024474 History: Received January 22, 2013; Revised April 29, 2013

The principles of the freedom and constraint topologies (FACT) synthesis approach are adapted and applied to the design of parallel flexure systems that mimic degrees of freedom (DOFs) primarily achievable by serial flexure systems. FACT provides designers with a comprehensive library of geometric shapes. These shapes enable designers to visualize the regions wherein compliant flexure elements may be placed for achieving desired DOFs. By displacing these shapes far from the point of interest of the stage of a flexure system, designers can compare a multiplicity of concepts that utilizes the advantages of both parallel and serial systems. A complete list of which FACT shapes mimic which DOFs when displaced far from the point of interest of the flexure system's stage is provided as well as an intuitive approach for verifying the completeness of this list. The proposed work intends to cater to the design of precision motion stages, optical mounts, microscopy stages, and general purpose flexure bearings. Two case studies are provided to demonstrate the application of the developed procedure.

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References

Blanding, D. L., 1999, Exact Constraint: Machine Design Using Kinematic Principles, ASME Press, New York, NY.
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: Principles,” Precis. Eng., 34(2), pp. 259–270. [CrossRef]
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. [CrossRef]
Hopkins, J. B., and Culpepper, M. L., 2011, “Synthesis of Precision Serial Flexure Systems Using Freedom and Constraint Topologies (FACT),” Precis. Eng., 35(4), pp. 638–649. [CrossRef]
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, Cambridge, UK.
Merlet, J. P., 2000, Parallel Robots, Kluwer Academic Publishers, The Netherlands.
Klein, F., 1921, Die Allgemeine Lineare Transformation der Linienkoordinaten, Gesammelte math. Abhandlungen I, Springer, Berlin.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford University Press, London.
Phillips, J., 1984, Freedom in Machinery, Cambridge University Press, New York, NY.
Murray, R. M., Li, Z., and Sastry, S. S., 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press LLC, Boca Raton, FL.
Bothema, R., and Roth, B., 1990, Theoretical Kinematics, New York, Dover.
Su, H., 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. [CrossRef]
Su, H., and Tari, H., 2010, “Realizing Orthogonal Motions With Wire Flexures Connected in Parallel,” ASME J. Mech. Des., 132(12), p. 121002. [CrossRef]
Su, H., and Tari, H., 2011, “On Line Screw Systems and Their Application to Flexure Synthesis,” J. Mech. Rob., 3(1), p. 011009. [CrossRef]
Merlet, J. P., 1989 “Singular Configurations of Parallel Manipulators and Grassmann Geometry,” Int. J. Rob. Res., 8(5), pp. 45–56. [CrossRef]
Hao, F., and McCarthy, J. M., 1998, “Conditions for Line-Based Singularities in Spatial Platform Manipulators,” J. Rob. Syst., 15(1), pp. 43–55. [CrossRef]
Hopkins, J. B., 2007, “Design of Parallel Flexure Systems Via Freedom and Constraint Topologies (FACT),” Masters thesis, Massachusetts Institute of Technology, Cambridge, MA.
Hopkins, J. B., 2010, “Design of Flexure-Based Motion Stages for Mechatronic Systems Via Freedom, Actuation and Constraint Topologies (FACT),” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Awtar, S., and Slocum, A. H., 2007, “Constraint-Based Design of Parallel Kinematic XY Flexure Mechanisms,” ASME J. Mech. Des., 129(8), pp. 816–830. [CrossRef]
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. [CrossRef]
Li, Y., and Xu, Q., 2011, “A Totally Decoupled Piezo-Driven XYZ Flexure Parallel Micropositioning Stage for Micro/Nanomanipulation,” IEEE Trans. Autom. Sci. Eng., 8(2), pp. 265–279. [CrossRef]
Dimentberg, F. M., 1968, Screw Calculus and Its Applications to Mechanics, Foreign Technology Division, WP-APB, Ohio.
Gibson, C. G., and Hunt, K. H., 1990, “Geometry of Screw Systems-I, Classification of Screw Systems,” Mech. Mach. Theory, 25(1), pp. 1–10. [CrossRef]
Gibson, C. G., and Hunt, K. H., 1990, “Geometry of Screw Systems-II, Classification of Screw Systems,” Mech. Mach. Theory, 25(1), pp. 11–27. [CrossRef]
Rico, J. M., and Duffy, J., 1992, “Classification of Screw Systems—I: One- and Two-Systems,” Mech. Mach. Theory, 27(4), pp. 459–470. [CrossRef]
Rico, J. M., and Duffy, J., 1992, “Classification of Screw Systems—II: Three-Systems,” Mech. Mach. Theory,” 27(4), pp. 471–490. [CrossRef]
Rico, J. M., and Duffy, J., 1992, “Orthogonal Spaces and Screw Systems,” Mech. Mach. Theory,” 27(4), pp. 451–458. [CrossRef]
Coxeter, H. S. M., 1987, Projective Geometry, 2nd ed., Springer Press, New York.
Su, H.-J., 2011, “Mobility Analysis of Flexure Mechanisms Via Screw Algebra,” ASME J. Mech. Rob.3(2), p. 041010. [CrossRef]
Hopkins, J. B., and Culpepper, M. L., 2010, “A Screw Theory Basis for Quantitative and Graphical Design Tools That Define Layout of Actuators to Minimize Parasitic Errors in Parallel Flexure Systems,” Precis. Eng., 34(4), pp. 767–776. [CrossRef]
Hopkins, J. B., and Panas, R. M., 2013, “Eliminating Parasitic Error in Dynamically Driven Flexure Systems,” Proceedings of the 28th Annual Meeting of the American Society for Precision Engineering, St. Paul, MN.

Figures

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Fig. 3

Parameters for quantifying the approximation errors of parallel flexure systems that mimic the kinematics of serial flexure systems

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Fig. 5

Comprehensive library of freedom and constraint spaces for flexure synthesis. For details, refer to Ref. [18].

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Fig. 4

Twist parameters defined (a), DOFs of a parallel flexure system (b), (c), (d), freedom space (e), complementary shapes (f), constraint space (g), and other flexure concepts (h), (i)

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Fig. 2

Three DOF (XYZ) serial flexure system (a), wire flexure removes one translation (b), parallel flexure that mimics XYZ translations (c), and geometric shapes used to synthesize flexure elements (d)

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Fig. 1

Parallel (a) and serial (b) flexure system examples

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Fig. 6

A planar freedom space of rotation lines and an orthogonal translation (a) displaced to infinity in the direction of the translation manifests as a sphere of pure translations (b)

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Fig. 7

A disk of rotation lines (a) displaced to infinity along one of the axes of its lines manifests as a plane of parallel rotation lines and an orthogonal translation (b)

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Fig. 12

Freedom space that contains the desired motions (a), 4 DOF type 1 freedom and constraint spaces (b), approximate freedom space displaced to infinity (c), a long stage enables the freedom space to mimic the desired motions (d), selecting constraints from the constraint space (e), final parallel flexure concept (f), serial concept that achieves the same kinematics (g), and parts that make up the two concepts (h)

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Fig. 8

A disk of rotation lines (a) displaced to infinity in a direction perpendicular to its plane manifests as a disk of translation arrows (b)

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Fig. 9

A disk of rotation lines displaced to infinity in a direction not along the coordinate system's axes (a) manifests itself as a disk of translation arrows oriented perpendicular to the direction in which it is displaced (b)

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Fig. 10

Type 7 (a), type 18 (b), and type 2 (c) freedom spaces from the 3 DOF column of Fig. 5

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