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Research Papers

A Visualization Approach for Analyzing and Synthesizing Serial Flexure Elements

[+] Author and Article Information
Jonathan B. Hopkins

University of California–Los Angeles
46-147F Engineering IV Bldg.,
420 Westwood Plaza,
Los Angeles, CA 90095
e-mail: hopkins@seas.ucla.edu

Manuscript received January 6, 2014; final manuscript received September 1, 2014; published online December 4, 2014. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 7(3), 031011 (Aug 01, 2015) (12 pages) Paper No: JMR-14-1005; doi: 10.1115/1.4028727 History: Received January 06, 2014; Revised September 01, 2014; Online December 04, 2014

In this paper, we extend the principles of the freedom and constraint topologies (FACT) synthesis approach such that designers can analyze and synthesize serial flexure elements—not to be confused with serial flexure systems. Unlike serial systems, serial elements do not possess intermediate rigid bodies within their geometry and thus avoid the negative effects of unnecessary mass and underconstrained bodies that generate uncontrolled vibrations. Furthermore, in comparison with other common parallel flexure elements such as wire, blade, and living hinge flexures, serial elements can be used within flexure systems to achieve (i) a larger variety of kinematics, (ii) more dynamic and elastomechanic versatility, and (iii) greater ranges of motion. Here, we utilize the principles of FACT to intuitively guide designers in visualizing a multiplicity of serial flexure element geometries that can achieve any desired set of degrees of freedom (DOFs). Using this approach, designers can rapidly generate a host of new serial flexure elements for synthesizing advanced flexure systems. Thirty seven serial flexure elements are provided as examples, and three flexure systems that consist of some of these elements are synthesized as case studies.

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Figures

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Fig. 1

Flexure system categories with examples (a), common parallel flexure elements—wire (b), blade (c), and living hinge (d)

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Fig. 2

Example parallel (a), serial (b), and hybrid (c) flexure elements

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Fig. 3

Parallel system (a), stacked blades (b), cylindrical serial element (c), and hybrid system (d)

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Fig. 4

A serial flexure system (a) with an intermediate rigid body that cannot be eliminated without producing a serial flexure element (b) that possesses different DOFs

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Fig. 5

Independent wrenches (a), freedom and constraint spaces (b), and independent twists (c)

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Fig. 6

Living hinge’s constraint space (a), complementary spaces (b), and freedom space (c)

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Fig. 7

Effective constraint space (a), complementary freedom space (b), curved blades (c), bent blade (d), blade with two bends (e), and curled flexure (f)

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Fig. 8

Bent wire (a), curved wire (b), serpentine flexure (c), and coil spring (d)

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Fig. 9

Notched blade (a), nub flexure (b), intermediate constraint spaces (c), effective constraint space (d), complementary spaces (e), and freedom space and DOFs (f)

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Fig. 10

Serial element that imposes a pure moment only (a), constraint space of parallel wires (b), and the serial element’s intermediate constraint spaces (c)

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Fig. 11

DOFs and complementary spaces (a), intermediate constraint space (b), parameters defined (c), stacked intermediate spaces (d), generating parallel element constituents (e), and symmetric hybrid system (f)

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Fig. 12

DOFs and complementary spaces (a), intermediate constraint space selected (b), two spaces arranged such that only the moment is shared in common (c), final serial element generated (d) and (e), other kinematically equivalent serial elements (f) and (g)

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Fig. 13

Parallel elements (a), serial systems that consist of rigid bodies joined together by parallel elements (b)

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Fig. 14

Serial flexure element examples

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Fig. 15

Desired DOFs and complementary spaces (a), selecting the constraint spaces of individual elements (b), serial element used (c), and final hybrid system (d)

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Fig. 16

Desired DOFs and complementary spaces (a), selecting the constraint spaces of individual elements (b), symmetric hybrid system used (c), and final hybrid system (d)

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Fig. 17

Desired DOFs and complementary spaces (a), selecting the constraint spaces of individual elements (b), serial element option (c), modified element (d), fabricating the element’s planar design (e), and final hybrid system (f)

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Fig. 18

Comprehensive library of complementary freedom and constraint space types

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