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Research Papers

Mobility Analysis of Flexure Mechanisms via Screw Algebra

[+] Author and Article Information
Hai-Jun Su

 Assistant Professor Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250haijun@umbc.edu

J. Mechanisms Robotics 3(4), 041010 (Oct 24, 2011) (8 pages) doi:10.1115/1.4004910 History: Received May 12, 2011; Revised August 04, 2011; Published October 24, 2011; Online October 24, 2011

This paper presents a general framework for studying the mobility of flexure mechanisms with a serial, parallel or hybrid topology using the screw algebra. The current approach for mobility analysis of flexures is ad hoc and mostly done by intuition. In this methodology, we first build a library of commonly used flexure elements, flexure joints, and simple chains. We then apply the screw algebra to find their motion and constraint spaces in the form of twist and wrench matrices. To analyze a general flexure mechanism, we first apply a top-down approach to hierarchically subdivide it into multiple modules or building blocks down to the level of flexure structures that are already provided in the library. We then use a bottom-up routine to study the mobility of each module up to the level of the overall mechanism. Examples and case studies from simple flexure joints, chains to spatial compliant platforms are used to demonstrate the methodology. This systematic methodology is an important tool for guiding the qualitative design of flexure mechanisms.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A typical blade flexure. The thickness is much smaller than the length, i.e., t≪l.

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Figure 2

The pseudo-rigid-body model for a blade flexure subject to (a) a small lateral force and (b) a small moment

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Figure 3

A general serial flexure system

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Figure 4

A serial compliant mechanism formed by two perpendicular blade flexures

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Figure 5

A parallel flexure mechanism formed by two parallel ideal blade flexures

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Figure 6

(a) a typical cross strip flexure pivot and (b) a parallelogram linear spring

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Figure 7

A xy flexure stage reproduced from Ref. [16]

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Figure 8

A serial-parallel flexure mechanism that provides the translation along x and y axes

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Figure 9

A serial chain of two spherical notch hinges

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Figure 10

A flexure platform mechanism with three identical chains of two spherical notches

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