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Research Papers

Screw Theory Based Methodology for the Deterministic Type Synthesis of Flexure Mechanisms

[+] Author and Article Information
Jingjun Yu

Shouzhong Li

 Robotics Institute, Beihang University, Beijing 100191, China

Hai-jun Su

Mechanical Engineering Department,  University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250 e-mail: hai-jun@umbc.edu

M. L. Culpepper

 MIT Department of Mechanical Engineering, 77 Massachusetts Avenue, Cambridge, MA 02139 e-mail: culpepper@mit.edu

J. Mechanisms Robotics 3(3), 031008 (Aug 10, 2011) (14 pages) doi:10.1115/1.4004123 History: Received August 17, 2010; Revised April 16, 2011; Published August 10, 2011; Online August 10, 2011

Flexure mechanism synthesis, however, is still a comparably difficult task. This paper aims at exploring a simple but systematic type synthesis methodology for general flexure mechanisms. The applied mathematical tool is reciprocal screw system theory in geometric form, and the proposed approach is an improvement of freedom and constraint topology (FACT), which is based on the FACT approach, combining with other methods including equivalent compliance mapping, set operation on building blocks, etc. As a result, it enables the type synthesis of flexure mechanisms simple, complete, and effective. What is more significant is that the proposed approach makes the unified type synthesis of both constraint-based and kinematics-based flexure mechanisms available. That is also the new contribution to the flexure de-sign.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Two special cases of a unit screw: (a) a line (b) an infinite-pitch screw

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Figure 2

Examples of line screw spaces: (a) 1D case; (b) 2D case; and (c) 3D case

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Figure 3

A hierarchy of FBBs

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Figure 4

Illustration of an improved FACT approach

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Figure 6

Some flexure primitives

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Figure 7

Freedom and constraint space

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Figure 8

Two 3T2R con-figurations: (a) RPS [9] and (b) PRS [54]

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Figure 9

L(N,n)∪L(N′,n′). References cited in the figure are [22] and [35].

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Figure 10

L(N,n)∪L(N′,n′). Reference cited in the figure is [53].

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Figure 11

Advantages of serial flexure mechanisms: (a) larger displacement and (b) more DOF [26]

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Figure 12

Three-dimensional FS L(N,n) and its CS

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Figure 13

Three-dimensional freedom space L(N,n)

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Figure 14

Seven 2R1T KPM prototypes: (a) Pham [54]; (b) Choi and Lee [55]; (c) Canfield and Beard [56]; (d) Bi and Zong [9]

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Figure 15

Hybrid 6 DOF parallel KPMs [55]

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