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Research Papers

A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms

[+] Author and Article Information
Hai-Jun Su1

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

Denis V. Dorozhkin

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011dorodv@iastate.edu

Judy M. Vance

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011jmvance@iastate.edu

1

Corresponding author.

J. Mechanisms Robotics 1(4), 041009 (Sep 28, 2009) (8 pages) doi:10.1115/1.3211024 History: Received January 14, 2009; Revised June 11, 2009; Published September 28, 2009

This paper presents a screw theory based approach for the analysis and synthesis of flexible joints using wire and sheet flexures. The focus is on designing flexure systems that have a simple geometry, i.e., a parallel constraint pattern. We provide a systematic formulation of the constraint-based approach, which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint, which can be described by a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis, and constraint pattern design are discussed with examples in details. Lastly, a case study is provided to demonstrate the application of this approach to the design of compliant prismatic joints. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A general wrench Ŵ does work on a body with the motion defined by a general twist T̂

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Figure 2

An unconstrained rigid body has three translations and three rotations represented by six principle twists

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Figure 3

An ideal wire flexure imposes on a rigid body an ideal constraint, which removes the translational freedom in the axial direction of the wire flexure

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Figure 4

Two-dimensional freedom space generated by (a) two parallel lines, (b) two intersecting lines, and (c) two skew lines

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Figure 5

Constraint and freedom space of a rigid body constrained by an ideal sheet flexure

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Figure 6

A body constrained by a pattern of ideal constraints can have a screw motion in space

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Figure 7

Four ideal constraints found for given a pattern of 2 DOF

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Figure 8

The constraint space for a compliant prismatic joint

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Figure 9

Design of a compliant prismatic joint using (a) five wire flexures or (b) one flexure sheet and two wire flexures

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Figure 10

Design of a compliant prismatic joint using two parallel flexure sheets

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