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Research Papers: Mechanisms and Robotics

Synthesizing Single DOF Linkages Via Transition Linkage Identification

[+] Author and Article Information
Andrew P. Murray

Mechanical & Aerospace Engineering Department, University of Dayton, Dayton, OH 45419murray@udayton.edu

Michael L. Turner

Mechanical & Aerospace Engineering Department, University of Dayton, Dayton, OH 45419michael.turner@notes.udayton.edu

David T. Martin

 Ethicon Endo-Surgery, Cincinnati, OH 45242dmarti29@eesus.jnj.com

J. Mech. Des 130(2), 022301 (Dec 27, 2007) (8 pages) doi:10.1115/1.2812418 History: Received April 07, 2006; Revised May 09, 2007; Published December 27, 2007

A linkage is partially classified by identifying those links capable of unceasing and drivable rotation and those that are not. In this paper, we examine several planar single degree-of-freedom linkages to identify all changes to the physical parameters that may alter this classification. The limits on the physical parameters that result in no change in the classification are defined by transition linkages. More rigorously, a transition linkage possesses a configuration at which the matrix defined by the derivative of the loop closure equations with respect to the joint variables loses rank. Transition linkages divide the set of all linkages into different classifications. In the simplest cases studied, transition linkage identification produces a comprehensive classification scheme. In all cases, this identification is used to alter a linkage’s physical parameters without changing its classification and produces insight into the selection of these parameters to produce a desired classification.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Linkages , Functions
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References

Figures

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Figure 1

The behavior of a 4R linkage is defined by a, b, g, and h.

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Figure 2

The curves defining the refine procedure for the location of Pivot A. Placing Pivot A on any of the curves results in OABC being a transition linkage.

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Figure 3

The layout routine for selecting Pivot B (at left) and Pivot C (at right) that results in a crank rocker

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Figure 4

A slider-crank linkage’s behavior is defined by the three link lengths a, b, and h

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Figure 5

For a fully rotatable input link, the Location B of the last R (and P) joint must lie outside both parabolas in Region 4. Locating B on a curve results in a transition linkage.

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Figure 6

An inverted slider-crank linkage’s behavior is defined by the link lengths a, b, g, and the fixed angle γ

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Figure 7

To preserve the motion behavior of the inverted slider-crank mechanism, the Location A of the R joint may be moved to any location in Region 1

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Figure 8

The Watt II six bar with rotating output can exhibit a variety of motion behaviors depending on which links are capable of a full rotation and which links align to limit its motion.

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Figure 9

The curves show locations of the fixed Pivot F, which results in a transition linkage. The inset shows all of the transition functions.

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Figure 10

A Watt II six bar with sliding output

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Figure 11

The curves that govern the layout of a Watt II six bar with sliding output. The inset shows all of the transition functions.

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Figure 12

A Stephenson III six bar

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Figure 13

A Stephenson III six bar needs Pivot F in Region 1 for OA to be a crank

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