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.

Copyright © 2013 by ASME
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Fig. 1

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

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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. 3

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

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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. 5

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

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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. 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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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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